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Implications of stock ownership restrictions and asymmetric compensation for equilibrium asset pricing… Diao, Xifeng 2002

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IMPLICATIONS OF STOCK OWNERSHIP RESTRICTIONS AND A S Y M M E T R I C COMPENSATION FOR EQUILIBRIUM ASSET PRICING: THEORY AND EMPIRICAL EVIDENCE By XIFENG DIAO B.A., Harbin Institute of Technology, 1993 M.Sc, Shanghai Jiao Tong University, 1996 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF T H E REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in FACULTY OF C O M M E R C E AND BUSINESS ADMINISTRATION Ph.D. Program in Finance We accept this thesis as conforming o^ the required standard T H E UNIVERSITY OF BRITISH COLUMBIA October 2002 © Xifeng Diao, 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of 'f'l nam r.^ ^ ^Msulfa^ 6^ (>^r\&rZC The University of British Columbia Vancouver, Canada Date p£ / U ^ . 1S>0\ DE-6 (2/88) Abstract In China the shares open to foreign investors, B-Shares, have much lower prices relative to shares open to domestic investors, A-Shares. In Chapter I, we study the impact of the monopolistic government within a general equilibrium framework, and explain why A-Share prices are higher than B-Share prices. Further, we provide a possible explanation of the relative size of A- and B-Share markets in China. We also apply our analysis to other countries and find implications different from the literature, in addition to the use a unified model of demand elasticity and liquidity in asset pricing. Chapter II explores the link between fund manager compensation and asset pricing in a setting where managers receive a larger reward per $1 profit than the penalty per $1 loss. This type of compensation, which we call UMC, is common in China, and leads to interesting results. In the final Chapter, we test the implications of Chapter I and Chapter II. Regarding Chapter I, we examine the values of A- to B-Share price ratios, the relationship between international betas of individual firms and the share issuance decisions as well as the price ratios of A- to B-Shares, and the impact of market liquidity on asset prices. All the findings from these tests are consistent with predictions of our model. Further, we show that the regime-switching (governmental) risk from foreign exchange rates also matters. In our empirical examination of the implications of Chapter II, we employ a method with improved efficiency over Fama-MacBeth (1973) and Ferson and Harvey (1999), and find a negative risk-return relationship in China, which is statistically and economically significant. i i Contents Abstract ii Table of Contents i i i List of Tables xi List of Figures xiii Acknowledgements xiv 1 Stock Ownership Restrictions and Asset Pricing in China 1 1.1 Introduction and Review of Literature 1 1.1.1 The Situation in China 3 1.1.2 Ownership Restrictions in Other Countries 8 1.1.3 Outline of This Study 9 1.2 Chinese Stock Markets 13 iii 1.2.1 Development of Chinese Stock Markets 13 1.2.2 The classes of shares issued by Chinese firms 15 1.3 The Model 18 1.3.1 Setup 18 1.3.2 Domestic Demand 23 1.3.3 Foreign Demand 26 1.3.4 The Supply 30 1.4 General Equilibrium 35 1.4.1 A-Share and B-Share Price Differences 37 1.4.2 Relative Supply of A- and B-Shares 39 1.5 A Simplified Approach and Analysis of Finland 44 1.5.1 A Simplified Approach 44 1.5.2 Implications Beyond China: The Case of Finland 48 1.6 Extension 52 1.6.1 Liquidity 53 1.7 Discussion 56 iv 1.7.1 Further Extension 56 1.7.2 Alternative Hypotheses 57 1.7.3 Empirical Implications 59 1.8 Conclusion 61 2 Unbalanced Management Compensation and Equity Prices: A n Agency Asset Pricing Model for China 72 2.1 Introduction 72 2.2 Literature Review 79 2.2.1 Agency, Incentive Compensation, and Managerial Risk Choices 79 2.2.2 SBC in Transitional Economies 84 2.2.3 Bubbles 86 2.2.4 Chinese Stock Markets 88 2.3 Agency Capital Asset Pricing Model ( A C A P M ) 90 2.3.1 Setup 90 2.3.2 Managers with Balanced Compensation 93 2.3.3 Managers with Unbalanced Compensation 94 v 2.3.4 Equilibrium 97 2.4 Characterization of the A C A P M 98 2.4.1 U M C and Price 99 2.4.2 Risk and Price 101 2.4.3 Price and Demand 103 2.4.4 Fundamental Value and Market Value 103 2.5 Numerical Analysis 105 2.5.1 Analysis of Market Price and Compensation Ratios 106 2.5.2 Analysis of Market Price and the Number of U M C Managers . 109 2.5.3 Analysis of Demand 109 2.5.4 Analysis of Managers' Utility 110 2.6 Bubbles I l l 2.7 North American Stock Markets 112 2.7.1 Capital Gains Taxes and the Equity Premium Puzzle 113 2.7.2 Index-adjusted Management Compensation 118 2.7.3 Implications in Corporate Finance 118 vi 2.8 Conclusion 121 References 123 3 Equity Pricing in China: Empirical Tests 138 3.1 Introduction and Review of Literature 138 3.2 Testable Implications 146 3.2.1 Implications from Chapter I 146 3.2.2 Implications from Chapter II 149 3.3 Data Description 150 3.4 Empirical Methodology 154 3.4.1 Thin Trading 154 3.4.2 Panel Data Analysis 155 3.5 Tests of Chapter I 162 3.5.1 International Betas and Price Ratios 162 3.5.2 Test of Other Factors 163 3.6 Empirical Evidence and Tests on Chapter II 169 3.6.1 Empirical Evidence 169 vii 3.6.2 A n Event Study: Crack-down on U M C Managers 174 3.6.3 Tests of the Risk and Return Relationship in China 176 3.6.4 Tests of the Risk-Return Relationship in the U.S.: A Comparisonl79 3.7 Conclusion 183 References 185 A Appendix of Chapter I I 217 A.1 Managers' Personal Investment 217 A.1.1 Setup 218 A. 1.2 Managers with Balanced Compensation 218 A. 1.3 Managers with Unbalanced Compensation 220 A. 1.4 Conclusion 223 A.2 A n Extension to Multiple Assets 224 A.2.1 Setup 224 A.2.2 Managers with Balanced Compensation 225 A.2.3 Managers with Unbalanced Compensation 226 A.2.4 A Numerical Explanation 230 viii A.2.5 Conclusion 232 A.3 Index-Adjusted Incentive Compensation in North America 234 A.3.1 Setup 235 A.3.2 Discussion 236 A.4 General Equilibrium 239 A.4.1 Foreign Investors 240 A.4.2 Domestic Investors, Monopolistic Government and the Equilib-rium 241 A.5 Proofs 243 A.5.1 Properties of Several Mathematical Functions 243 A.5.2 Proof of Lemma 1 244 A.5.3 Proof of Lemma 2 246 A.5.4 Proof of Proposition 1 247 A.5.5 Proof of Proposition 2 248 A.5.6 Proof of Proposition 5 249 B Appendix of Chapter III 250 ix The 1997 Announcement of Crack Down x List of Tables 1.1 Ownership Restrictions in Different Countries 68 3.1 The Statistics of A- to B-Share Price Ratios 197 3.2 Auto-correlations of A- and B-Share market index returns 198 3.3 International Betas and Issuance of A- vs. B-Shares 199 3.4 International Betas and Price Differences: Fama-MacBeth T-Test . . 200 3.5 International Betas and Price Differences: Panel with Fixed Effects . 201 3.6 Factors in Pricing Differences: Panel with Fixed Effects 202 3.7 The Statistics of E / P Ratios in China 203 3.8 The Comparison Between E / P Ratios and Interest Rates in China . . 204 3.9 Pearson Correlations Between Risk and Return in China 205 3.10 Spearman Correlations Between Risk and Return in China 206 3.11 Kendall's tau-b Between Risk and Return in China 207 3.12 Event Study of the Crack-Down on U M C in May 1997 208 3.13 Fama-MacBeth Regression Coefficients in China 209 3.14 Fama-MacBeth Regression Coefficients in SHSE 210 xi 3.15 Fama-MacBeth Regression Coefficients in SZSE 211 3.16 Panel Data Analysis with Fixed Time Effects in China 212 3.17 Panel Data Analysis with Fixed Time Effects in the SHSE 213 3.18 Panel Data Analysis with Fixed Time Effects in the SZSE 214 3.19 Fama-MacBeth Regression Coefficients in the U.S. . . 215 3.20 Panel Data Analysis with Fixed Time Effects in the U.S 216 xii List of Figures 1.1 The Government's Optimal Supply Schedule 69 1.2 The Case of China 70 1.3 The Case of Finland 71 2.1 Agency Asset Pricing Model — The Case of One Asset 127 2.1 A: Price-Penalty Rate Curves — Cross-sectional Views 128 2.1 B: Price-Risk Curves — Cross-sectional Views 129 2.1 C: A Special Price-Risk Curve — A Close View 130 2.2 Market Price and the Number of U M C Managers 131 2.2 A: Price Difference versus Penalty Rate Curve — A Cross-sectional View 132 2.3 Managers' Demand 133 2.3 A: Managers' Demand — A Cross-sectional View 134 2.4 Managers' Utilities 135 2.4 A: Managers' Utilities — A Cross-sectional View 136 2.5 U M C Manager's Portfolio Choice 137 3.1 Agency Capital Asset Pricing Model — Cross-sectional Views . . . . 192 xiii 3.2 SHSE A- and B-Share Index Level and Returns in 1992 193 3.3 SHSE A- and B-Share Index Level and Returns during 1993-2000 . . 194 3.4 SZSE A- and B-Share Index Level and Returns during 1993-2000 . . 195 3.5 The Development of A- vs. B-Share Markets 196 xiv Acknowledgements I wish to thank a travel grant from Air Canada for my field research in China, and am grateful to Liyang Jin of the Shenzhen Stock Exchange, Donghui Shi of the Shanghai Stock Exchange, Jing Xing of Shenyin Wanguo Securities Company, and Chaojun Yang of Shang-hai Jiao Tong University for help with data collection and answers to many questions. I also wish to thank Stephen Burke, Gilles Chemla, Lorenzo Garlappi, Gerald Garvey, Robert Heinkel, Kai L i , Joshua Slive, and James Storey for helpful comments and discussions, and much oblidged to my research advisors, Burton Hollifield and Alan Kraus, and thesis su-pervisors, Adlai Fisher, Ronald Giammarino, Maurice Levi, Ban Vertinsky, and Tan Wang for close guidance and extensive feedback. Ronald Giammarino, Alan Kraus, and Maurice Levi have given me key inputs in Chap-ter I. Both Ronald Giammarino and Maurice Levi have given me valuable help throughout the three chapters. Maurice Levi has devoted huge amount of time to guide me closely in the development of the theory, design of the empirical tests, and even the writing of nu-merous revisions. Tan Wang has gone far beyond the role of a research advisor, and given me crucial help and guidance both inside and outside my academic life. Adlai Fisher's encouragement and generous support in many aspects is indispenable. All these have made a distinctive difference not only in my thesis, but also in my life and career. I wish to dedicate this thesis to my parents and my family. I also wish to take this instance and pay my tribute to the brilliance of Jing Xing, my best friend in Shanghai who was a rising star in Chinese financial consulting industry but passed away in his twenties. xv Chapter 1 Stock Ownership Restrictions and Asset Pricing in China 1.1 Introduction and Review of Literature As financial markets evolve and the interest in emerging stock markets grows, more and more attention is being directed to both empirical and theoretical issues in inter-national asset pricing. Examples include the papers by Stulz and Wasserfallen (1995) on Switzerland, Beiley and Jagtiani (1994) on Thailand, Domowitz, et al (1997) on Mexico, Hietala (1989) on Finland, and Bergstorm, et al (1993) on Sweden. The common phenomenon among these countries is a lower price of the shares restricted to domestic investors relative to that of the corresponding shares accessible to foreign 1 investors. In China, however, the price difference is the other way around: the shares restricted to domestic investors (A-Shares) have a higher price level than the corre-sponding shares accessible to foreign investors (B-Shares). Considering the sizable scale of Chinese economy and hence its potential of providing huge diversification benefit to international investors, the unique phenomena in Chinese stock markets are even more intriguing1 In this chapter, we study the situation in China and ex-plain why the A-Share price level is higher than the B-Share price level. In addition, we offer an explanation for the structure of the dual market structure that has been developed in China. We also use our analysis to explain the situations in some other emerging markets outside China, and thanks to a more rigorous setup, our results have different implications than some previous studies in the literature, such as Hi-etala (1989) on Finland. In brief, the argument in this paper is as follows. In China, domestic investors cannot invest in foreign markets because of strict investment controls. Therefore, Chinese investors, with fewer investment opportunities, are less sensitive to the price level of domestic shares. Meanwhile, all listed firms in China are state-owned enter-prises (SOEs), and the government chooses the optimal issuing price and volume for each listed firm so as to maximize the value of state-owned property. This is akin to what a monopolist supplier would do in a free market. The monopolist government 1Based on information from the World Bank in April 2002, the 2000 GDP of China (mainland only) ranks #6 in the world. Furthermore, Chinese economy has a global rank of #2 based on Purchasing Power Parity (PPP), 50% larger than Japanese economy, which ranks #3. 2 has the ability and incentive to discriminate between domestic and foreign investors by imposing ownership restrictions. We show in this paper that such a monopolist government will make A-Share prices higher than B-Share prices in equilibrium. 1.1.1 The Situation in China There is a growing literature on Chinese stock markets, especially on price differences between A- and B-Shares. However, most of the papers take the ownership restrictions and the share supply as given, except for the concurrent study by Gordon and L i (2001) and us who have endogenized the investment restrictions by studying the government's monopolistic decision in share supply. As explained in most economics textbooks such as Katz and Rosen (1998), third-degree price discrimination results in different prices for the same commodities in different markets. Meanwhile, as discussed later in this chapter, Chinese government is the monopolist behind all firms listed in Chinese stock markets. Therefore, it is important to study the role of the government in the investigation of the A- versus B-Share price differences in China. In the following, we are going to first review these papers who do not consider the government's role as a monopolist in the equity market, and then move on to a comparison between Gordon and L i (2001) and our work. In an intertemporal setting, Dongwei Su (1999) takes the ownership restrictions 3 as given, and explains the cross-sectional variations of A- and B-Share returns with international and domestic market betas. He does not consider the government's decision on issuing A- and B-Shares, and offers no explanation for the higher A-Share price versus B-Share price. The similarity between Dongwei Su (1999) and our work is limited to the implication of the international and domestic betas for the cross-sectional differences between A- and B-Share price. Fernald and Rogers (1998) point to the lack of investment opportunities for Chi-nese investors, and then assert that domestic investors require a lower rate of return which in turn offers an explanation for the higher prices of A-Shares relative to B-Shares. However, as in the paper by Dongwei Su, they do not model the government's monopolist role in the supply of A- and B-Shares, and so can explain neither why the government has the incentive to impose the ownership restrictions, nor why the price of A-Share is always higher than that of B-Share. Moreover, they do not address the issue of why the size of A-Share market is larger than that of B-Share market. In fact, the argument in Fernald and Rogers (1998) is similar to what can be derived from a simplified version of our model with exogenous, rather than endogenous, supply of domestic shares. There are also other types of explanations for the price differences between A-and B-Shares. Sarkar, Charkravarty, and Wu (1998) propose an explanation with in-formation asymmetry. Chen, L i , and Rui (2000) explain the difference with liquidity. 4 Gordon and L i (2001) are the closest in spirit to ours. In their model, they also consider the decision-making process of the government and study the impact of the government's discriminating behaviour on pricing of different shares. Both Gordon and L i (2001) and our study are based on a static two-period model, with the supplies of A- and B-Shares being endogenized. In contrast, other papers on Chinese stock markets, such as Dongwei Su (1999) and Fernald and Rogers (1998), only develop a partial equilibrium where supplies of A- and B-Shares are exogenous. This is the major feature which discriminates the model by Gordon and L i (2001) and our work from other papers trying to explain the differences between Chinese A- and B-Share prices. Despite the similarities between this paper and Gordon and L i (2001), some im-portant differences do exist, such as how the model is set up and how the analysis is carried out. In the setup, Gordon and L i (2001) assume a different set of assets accessible to domestic investors, specifically non-state assets. After the inclusion of investment opportunities in non-state sectors, Gordon and L i (2001) have to argue that the covariance between Chinese non-state sectors and state sectors is smaller than the covariance between Chinese non-state sectors and foreign firms, in addition to other items in their list of presumptions for A-Share prices to be higher than B-Share prices. In our opinion, there is serious doubt whether this claim is true or not, for it is natural for the firms in China to vary more with each other than with foreign firms because of many unique characteristics of the Chinese economy. In fact, as 5 discussed earlier in this chapter, the opportunity to invest in non-public firms, which should be similar to non-state sectors referred in Gordon and L i (2001), is just the main reason why the level of C-Share prices is much lower than the price level of A-Shares. Another difference in Gordon and L i (2001) lies in the objective function of the government. After taking the social welfare into consideration, Gordon and L i (2001) infer that the government is giving a very low weight to individuals' utilities from consumption of personal wealth. In our opinion, their analysis means that the government is not really using the social welfare function as the objective function. In fact, we do not have the social welfare function in our setup, for it is our belief that the Chinese government does not care as much about the personal utilities of Chinese investors in A-Share markets as the revenue of the government. Moreover, our model derives the development path of Chinese A-Share versus B-Share markets, and our model explain more clearly the fact that the size of A-Share market is larger than the size of B-Share market in China, and the A-Share market was established earlier than B-Share markets. A further difference between Gordon and L i (2001) and this chapter is that Gor-don and L i allow the interest rate to be a controllable variable without considering intertemporal smoothing of consumption in their static one period model. Conse-quently, social welfare is always increasing when the government removes the restric-tion on domestic investors to invest abroad. To justify such restrictions, they have to assume that the government is putting little weight on individual consumption. k 6 Moreover, only without intertemporal smoothing of consumption can they allow the government to raise more money by simply choosing a lower interest rate, as they as-sume in their model. This paper does not allow the government to raise more money from the stock market by changing the interest rate. In addition, Gordon and L i (2001) do not relate to the literature as closely as us. They do not point out that the analysis of Chinese stock market can shed more light on the situations in other countries and related studies in the literature, such as Hietala (1989) and Bailey and Jagtiani (1994). We apply our analysis to other countries similar to China, such as Finland and Thailand, and offer an explanation for issues unexplained in previous studies on these countries. Meanwhile, we also derive different arguments for the high B-Share prices in these countries. Some people may also argue that the price differences between A- and B-Shares may result from the different risk aversions between Chinese and international in-vestors. On one hand, we show later in this chapter that the risk aversion coefficient does not matter in the price differences between A- and B-Shares owing to the mo-nopolistic pricing by the government. On the other hand, Kachelmeier and Shehata (1992) do not find any significant difference in risk preferences between the Chinese and North American people. With student subjects at universities in China versus Canada and the U.S., they conducted a series of well-designed experiments giving real monetary payoffs, and then used the data to empirically determine whether any significant difference exist between the East and the West. 7 1.1.2 Ownership Restrictions in Other Countries Both Gordon and L i (2001) and this paper are closely related to Stulz and Wasser-fallen (1995), the pioneer study in the area, and Domowitz, Glen, and Madhavan (1997). The common feature among these studies is the setup of an equilibrium where a discriminating monopolist controls the supply of domestic shares. However, the ownership restrictions in China are different from those in Switzerland and Mex-ico, and so the analysis differs as well. Table 1.1 shows the key differences in market structure among different countries. INSERT T A B L E 1.1 H E R E From the table, we can see that the situation in China is unique in the sense that domestic investors face ownership restrictions not only in the foreign market, but also in the domestic market. Stulz and Wasserfallen (1995) are among the first who have developed a general equilibrium model with endogenous supply of listed stocks. However, in Stulz and Wasserfallen (1995) the differential demand of a firm's shares comes from the differ-ence in deadweight costs of investing abroad versus home, not from different sets of accessible securities as in our model. Such an assumption helps Stulz and Wasser-fallen explain why the equivalent of B-Share prices are higher than A-Share prices in Switzerland. Meanwhile, it also fits well into the real situation in Switzerland, which 8 has a unique financial environment. Domowitz, Glen, Madhavan (1997) considered a similar framework based on ownership restrictions and explained the higher price of Mexican shares issued to foreign investors. Both papers are close to what we do in the modeling of a monopolist supplier in the stock markets. Another class of papers on international market segmentation, including Eun and Janakiramanan (1986), Errunza and Losq (1985), Eun and Janakiramanan (1986) and Basak (1996), take the supply of shares as given. These papers are mostly based on a static two-period model, and while their analysis is related to ours, it is not as close as Stulz and Wasserfallen (1995) and Domowitz, Glen, and Madhavan (1997). Eun and Janakiramanan (1986) are among the first to study how the price can be different for identical shares issued by the same company in segmented markets. Errunza and Losq (1985) build a two-country model where investors in one country have free access to the stock market of the other country, but not vice versa. Eun and Janakiramanan (1986) further extend the model to a multi-country framework and conduct a welfare analysis. Basak (1996) put together different degrees of market segmentation and examines welfare implications when switching between different market structures. 1.1.3 Outline of This Study Overall, the Chinese capital market is of particular interest in the study of market segmentation because it differs from other countries not only in the sign of A- and 9 B-Share price differences, but also in the structure of ownership restrictions. Conse-quently, it is a valuable source for the further study in the area of market segmentation both in theory and empirical analysis. This paper develops a static one-period model to study the situation in China. The price level of A- and B-Shares are determined in the equilibrium with supply of A- and B-Shares being endogenized. Rather than an anomaly, the higher prices of A-Shares than those of B-Shares in China are shown to be the normal situation when the supplier of domestic shares, the Chinese govern-ment, has monopoly power. In the setup, we assume there are only two countries, a domestic country and a foreign country, both of which have a limited number of firms and atomistic investors. Domestic firms issue two series of shares which are represented by A-Shares and B-Shares respectively, with A-Shares restricted to do-mestic investors and B-Shares restricted to foreign investors. Foreign firms issue only one type of shares which are not accessible to domestic (Chinese) investors owing to the capital control in the domestic country. Considering the small scale of Chinese B-Share Market relative to the world capital market, the prices of foreign shares are set to be constant so that we can focus on the pricing of A- and B-Shares in China. The markets for riskless assets are perfectly integrated in and outside China, and the riskless rates are exogenous and identical across countries. Finally, the setting assumes no friction costs or other forms of imperfections in the stock markets except for the ownership restrictions. To study investors' problems, we assume that each investor maximizes his period 10 1 utility by dividing his endowed wealth among risky and riskless assets. The major difference between a domestic investor's problem and a foreign investor's problem is that the foreigner has a larger set of investment opportunities which contains not only domestic shares but also foreign shares. In the analysis of the investors' demand functions, it can be inferred that the lack of the opportunity to invest in foreign risky assets tends to make A-Share prices higher than they would otherwise be, but before endogenizing the supply, one cannot tell whether A-Share prices shall be higher than B-Share prices or not. After studying the investors' problems, we go on to solve the government's prob-lem of share supply, namely how many A- and B-Shares to issue respectively. Unlike a firm in the foreign market which faces a competitive market, the domestic government acts as a monopolist and can discriminate between domestic and foreign investors by imposing ownership restrictions. Trying to maximize the state-owned fraction of do-mestic firms' payoff while raising a fixed amount of capital, the government chooses the optimal level of supply of A- and B-Shares respectively. The government's prob-lem here is not the same as in Stulz and Wasserfallen (1995) and Domowitz, Glen, and Madhavan (1997) although it is close to them in spirit, especially the one in Stulz and Wasserfallen (1995). On one hand, the setting here is more consistent with the real situation in China by not allowing domestic investors to invest abroad. On the other hand, unlike the assumption of a fixed amount of domestic shares to sell in Stulz and Wasserfallen (1995), this paper assume a fixed amount of capital to raise, 11 which allows us to derive the explicit relationship between the supply of shares in the A- and B-Share Markets. Putting together the results from both the government's and investors' budget maximization problems, we show clearly that A-Share prices are higher than B-Share prices regardless of relative numbers of investors in the A- and B-Share markets. Relative to previous studies on Market Segmentation in other countries, our work obtains streamlined results based on a standard setting with no friction costs in the market. Such a standard setting in our model allows us to focus on the consequences of the core issues in Chinese stock markets: unequal investment opportunities and the government's discriminating power. In what follow we see that the optimal choice of supply involves the government issuing only A-Shares as long as the total capital to be raised falls below a certain threshold. If the capital to be raised exceeds this threshold, B-Shares are issued. It offers an explanation of the size of B-Share Market relative to A-Share Market. We also extend our model to incorporate the liquidity factor, which is an addi-tional channel to explain A- and B-Share price differences. This chapter proceeds as the following: Section 2 gives an introduction to the Chinese stock market, and Section 3 sets up the model and solves the problems of different groups of investors and the monopolistic government. Then Section 4 goes on to analyze the differences in prices and amounts of supply between A- and B-12 Shares in equilibrium. After giving a simplified approach in Section 5, we extend our study to include the liquidity factor in Section 6, and furhter possible extensions in Section 7. Section 8 concludes the chapter. 1.2 Chinese Stock Markets The shares issued by Chinese firms have a complicated structure. For a better under-standing of the model used to characterize this structure and investigate its implica-tions, this section provides an introduction of the background information related to Chinese stock markets. 1.2.1 Development of Chinese Stock Markets In 1984, Shanghai Feile Audio Corporation made its initial public offering, the first of its kind since the founding of the People's Republic of China in 1949. Two years later, after a few other IPOs, Shanghai, Shenyang and Shenzhen began engaging in unofficial over-the-counter trading of stocks until the Shanghai and Shenzhen Stock Exchanges officially went into operation at the beginning of 1990s. The Shanghai Stock Exchange was established in December 1990, and the Shenzhen stock exchange formally went into operation in July 1992 after obtaining final approval in Apri l of the 13 same year. These are the only two stock exchanges in China where A- and B-Shares2 are traded. There were also two other small stock markets in Beijing: Security Trading and Automatic Quote System(STAQS) and National Electronic Trading System(NETS). These exchanges went into operation in July 1992 and April 1993 respectively. How-ever, only C shares3 were listed, and the number of listing firms in each market was very small — 8 in STAQS and 7 in NETS as of 1997. The stocks were very thinly traded in these two markets, and it was not uncommon for a firm to have no trading for many consecutive days. In 1999 the government closed these two markets. In addition, there are also 6 other securities trading centers for bonds and money funds including Shenyang, Wuhan and Tianjin. No stocks are listed in these trading centers. In 1992, the first B-Series was listed in Shanghai Stock Exchange. By October 1999, in total there were 462 A-Series and 54 B-Series shares listed on the Shanghai Stock Exchange, and 441 A-Series and 54 B-Series shares listed on the Shenzhen Stock Exchange. By the end of December 2001, in total there were 636 A-Series and 54 B-Series shares listed on the Shanghai Stock Exchange, and 494 A-Series and 56 2In this subsection, the term B-Shares does not include H Shares. H Shares are those available only to investors in Hong Kong Stock Exchange. 3C Shares are also called Legal Person Shares, which are issued only to corporations and/or institutional investors. See next subsection for details. 14 B-Series shares listed on the Shenzhen Stock Exchange. The numbers of all listed firms are 646 and 517 in the Shanghai Stock Exchange and Shenzhen Stock Exchange respectively. Based on the statistics of year 2001, The combined market value of the firms listed on the two stock exchanges has now exceeded that of the Hong Kong Stock Exchange, and the average daily turnover is more than double that of the H K S E . One other important feature to note is that short sales are prohibited in both A-and B-Share markets. 1.2.2 The classes of shares issued by Chinese firms In China, many different classes of shares are issued by the same firms. Different series of shares generally have the same voting rights and identical claims on the issuing firms' payoffs, though they have different ownership restrictions and negotiability. In the following, the different classes of shares are divided into two big categories based on the nationality of shareholders: domestic investors and foreign investors. 1. Shares Accessible to Domestic Investors • Public Individual Shares (A-Shares) : Accessible to all domestic investors. Listed in Shanghai Stock Exchange or Shenzhen Stock Exchange. Denom-inated in R M B . • Employee Shares: Only accessible to the employees of a listing firm before 15 it went public. Not negotiable at time of issuance, but generally convert-ible to A-Shares a few years after the time of initial public offering upon approval by the government. • Legal-person shares (Corporate shares, or C shares): accessible to domestic corporations or institutions, but not to individuals. In general, such shares are non-negotiable, though a few companies' C shares were listed and thinly traded in STAQS and NET. However, as mentioned earlier, both STAQS and N E T were closed in 1999, and none of the firms listed in STAQS or N E T had ever been cross-listed in other domestic or international stock exchanges. • State Shares: The shares kept by the national government. They are nontransferable. Shares Accessible to Foreign Investors • B-Shares : Listed in the Shanghai Stock Exchange (SHSE) or the Shenzhen Stock Exchange (SZSE). These are denominated in US$ on the Shanghai Stock Exchange and in HK$ on the Shenzhen Stock Exchange. • H shares : Listed in the Hong Kong Stock Exchange (HKSE), denominated in HK$. • A D R / N shares : Listed in the New York Stock Exchange, denominated in US$. So far only a few firms in China have issued such shares, and few 16 of them are cross-listed in other stock exchanges such as SHSE, SZSE, or H K S E . Although our analysis in this chapter covers only A-Shares and B-Shares, it may also be used to justify the existence of other types of share, such as C-Shares. Like B-Share prices, C-Share prices are also much lower than A-Share prices4. This may be explained with different price elasticities of demand between different group of investors as well. Corporations can invest in non-public sectors (non-state sectors or private state sectors that are not available in stock markets) inside China, and hence have different investment opportunities than individual investors because of the difficulty for individuals to invest in non-public sectors in China. Therefore, the government can benefit from price discrimination between the two different groups of investors in China: corporations and individuals. This offers an explanation why C-Shares exist, and why C-Share prices are much lower than A-Share prices. However, we choose not to discuss issues related to C-Shares any further since the logic is quite similar to our following analysis of A-Shares and B-Shares in this chapter. For these people who are concerned about why institutional investors still purchase A-Shares with opportunities to purchase C-Shares and/or invest in non-state sectors, please note that institutional investors in A-Share markets normally demand high 4Such a comparison of prices are based on information from two dimensions. First, P / E ratios, M V / B V ratios, and P/Sales ratios in the STAQS and NET are lower than corresponding ratios in SHSE and SZSE on average. Second, the IPO prices of C-Shares are lower than IPO prices of A-Shares issued by the same firms. 17 liquidity of their investment, while C-Shares obviously have very poor liquidity. In this chapter, we focus our attention to the classes of shares that are negotiable — A-Shares and B-Shares. In what follows, the term B-Shares refers to all the shares owned by foreign investors. 1.3 The Model 1.3.1 Setup; '\ For simplicity, this paper uses a static one-period model. There are only two countries, domestic country D and Foreign country F. The domestic country represents China, and the foreign country stands for the rest of the world. There are domestic firms and mj foreign firms. Foreign firms issue only one type of share, F, which are available only to foreign investors because of capital out-flow restrictions in the domestic country. Domestic firms issue two types of shares denoted by A-Share and B-Share respectively. A-Shares are open to domestic in-vestors only, and B-Shares are open to foreign investors only. A-Shares and B-Shares are identical in every sense except for ownership restrictions5. 5Although the distribution policy of a Chinese firm might differ slightly across different types of shares so as to match the diverging interests of different shareholders, most firms choose exactly the same distribution policy for both A- and B-Shares 18 The following assumptions are made in this model: 1. Differential investment opportunities. As stated above, the set of risky assets available to foreign investors consists of foreign shares and domestic B-Shares, while that available to domestic investors includes only A-Shares. 2. Market perfection. The markets are perfect except for ownership restriction. That is, there are no transaction fees, no friction costs, no information costs, etc. 3. Atomistic investor and monopolistic government. The demand in both domes-tic and foreign market is competitive, hence each investor has little power to influence the market price. However, it is different for the supply side because the domestic government that chooses the number of A- and B-Shares to issue acts as a monopolist. 4. Interest rate parity. The money market is well integrated, and the two countries have the same real interest rate. 5. Constant Absolute Risk Aversion (CARA) utility function. Both domestic and foreign investors have the following C A R A utility function: U(w) = —exp{—aw}, a > 0. The coefficient a is identical across different investors. Kachelmeier and Shehata (1992) have conducted a test on the risk preferences with experiments done in China, Canada, and the US. They do not find any difference between Chinese and North American people, and so there is no reason for us to assume 19 otherwise in this chapter. Anyhow, it is shown later that our result holds even if the risk aversion coefficients do differ. The government is also assumed to have a C A R A utility function of state-owned wealth, which means that the objective of the government is to maximize the standard mean variance equivalent of state-owned assets. In fact, in the case of one single asset in Chinese equity market, the choice between a risk-averse and risk-neutral government does not make any difference in the results of this model, for maximizing the mean variance equivalent of state shares is equivalent to maximizing the mean of state shares. In the case of multiple assets, an alternative assumption of a risk-neutral government will drive the government to issue more shares of less risky state-owned firms so as to take advantage of the higher valuation of firms with less risk by the investors. Meanwhile, the government still discriminates between A- and B-Share investors, and hence the aggregate price differences between A- and B-Shares are expected to remain similar. This will become clearer by end of the analysis in this chapter, though we are not going to give formal analysis based a risk-neutral government since we believe that both the decision makers of the government and the Chinese citizens, whose interests are supposed to be represented by the government, are risk-averse individuals as well. Different numbers of investors. The number of investors in A-Share market is na, and the number of investors in B-Share market is rib. These parameters 20 are included to measure the potential impact on share prices from differential demands across markets. 7. Normal distribution of the final payoff. The liquidating payoffs of both domestic and foreign firms at end of the period follow a multi-normal distribution, with the covariance being strictly positive6, if a, the vector of ma domestic firms' payoffs, follows multi-normal distribution i V ^ , f2rj). ^f, the vector of nij for-eign firms' payoffs, follows multi-normal distribution N(flf, O^)- The covariance matrix among domestic and foreign firms' future payoffs is QDF-8. The prices of foreign shares are given. This is consistent with the fact that the Chinese stock market is very small relative to the size of international capital markets. 9. Unlimited riskless lending and borrowing. In the market, each investor can either borrow or lend unlimited amount of money at the riskless rate r. The net amount of investors' aggregate lending or borrowing can be nonzero, which 6There is a potential problem with the normal distribution. The payoffs of stocks are lower bounded by 0, while the normal distribution allows for negative payoff, though the possibility can be made very small by choosing reasonable parameters. In this aspect, lognormal distribution may be better in modeling. However, this chapter uses only a one-period model limiting the difficulties, and the lognormal distribution also has its disadvantages. For example, a linear combination of lognormal variables does not follow lognormal distribution any more, while a linear combination of normal variables is still a normal variable. This gives normal distribution a great advantage over lognormal distribution when two or more risky assets are involved in the modeling, as in this chapter. 21 is supposed to be cleared by an outside agent. 10. No short sales. Short sales are not allowed in Chinese stock markets. For ease of notation, we define - l = r r Y (i-i) where ft is the variance-covariance matrix of both domestic and foreign firms. The vec-tor of expected payoffs for the ra^ domestic firms and ra/ foreign firms is ft = [£tD, ffF]', the demand of domestic investor i for domestic assets is Di = DA,%, the vector of for-eign investor j 's demand for domestic and foreign firms is Dj = [DB •, D'Fj}', the price vector of domestic assets for domestic investor i is Pj = PA, and the price vector of domestic and foreign shares for foreign investor j is Pj = [P'B, P'F]'. Note that supplies oi A- and B-Shares, Sa and Sb, are proportions of domestic firms' equity. The total outstanding shares of each firm is normalized to 1 unit, which is infinitely divisible among investors. Correspondingly, the demand of each investor is also a relative demand. For consistency with normal terminology, despite the normalization to a single divisible share, we nevertheless use the term shares, the plural form of the word share, when referring to the amount of demand or supply in this chapter. In this one period model, the vector of foreign share prices and the riskless interest rate are exogenous. At the beginning of the period, every investor maximizes his 22 T = YD TDF n D ft DF ^DF expected utility at end of the period. Meanwhile, by choosing the optimal amount of A- and B-Shares to issue, the government minimizes the proportion of Jrd rendered to all A- and B-Share investors while meeting the requirement of raising the pre-determined amount of capital, K. Thus, both the share prices and the amount of supply in the domestic market are endogenized in the equilibrium. 1.3.2 Domestic Demand At the beginning of the period, a representative domestic investor i maximizes his expected end-of-period utility by choosing his investment portfolio subject to bud-get constraints. Since B-Shares and foreign shares are not accessible to domestic investors, investor i can only allocate his endowed wealth WQ between ma domestic firms and riskless assets. Denoting investor i's investment in domestic firms as vector DA,I and the amount of investment in riskless assets as Ci, we can write investor i's maximization problem as: max E[U(w[)] = E[-exp{-aw\}} (1.2) S.t. W* = &AtiPA + d w\ = D'Atind + (l + r)Ci DA,i > 0 23 In the problem above, the first constraint is the budget constraint, and the second one gives the end-of-period wealth w\. PA is the price vector of A-Shares, which is taken as given by investor i because the market is competitive. D A I is investor i's demand for A-Shares, and the end of period payoff from such investment is D'A(Kd. The riskless rate is r, and so rCi is the end-of-period return on the investment Cj. From the no short sale constraint, we know that DATI is non-negative. Since the end-of-period payoffs of domestic firms follow multi-variate normal dis-tribution, it is well-known that investor i's objective is equivalent to maximizing the certainty equivalent of his end-of-period wealth: a max CEQi = DAi{jid - (1 + r)PA) + (1 + r)WLQ - -D'AIQDDAI (1.3) DA,i ' Z Taking the first order condition w.r.t. D A I , and rearranging, yields _ ftp - aVtDDATI ^ ^ 1 + r The market price vector of A-Shares must satisfy the market clearing condition nADA,i = SA. Substituting (1.4) into nADATI = SA and solving out P A , yields _ Un — — dnSA PA = (1.5) 1 + r where SA is the total supply of A-Shares set by the government, and na is the total number of A-Share investors. The first term on the right side of (1.5), /7/(l + r), is 24 the expected payoff discounted at riskfree rate. The second term on the right hand side of (1.5), ——VtDSA/{l + r), is investor i's price of risk. From equation (1.4), we can get the elasticities of investor i's demand with regard to A-Share prices. Since it is easier to see the economic meaning of the formula under a scalar case, we consider the situation where only one domestic firm is listed in the stock market. In this case, the elasticity of investor i's demand is as follows = 8 D A A P ± ^ 1 £ l dPA DAii l-nD[PA(l + r)]-i K ' } From the aggregate demand function for domestic investors, which is the same as equation (1.5), we get exactly the same elasticity of demand as shown in equation (1.6). This indicates that the number of investors doesn't change the aggregate elas-ticity of demand because they are identical. Following the same logic, we can also infer that the coefficient a doesn't change the aggregate elasticity of demand either. However, the different investment opportunities may result in different elasticities of demand, which is to be shown in next subsection through consideration of the foreign investors' demand function. As discussed in economics textbooks and earlier literature on price discrimination, such as Tirole(1988) and Stulz and Wasserfallen (1995), a monopoly can benefit from price discrimination when different groups of customers have different elasticities of demand and cannot trade with each other. In next subsection, we will study the demand function of foreign investors and see whether they have a different elasticity 25 of demand. 1.3.3 Foreign Demand Unlike domestic investors, foreign investors can invest not only in domestic shares, but also foreign shares. In this subsection, we study how such a different set of investment opportunities will affect the foreign investors' demand function. A representative foreign investor, j , has access to B-Shares, F-Shares, and riskless assets. Endowed with an initial wealth of WJ at the beginning of the period, investor j chooses the optimal portfolio of stocks and riskless assets so as to maximize his expected utility at end of the period. Mathematically, investor j's budget maximization problem can be written as: max E[U{w{)} = E[-exp{-aw{}} (1.7) s.t. W> = D'BJPB + &FJPF + Cj w{ = D'BJnd + D'FjiTf + (1 + r)Cj where DB,J and DFj denote the numbers of B and F shares in investor i's portfolio, and PB and PF are the prices for B and F Shares at the beginning of the period. Other notations are the same as earlier in this chapter. 26 Similar to investor i's maximization problem, we get the first order conditions of ;i.7): r _ i r i _ 1 r jlD - (1 + r)PB jlF - (1 + r)PF - -1 -1 flDF a DFJ ;i.s) That is, PB PF l + r O D flop ^DF DF, ;i.9) Rearranging to obtain PB PB = T^i^D ~ a(nD - SlDFSlFltiDF)DBj - SlDFQ.FlfpiF - (1 + r)PF)} (1.10) Substituting the market clearing condition nbDB,j = SB into the equation above, gives PB = YJT^D ~ —{nD - ttDFSlFltiDF)SB - Q.DFnF\p.F - (l + r)PF)] (1.11) The first term on the right side, /i~b/(l + r), is the expected payoff discounted at the riskfree rate. We leave aside the economic meaning of the second term until after we have discussed the meaning of the third term. The third term on the right side, CIDFQf1(J3F ~ (1 + r ) ^p ) / ( l -f-r), is the price of domestic firms' foreign risk. (2F — (1 + r)PF can be taken as the price of foreign risk, and VtDF^lFl l s t n e Beta Matrix which measures the amount of undiversified foreign 27 risk of domestic firms' payoffs7. Now we return to the meaning of the second term. We can rewrite the second term as ^ ( / - Q O F ^ F ^ ' D F ^ D 1 ) ^ ^ ' where / is the identity matrix of dimension nid and QDFQ^n'pjrQp1 is the correlation matrix between domestic and foreign firms8. Hence, the second term is the price of aggregate foreign investors' portfolio's pure domestic risk that is uncorrelated to foreign firms' payoffs. In short, equation (1.11) shows that the price of B-Shares is composed of three parts: the expected payoff, the price of foreign risk, and the price of pure domestic risk. From the above, we see that the B-Share price has different components from the A-Share price because of the different investment opportunities available to domestic and foreign investors. Therefore, it is natural to conjecture that foreign investors' aggregate elasticity of demand is different from that of domestic investors, in which case the government will have the incentive to offer the same shares at different prices to the two groups of investors. To have a close look at the difference between foreign and domestic investors' elasticity of demand, we calculate foreign investor j 's elasticity of demand in the case of one firm in each country. Since (1.10) collapses to 7If we assume there is only foreign asset, which is the market index of the foreign stock market, then Q/jfQp1 is exactly the vector of domestic firms' betas with the foreign market index being the benchmark portfolio. 8In the case of one domestic firm and one foreign firm, it is easy to see that the correlation matrix ^ D F ^ / t ^ O F ^ / } 1 re<luces to p2, where p is the standard moment correlation between the domestic firm's payoff and that of the foreign firm. 28 DBj = -[aQD(l - /o 2 )] _ 1 {(l + r)pB - + ^DF^Fl[^i - (1 + r)PF]} in the case of md = rrif = 1, investor j 's elasticity of demand is _ dDB)j PB , -tip + nDFSlF\iJ.f - (1 + r)PF)^ £ j ~ ~dPB~Ds~ - 1 / ( 1 + PBJTT?) : J ( L 1 2 J Comparing (1.6) with (1.12), we can see that foreign investors' elasticity of demand is different from that of domestic investors. From previous studies on price discrimi-nation such as documented in Tirole (1988), such a difference in elasticity of demand should enable the government to profit from price discrimination. The sign of elasticity of demand should be negative, while the sign of ftp^C^1 (fif — (1 + r)PF) should be positive in general, and so (1.6) has a smaller absolute value than (1.12) as long as PA = PB- This means that domestic investors, because of the investment restrictions on foreign stocks, have more inelastic demand than foreign investors. Hence, we can infer that it is better for the government to charge the domestic investors a higher price when issuing shares of domestic firms. As in the case of aggregate demand function of domestic investors, the aggre-gate demand function of foreign investors depends on neither the number of foreign investors nor the value of coefficient a in foreign investors' utility function. There-fore, the different elasticities of demand between domestic and foreign investors result from different investment opportunities, not different numbers of investors or differ-ent degrees of risk aversion. In other words, the ownership restrictions imposed by the government make price discrimination not only feasible, but also profitable to the 29 government. 1.3.4 The Supply In this section we investigate the government's choice of the optimal amount of A-and B-Shares to issue for each listed firm. It is assumed that the government must raise a certain amount of capital, K, by selling a percentage ownership of state-owned firms. A-Shares and B-Shares are the claims sold to the domestic and foreign investors respectively, and State Shares are the remaining claims to be kept by the government. The objective of the government is to maximize its utility from the consumption of State Shares at end of the period subject to the budget constraints. Assuming the utility function of the government is also of C A R A type, the government's objective is equivalent to maximizing the certainty equivalent of state-owned claims on listed firms' future payoffs. Here is a key difference between the model by Gordon and L i (2001) and ours. In Gordon and L i (2001), the government's objective function is a social welfare function where the government tries to maximize a combined utility from individuals' consumption of state-owned property and personal investment. In this chapter, it is implied that the government gives no or little weight to stock investors' utility from consumption of personal investment. As discussed later, the real situation in China indicates that the government does give little weight, if any, to stock investors' 30 personal utility. There have been expressed interests in discussing possible alternative objective functions of the government. For example, the government may try to maximize the foreign reserve rather than just only the market value of state-owned shares. A government may need to do so when facing a deficit in foreign reserve, in which case the fund raised from issuing B-Shares means more to the government than its market value. However, this is not true in China, for there is a huge foreign reserve in the Central Bank of China. In fact, the foreign reserve in China ranks #3 in the world, which guarantees the government credible ability of paying back foreign loans in a timely manner. Therefore, this alternative objective function is not considered in our model. There are a number of reasons why the assumptions in this model, as discussed in the above, are consistent with the real situations in China. First, only state-owned firms can go public, and the government picks up the firms and sets the amount of shares to issue as well as the level of initial offering price. Therefore, in China one need not worry much about the interplay among different firms' strategies, for in reality the government is the single decision maker behind all the firms. Second, each firm must specify the amount of capital to raise and which project to invest in their IPO or SEO application, which is to be reviewed by the government for approval. It implies that the number of shares to offer should depend on the amount of capital needed to finance the firm's project. Third, the investors in China composes only a 31 small portion of the Chinese nationals9, and this offers a reason why the government need not consider the stock investors' utility from personal investment. In short, the objective of the government in our model is to maximize the certainty equivalent of State Shares' end-of-period payoffs. Mathematically, the government faces the following problem: max hT!D{lmd - SA - SB) ~ ^(lm d - SA - SB)'VlD(lmd - SA - SB) (1-13) S.t. P'A(SA)SA + P'B(SB)SB = K (1.14) S A > 0 , S B > 0 (1.15) where P'A(SA)SA and P'B(SB)SB are defined as in (1.5) and (1.11). Assuming that (1.15) 9 By the end of 1999, around 2% of Chinese have opened accounts in the stock markets, and only a portion of the account holders actively invest in the markets. Moreover, to protect the interests of the general public rather than just only the stock investors, the government prohibit Chinese insurance companies and various funds from investing in the Chinese stock markets, for the government considers the stock markets are too risky to be reliable investment instruments for these funds whoes performance has important impact on social stability. Thus, most of the Chinese do not invest in the stock markets, no matter directly or indirectly. Recently the government begins to relax such investment restrictions on some insurance companies and investment funds, but there are still significant barriers imposed by the government for these funds to freely invest in stock markets. 32 is not binding, get the first order conditions of (1.13) as the following: anD(lmd - S A - Sb) - flo - >^[PA + [^^-}'SA] = 0 oSA and anD(lmd -SA- SB) - jlD - X[PB + [ 9 P * L S B ) ] ' S B ] = 0 dS'B where A is a Lagrangian multiplier. Since constraint (1.14) must be binding, A is not equal to 0. Rearranging the first order conditions, yields PA + [ d - ^ } ' S A = Ps + [ d - ^ ] ' S B (1.16) dS'A dS'B In equation (1.16), the left side is the marginal revenue from issuing one unit portfolio of A-Shares, and the right side is the marginal revenue from issuing one unit portfolio of B-Shares. Therefore, the equation (1.16) indicates that the marginal revenue from issuing any more of A-Shares must be equal to the marginal loss from reducing the same amount of B-Shares. In this case, the government cannot raise more capital by reallocating the amount of A- and B-Shares without increasing the total amount of shares issued to both domestic and foreign investors. In the case of one firm in each country, equation (1.16) can also be rewritten as PA(1 +-) = PB(1 + —) (1.17) where EA = §75^5^ a n d £B = apf sf- £A is the aggregate elasticity of demand by domestic investors, and eB is the aggregate elasticity of demand by foreign investors1 0. 1 0 As discussed earlier, the aggregate elasticity of demand is the same as corresponding represen-33 From the equation above, it is easy to see that the government would have no incentive to sell A-Shares and B-Shares at different prices if the domestic and foreign investors had the same elasticities of demand. Based on a setting where the objective function of the monopolist supplier is to maximize the amount of capital to be raised with the sum of A- and B-Shares being fixed, Stulz and Wasserfallen (1995) get the same result on elasticities of demand as shown above. In our model, it is not the total number of domestic shares being issued, but the amount of capital to be raised, that is fixed. On one hand, this setup is closer to the real situation in China; on the other hand, it offers us a chance to explicitly study the relationship between the size of the market and the relative supply of A-and B-Shares. The fact that we reach the same conclusion with different setup also implies the generality of the result. In addition, Domowitz, Glen, and Madhavan (1997) assume a fixed production technology in their model with the firm trying to maximize the profits from issuing new shares, and we find that the result above also holds based on the unconstrained maximization problem under their setting. This gives further support to the validity of this result. By intuition, the statement above is consistent with the fact that the A-Share prices are higher than B-Share prices. Compared with the riskless assets, foreign shares are better substitutes for domestic shares as long as the liquidating payoffs of tative investor's elasticity of demand for both A-Shares and B-Shares, and so eA = £i, which is defined in (1.6), and EB = £j, which is defined in (1.12). 34 foreign firms are positively correlated with those of domestic firms. Since the domestic investors cannot purchase foreign shares, the price elasticity of demand for A-Shares should be less sensitive than that for B-Shares, and so from (1.17), the price of A-Shares tends to be higher than the price of B-Shares. Anyhow, this inference is kind of ambiguous in the sense that ex itself depends on optimal values of Sx*, x — a,b. Here are two comments on this: First, the firm would choose to discriminate between the domestic and foreign investor groups if lims a is 6^o ^ 1 and K is small enough. Second, it is necessary to get more specific information about the demand functions so as to get more accurate inference. In the following analysis of the equilibrium, the demand functions derived from the investors' maximization problems will be employed in further study. 1.4 General Equilibrium In earlier sections, we have studied the decision-making processes of both the investors and the government. Now we are going to put together the domestic investors, foreign investors, and the government so as to study the characteristics of the domestic market in equilibrium. A l l investors and the government should reach their optimal solution in equilibrium, and so the results in section Modeling of Demand and section Modeling of Supply must hold simultaneously. Denoting the optimal amount of A-Share and 35 B-Share supply as SA and SB , (1-5) and (1.11) can be rewritten as: -, LLn — — £IOSA PA = 1-18 1 + r and PB = T^—WD - —(fio - nDFD.F^DF)SB ~ SlDFnF\u:F - (1 + r)PF)] (1.19) Taking derivatives of price vectors with regard to the corresponding quantities of supply, we get [dpA&)], = z ^ h n D (i.2o) 1 dS'A J l + r 1 and jdPB(SB)v _ -a/nb 1 ^ < 9 ^ 1 + r where T o is as defined in (1.1) . From the equations above, it is clear that each derivative is constant independent of the corresponding amount of supply. Substituting (1.18), (1.19), (1.20), and (1 .21) into (1.16), rearranging, yields anDs7/na = aT'Dls7/nb - J t ^ T D ^ - (1 + r)PF] (1.22) The equation above shows the relationship between the optimal A-Share and B-Share supply in equilibrium. This is the core relationship in equilibrium, which also determines the price difference between A-Shares and B-Shares. In the following, we are going to first discuss the differences between A- and B-Share prices, and then the differences between A- and B-Share supplies. 36 1.4.1 A-Share and B-Share Price Differences After we have put together the characteristics of both the demand and the supply, we can finally calculate the price differences between A- and B-Shares, as shown in the following. Statement 1 Under the assumption PDF > 0, in equilibrium the prices of A-Shares are higher than those of B-Shares. The Beta Matrix, PDF, is fl^F^F1 by definition. Proof: Combining (1.18), (1.18), and (1.22), have PA-PB = -Ta—-\-T-DlTDF(pF - (1 + r)PF) (1.23) 1 + r 2 u From (1.1), we can infer that TDF = —To^DF^p1, and so T ^ T p f = —QoF^p1- Substituting T^TQF = -QDFQF1 = —PDF into (1.23), have PA-PB = T ^ - ~ - ( P F - ( 1 + T)PF) (1-24) 1 + r I Therefore, as long as the random payoffs of domestic firms are positively cor-related with those of foreign firms, or say PDF > 0 with at least one nonzero element in each row of the Beta Matrix, the prices of A-Shares should be higher than those of B-Shares. Proof Complete. The Beta Matrix, PDF, determines the pricing of domestic shares' foreign risk based on the variance-covariance matrix of domestic and foreign firms' liquidating 37 payoffs. It is easier to see the economic meaning of (3DF when mj = 1, which is a feasible assumption when there exists a well-defined market portfolio in the foreign country. In such a case, (3DF = CIDF^F1 is simply a vector of domestic firms' betas with the foreign market portfolio being the benchmark. The formula of price difference, (1.24), is very neat. From (1.24), it is clear that A-Share prices should be higher than corresponding B-Share prices no matter how many investors there are in each country, for neither rid nor rif shows up in the formula. This clarifies the doubt that B-Share prices might be higher than A-Share prices because of more foreign investors relative to domestic investors. Moreover, equation (1.24) holds even if the coefficient of risk aversion, a, differs across domestic and foreign investors. The proof is straightforward and available upon request. It is the monopolistic government and the different sets of investment opportunities, not the numbers of investors or the risk aversion coefficients, that make A-Share prices higher than B-Share prices. The right side of equation (1.24) does not depend on the amount of A- and B-Shares issued to the public. This indicates that price gaps between A- and B-Shares do not depend on the size of Chinese equity market. Equation (1.24) also demonstrates the benefit of our model. We cannot have such a clear-cut result of higher A-Share prices than B-Share prices if we put other factors into the model, such as non-state sector investment opportunities and/or 38 consideration of individual investors' utility from personal investment in government's objective function, as done in Gordon and L i (2001). 1.4.2 Relative Supply of A- and B-Shares Next we study the relationship between the optimal supply of A-Shares and B-Shares so as to explain the relative size of A- and B-Share markets in China. A few years before the first B-Share was issued to the public in 1992, a considerable amount of A-Shares had been sold and listed in Chinese stock exchanges. B-Shares followed the issuance of A-Shares, although the size of A-Share market remains much larger than the B-Share market. In this subsection, we investigate whether our model can shed some light on such a phenomenon, namely, that A-Shares were issued first, and then later B-Shares were issued alongside A-Shares. From equation (1.22) and (1.1), we derive the relationship between the optimal supply of A- and B-Shares in equilibrium: SA = —(ImDxmD ~ ^ClDpn^o^SB + ^ ^ ^ ^ ( / ^ F - (1 + r)PF) (1.25) TIQ Za Equation (1.25) show that the supply of A- and B-Shares are still positively correlated under plausible assumptions, and B-Shares shall not be issued as long as the the amount of capital to be raised in the stock market is below a threshold value. This offers an explanation why only A-Shares were issued in the early stage of Chinese stock markets. 39 In the rest of this subsection, we derive the functional relationship between the optimal supply of A- and B-Shares as the amount of capital to raise, K, varies. The purpose is to find a logical relationship between the size of A- and B-Share Market and see whether it is consistent with the development history of Chinese stock markets. To do so, it is not necessary to consider the case of multiple firms since the focus is at the market level, and so for ease of analysis, in the rest of this section we only consider the case of one firm in each country. Consequently, the equation (1.25) becomes: where l b = na(l - p2)/nb (1.27) and _ f3f[pf-(l + r)Pf} 7o = ~ 77 U-2o) 2aad2/na In this case of one firm in each country, it is clear that a linear relationship exists between the optimal amount of A-Share supply, Sa*, and the optimal amount of B-Share supply, Sb*. Meanwhile, dSa*/dSb* = jb = na(l — p2)/nb > 0, hence Sa* and Sb* are positively correlated. The following statement gives an accurate account why no B-Shares are issued when the capital to be raised by the government is very small. Statement 2 Under the assumption pd — Pf[p-f ~ (1 + r)Pf] > 0; n o B-Shares shall be issued as long as the amount of capital to be raised, K, is not more than the critical 40 value KQ, where K0 = {pd - iPfjUf - (1 + r)Pf]}0f\fif - (1 + r)Pf] 2(1 + r)aad2/na (1.29) Meanwhile, S* and S£ are increasing w.r.t. K. Proof: From (1.26), we can see that the domestic firm will choose to sell only A-Shares if the total shares for sale is less than or equal to 70, that is, if K < KQ where KQ = ^QP^Q). Substituting (1.5) and (1.28) into above, yields As for the proof of Sx* being increasing in K for x = a, b, it follows from the following discussion. Proof Complete. By intuition, the existence of the critical value 70 can also be deduced in the following way. From (1.5) and (1.11), one can see that Pa approaches pd when Sa* —* 0, while Pb approaches pd — Pf[p/ — (1 + r)Pf] when Sb* —> 0. So, if there is only a relatively small amount of capital to raise, the firm should prefer to issue only A-Shares unless the marginal revenue from issuing one more unit of A-Share is less than Pd — Bf[pf — (1 + r)Pf], or say, unless the amount of shares being issued exceeds the critical value 70. Assuming the total amount of capital to be raised from the stock market before 1992 is less than the critical value 70, one can use this to endogenize the Chinese government's decision of not issuing B-Shares in the early stage of the stock markets. K0 = 70 1 + 7-'O {pd - \Bf\pj - (1 + r)Pf]}3f\pf - (1 + r)Pf] 2(1 + r)acrd2/na 41 Now we calculate the amount of domestic share supply as a function of K, the amount of capital to be raised. First, we consider the case K < KQ, where KQ is defined as in (1.29). Since the assumption pd > Pf[p.f — (1 + r)Pf] is equivalent to 7o < Si, we have Sa* = M± - - [ ( 1 + r K ( . , 1 ^ 2 " f l a - K)]i, 0 < K < K0 (1.30) and Sb* = 0, 0 < A- < Ko (1.31) When i f > i\n, the government issues both A-Shares and B-Shares. Substituting (1.18), (1.19), (1.26) and (1.29) into (1.14), yields K-K = 1 + Ib(-1 + P2r^ ixd-Bf[fMf-(l + r)Pf] 2 {Hd-(3j[nf-{l + r)Pf]}2 0 1 + r inb/aad2[ b 2a(l - p2)ad2/nb J + 4a(l - p2)ad2/nb } (1.32) where 70, ~fb, and i\o are those parameters defined in (1.28), (1.27), and (1.29) re-spectively. The expression K — K0 in (1.32) takes its maximum value K2 at Sb* = 52&> where l + lb{pd-Pf[pf-(l-rr)Pf}}2 K 2 ~ T T 7 4a(i - fW/n,, { l - 6 6 ) and pd-pf[pf-{l + r)Pf] 2a(l - p2)crd2/nb Meanwhile, the total amount of domestic shares issued to the public, 52, is c (l + lb)Pd-Pf[Pf-(l + r)Pf] , , ^ 2 ~ —: o~~Ti 2i—27 (i--O0) 42 The feasible amount of total domestic A- and B-Shares cannot exceeds 1 because short sales are not allowed, and so we need to check whether 52 > 1 when calculating the maximum amount of capital, Kmax, that can be raised by issuing A- and B-Shares. S2 > 1 means that the original owner of the firm can always raise more capital by issuing new equities until all the claims on the firm's payoff are sold out. Otherwise, if S2 < 1) then the maximum amount of capital that can be raised by selling off the claims on the firm's payoffs is obtained when a proportion S2 of total claims is put in the capital market. In the latter case, the original owner of the firm will never sell off all the claims on the firm's payoff no matter how much capital he needs. Considering both S2 < I and S2 > 1, we have K0 + K2, S2<1 Kmax = I (1.36) ( ^o + ^ - ^ ^ P ^ ( T S - 5 2 b ) 2 , 5 2 > 1 Then, from (1.32) we can get the optimal supply schedule (Sa*, Sb*): Sb* = S2b - J(K0 + K2- K)} + T "» 2 , K0 < K < Kmax (1.37) y 1 + 76 a( l - p2)ad2 and, in conjunction with (1.26), Sa* = lbSb* + 7o, Ko < K < Kmax (1.38) Combining (1.30), (1.31),(1.38), and (1.37), we get the complete supply schedule of domestic shares. Figure 1.1 shows a numerical example. INSERT F I G U R E 1.1 H E R E 43 In short, we have derived in the above the relationship between the size of A-Share market and B-Share market when the capital to be raised by the government varies. The result contributes to the understanding of the market development in China. Meanwhile, the relationship is derived from a static one-period model, and there are issues to be heeded when making specific claims on the dynamic properties of the market. We are going to discuss this further in next section. 1.5 A Simplified Approach and Analysis of Fin-land In this section, we first develop a simplified approach to derive the key results in our model with some simple geometric analysis, and then compare our model for China with those for other countries discussed in the literature, especially Finland. 1.5.1 A Simplified Approach Figure 1.2 presents a simplified approach to solve the government's maximization problem and derive the main results of our model in the case of a single domestic asset. In the graph, SA and SB stand for aggregate demand curves of domestic and foreign investors respectively. The aggregate demand curves are given from the solutions of domestic and foreign investors' maximization problems, as in equations 44 (1.5) and (1.11). For any two points X and Y in the graph, we denote the length of the interal XY as XY. INSERT F I G U R E 1.2 H E R E First, marginal revenues from, selling A-Share and B-Shares are MRA and MRB respectively. These marginal revenue curves are typical ones of a monopolist supplier. Since SA is a straight line, it is easy to prove that MRA has a slope that is twice the slope of SA 1 1 • The same relationship holds for MRB and SB-Second, to maximize revenue, Chinese government need to set the amount of A-Shares and B-Shares such that marginal revenues oi A- and B-Shares are equal to each other. Under the assumption that OO' is the marginal revenue of the government in equilibrium, A- and B-Share prices should be OPA and OPB in equilibrium. Next we calculate the difference between PA and PB in this case. From the relationship between MRA and SA, we know that point J must be the middle point of the interval O'L. Since line VL is parallel to line AO', point V must be the middle point of interval AL. Further, we know that point PA should be the middle point of O'A because line PAV is parallel to line O'L. Similarly, point PB must be the middle point of BO'. Therefore, the difference between O'PA and 0'PB is half the difference between O'A 1 1Here is the proof. At any point V(xi,y\) on SA, the government's revenue Rg is equal to xi * (<5 — us * xi), where n$ is the slope of SA and S is the length of OA. The derivative of Rg with regard to Xi is S — 2K$ * xi, and this is the marginal revenue from issuing A-Shares at x\. 45 and O'B, or say the difference between A- and B-Share prices should be half of the length of interval BA. Since the analysis above holds as point O' moves along the open interval BO, we know that the price difference between A-Shares and B-Shares is always half BA. The analysis above does not depend on the slopes of SA and SB, and this illustrates why A-Share prices should be higher than B-Share prices regardless of the number of investors and the risk aversion coefficients. Although we assume that domestic and foreign investors have the same risk aversion coefficients in the setup, the relaxation of such an assumption doesnot affect the price difference between A-Shares and B-Shares in equilibrium since the risk aversion coefficients only affects the slopes of demand curves SA and SB, but not the length of interval BA. In addition, Figure 1.2 explains the interaction between investors' demand elas-ticities and the government's share supply. With investors' demand functions fixed, the higher prices of A-Shares than B-Shares is a natural result of the following two factors: the government is a revenue maximizer, and the government can effectively restrict the set of shares accessible to domestic investors. If the government could not prohibit domestic investors from investing abroad or purchasing B-Shares, the price differences between A- and B-Shares would be different in equilibrium. Figure 1.2 also gives a graphical presentation of the relationship between the size of A-Share market and the size of B-Share market. If the total amount of capital to 46 be raised from stock markets is less than OB * BW, then the amount of shares issued by the government is less than BW, and the government does not issue any B-Shares. On the other hand, if the need for capital exceeds OB * BW, the government needs to issue more shares than BW, and it is necessary to issue B-Shares in addition to A-Shares. The size of A-Share market should be larger than the size of B-Share market as long as the amount of shares issued to the public is less than twice ZX, assuming MRA and MRB do cross at point X. It is possible that MRA and MRB do not cross at a l l 1 2 , and in this case the size of A-Share market is always larger than the size of B-Share market regardless of the amount of capital to be raised. Meanwhile, because of the fact that the analysis above is based on a static model, caution is needed when applying the results above to explain the dynamic develop-ment of the Chinese stock markets. Specifically, in the attempt to explain why the Chinese government did not issue B-Shares until 1992, the shift of the demand curve over time needs to be taken into consideration to get rigorous results. Assuming the shares issued before 1992 was equal to the length of the interval BW as shown in Fig-ure 1.2, the domestic investors' demand curve that the government faced after 1992 should be different from SA- Instead, the government should face a demand curve that has the same slope as SA but intersects the Price axis at point T rather than point A. This shift of demand curve would not change the conclusion that A-Share 1 2 The slope of MRA and MRB depends on the number of investors in each market as well as investors' risk aversion coefficients, in additional to the covariance bettween domestic and foreign assets. Theoretically, there exist situations where MRA and MRB do not cross. 47 prices should be higher than B-Share prices, though, for T must be higher than B. To keep analysis simple, we are implicitly assuming that the domestic investors did not expect to have a second share issuance after 1992. To make the analysis more realistic, we should consider a multiple period model with a monopolistic supplier in the stock market, and employ game theory in the set up of the interplay of the government's share issuance strategy and investors' investment decisions. Such an analysis has the potential to explain further details in the Chinese stock markets, such as why the government has to announce the quota of new shares for each year, and why stock prices fluctuate wildly whenever the government changes its policy in setting the quota of new shares. However, a multiple period model is a direction for future research, and it is not expected to change the claim that A-Share prices should be higher B-Share prices, nor the claim that A-shares should be issued first when the amount of capital needed is below a certain point. In the following, we are going to apply the analysis in our simplified approach on some other stock markets outside China. 1.5.2 Implications Beyond China: The Case of Finland Finland (Heitala (1989)) and Thailand (Bailey and Jagtiani (1994)) are similar to China in that domestic investors face legal barriers to investment abroad. In these countries, however, B-Share prices are higher than A-Share prices. In the following, 48 we use the example of Finland to show how the implications of our model differ from those of related studies. The case of Finland is very close to the case in China, except for one key difference: Finnish firms do not have as much monopolistic power as the Chinese government. In China, the government has double roles: as regulator and as stock supplier. The stock supplier can choose the structure of ownership restrictions to maximize revenue. In Finland, however, the government is not the one selling shares to investors. Con-sequently, the stock suppliers in Finland, namely Finnish firms, face more constraints than the stock supplier in China. In the following, we show that this explains why B-Share prices are higher than A-Share prices in Finland. Different from the ownership restrictions in China, Finnish investors can invest in B-Shares in addition to A-Shares13. In addition, Finnish laws impose limits on foreign ownership restrictions. Specifically, there is a "20%" rule in Finland as de-scribed in Heitala (1989)14. Based on such a setting in Finland, Figure 1.3 shows how our analysis may offer an explanation of the situation in Finland. The solid lines, SA and SB, represent domestic and foreign demand curves respectively. Meanwhile, the dotted line Rs is a certain percentage of SA, and represents foreign ownership restric-tions imposed by Finnish laws. First, as shown earlier in our analysis, a monopolistic supplier like the Chinese government prefers to sell shares to domestic investors at 1 3To be consistent with the terminology in this chapter, we denote restricted shares in Finland as A-Shares, and unrestricted shares as B-Shares. 14Many Finnish firms cannot issue more than 20% of their outstanding shares to foreign investors. 49 higher prices than to foreign investors when domestic investors cannot invest abroad. In Finland, however, a firm cannot prohibit domestic investors from purchasing B-Shares, and so A-Share prices cannot be higher than B-Share prices. A firm can have two choices at most: selling shares at the same price, or selling B-Shares at higher prices than A-Shares. Under such a setting, a Finnish firm prefers selling all shares at the same prices rather than selling B-Shares at higher prices. This explains why insurance and foreign capital firms in Finland, which are exempt from the 20% rule, choose not to impose ownership restrictions at all. Moreover, even for a firm facing the foreign ownership restriction Rs, Figure 1.3 shows that the restriction is not binding as long as the amount of foreign shares to be issued is smaller than OG: we note that X is the intersection of SB and Rs- As the amount of shares to be issued takes on larger values, the ownership restriction becomes binding. For example, when the amount of outstanding A-Shares is OI, outstanding B-Shares can only be OH owing to the restriction Rs- Consequently, the ownership restriction in Finland results in a higher price of B-Shares, PB, than the price of A-Shares, PA-Since the amount of Finnish shares in the early stage of the Finnish market should be smaller than in later stages, Figure 1.3 helps to explain why there were no higher prices of B-Shares than A-Shares in Finland before 1983, and why more and more B-Share prices became higher than their A-Share counterparts afterwards. As mentioned before, this analysis is based on a simplification of the real situation. 50 INSERT F I G U R E 1.3 H E R E The analysis above gives different implications from literature. Observing higher B- than A-Share prices in 1984 and 1985, Heitala (1989) states that domestic investors may require a higher rate of return on domestic shares than foreign investors, because domestic investors are prohibited from investing abroad and are unable to diversify away the specific country risk as can foreign investors. This implies that the lack of opportunities to invest abroad is the reason why domestic investors are paying lower prices. The inference from our model, however, is different. First, the inaccessibility to foreign shares are shown earlier in our model to be the reason why domestic investors are willing to pay a higher price for the first infinitely small amount of domestic shares than foreign investors. This is why OA is higher than OB in Figure 1.3. Intuitively, a risk-averse domestic investor needs little risk premium for the first infinitely small amount of domestic shares. A risk-averse foreign investor, however, needs substantial risk premium even for the first tiny amount of domestic shares, for he needs compensation for the portion of domestic risk that covaries with the risk of foreign assets. Second, if Finnish firms faced no legal restrictions and could restrict domestic investors from buying B-Shares, domestic investors would have ended up paying higher prices than foreign investors. Therefore, the high B-Share prices in Finland lies in the fact that Finnish firms does not have as much freedom as the Chinese government in marker price discrimination. 51 In his conclusion, Heitala (1989) states that according to his model B-Share prices are higher when foreign investors require a lower rate of return than domestic in-vestors. At end of his section II, An Equilibrium Asset Pricing Model in the Finnish Stock Market, he says, "By coincidence, for some stocks the two risk premiums may be equal, and these stocks are held in equilibrium by both investor groups. The nor-mal situation is, however, that the equilibrium price of a stock will be determined solely by the demand from one investor group and the stock will appear overpriced to the other investor group.". Following this logic, it is natural that his model does not explain why NO B-Share prices were higher than A-Share prices in Finland be-fore 1983. Further, his study gives no explanation why all insurance firms and other Finnish firms established by foreign companies, who are not subject to the "20%" rule in Finland, choose to make all their shares accessible to foreign investors rather than imposing ownership restrictions on them. In summary, the analysis above demonstrates that our model can offer explana-tions to situations in some other countries, which are different from what have been offered in some previous studies. 1.6 Extension The model we have analyzed above is a standard one with no market imperfections other than the existence of a government with monopolistic power. The main advan-52 tage of the model is its simplicity and ability to explain several notable phenomena in China, such as higher prices of A-Shares versus B-Shares and the development path of A-Share versus B-Share markets. To address additional real world issues, such as liquidity, we can extend the base model presented earlier in this chapter to analyze how the pricing of A- and B-Shares wi l l be influenced. 1.6.1 Liquidity It is argued in previous papers, such as Domowitz, Glen, and Madhavan (1997), that liquidity may play an important role in the pricing of A- and B-Shares. Less actively traded shares tend to have a larger spread between bid and ask prices, and hence share holders incur a higher transaction cost, in our case, on B-Shares. Therefore, investors demand a larger discount in the market price for shares wi th lower liquidity. In China, there is a serious thin trading problem in the B-Share market, but not in the A-Share market. This create a substantial difference in l iquidity between A-Shares and B-Shares, and the investigation into liquidity should help to explain the difference in A- versus B-Share prices. For simplicity, we assume that there are two market mmakers called A and B serving A-Share market and B-Share market respectively. A n investor has to sell his shares to a market maker at end of the period, and each market maker charges a firm-specific percentage of each firm's final payoff as the transaction cost. This transaction 53 cost is called liquidity cost in this extension, and it is to be estimated by each firm's bid-ask spreads, in addition to other related data items, in empirical studies. This setup is similar to the liquidity model in Domowitz, Glen, and Madhavan (1997), and we add two market makers here so as to make our story self-contained. Set FA — Diagll — 'yf, 1 — T £ , 1 — 7 m J , which is a md by md diagonal matrix, and 7f is the liquidity cost charged by Market Maker A for firm i = l,..,md. Liquidity costs are measured in terms of percentages of final payoffs. By solving domestic investors' problems, we have 5 TAflD - aTAQ,DTASA/na . . 1 + r Similary, solving foreign investors' problems gives PB = ^B$D @>(F EJQQYB T sClDpCl^Q/ppT g^SslT'b rgO/_jf fi^1 (/7F ( l"f"^')^F')] (1.40) where TB — Diag[l — 7J, 1 — 7 3 , 1 — 7™ ], and 7^ is the liquidity cost charged by Market Maker B for firm j = 1, ..,mb. Solving the government's problem gives aTAQDTASA/na = (TA — Tb)P>D/2 (1.41) +CI(TB^D^B — TB^DF^F1^>DF^B)SB/'n'b +^TBnDFnFl[iiF- (i + r)PF] Substituting (1.41) into (1.40) and (1.39) shows a price difference to be: P a ~ P b = + zr7^-—SBnDFnF1[/lF - (1 + r)PF] (1.42) 2(1+ r) 2(l + r) 54 Because po is positive and larger than QOF^^IPF — (1 + T)PF\, this reveals that a much higher liquidity of A-Shares versus B-Shares in China can contribute to the explanation of a higher level of A-Share prices in equilibrium. On the other hand, if B-Share liquidity were higher than A-Share liquidity, as in some other countries, the impact of liquidity on price differences would be the opposite. Domowitz, Glen, and Madhavan (1997) also empirically investigate the role of liquidity in their study. However, rather than use a unified model such as ours, they give two alternative models. One is a liquidity model, and the other is a differential demand model. In their tests, they reject the liquidity model, and accept the dif-ferential demand model. In our empirical study in Chapter III of this thesis, Equity Pricing in China: Empirical Tests, we find empirical support to the liquidity factor, in addition to other factors in our base model. The rejection of their liquidity model in the empirical tests by Domowitz, Glen, and Madhavan (1997) may result from the following factors: the improper use of panel analysis with fixed individual effects in their tests as discussed in Chapter III, their small sample size, and/or a possible lack of significant differences between A- and B-Share liquidity in their sample of Mexican firms. 55 1.7 Discussion In this section, we first describe some possible extensions to our model, and then discuss some alternative hypotheses and the empirical implications. 1.7.1 Further Extension The model can be further developed into an intertemporal model wi th social welfare analysis. B y doing so, the interest rate can be endogenized, and the social welfare analysis can show that the social welfare of the domestic country may be decreased upon integration. This might offer a more general explanation for why the government wants to ban domestic investors from investing abroad, and why the government want to protect certain domestic industries from foreign investment. One other extension to be considered is the marginal impact of the foreign capital raised from the B-Share market on the real foreign exchange rate. Assuming that the amount of foreign capital raised from the B-Share market is large enough to significantly influence the effective foreign exchange rate of R M B versus U S D in the free money market, the foreign capital raised by issuing B-Shares may mean more than just its market value based on the spot exchange rate. This may offer more implications on the relative prices and supplies of A- and B-Shares in equilibrium. 56 1.7.2 Alternative Hypotheses Some alternative hypotheses may also contribute to the explanation of the differential pricing in China. The following is a list of such hypothesis, which are not necessarily in contradiction with our approach. In fact, some of them may be potential complements to our model 1 5. i . I N F O R M A T I O N E F F E C T In Merton (1987), it is shown that incomplete information may result in a higher discount of share prices. The investors tend to invest in only these firms that they know well, and hence the firms with a higher level of publicity enjoy higher prices than those firms with a lower level of publicity. Following this logic, Chinese investors may be willing to pay a higher price for domestic shares than foreign investors because of being more familiar with domestic firms. Moreover, a Chinese firm with better publicity abroad may have a lower price difference between its A- and B-Shares. In the literature on price differences in other countries, several papers have tried to employ the information factor in their modeling and empirical testing of the A- and B-Share price differences, such as 15Some people may be interested in the potential role of corporate control in the pricing of A- and B-Shares. However, the issue of corporate control is not discussed here, for in most cases neither A-Shares nor B-Shares could reach such a point to outnumber the shares kept by the Chinese government. This implies that there is no need to make domestic or foreign investors to evaluate the benefit of corporate control when investing in Chinese stock markets. 57 Beiley and Jagtiani (1994) and Domowitz, Glen, and Madhavan (1997). 2. OPTIMISTIC DOMESTIC INVESTORS Many people are concerned about whether the Chinese investors are overop-timistic about domestic firms' payoffs. Or say, domestic and foreign investors may have different beliefs about the same firms' expected payoffs. Mathemati-cally, if Ed(-Kd) > Ef(Trd), then the price of A-Shares relative to that of B-Shares would be higher because of the difference in perceived values of pd. 3. A G E N C Y P R O B L E M Agency problems can arise from the unbalanced compensation structure for investment managers. It is common practice, especially in China, for managers to receive incentive fees based on performance. That is, For fund managers who are making investment decisions for institutions or other people, they may gain more from their funds' $1 profit relative to their loss from their funds' $1 loss. Such a structure can extort the price of risk owing to the differing interests between the principal fund investors and the fund managers. Even risk-seeking behavior may be possible when short sales are not allowed. In China, the majority of the A-Shares are held by state-owned institutions or private groups who are managing money for other people. Therefore, serious agency problem exists in A-Share market. In addition, short sales are not allowed in Chinese stock markets, which further aggravates the distortion effect on asset pricing by agency problem. 58 1.7.3 Empirical Implications Our model has two major testable implications. First, from (1.24) we can see that a firm's A-minus-B share price difference is positively correlated with its foreign beta with a well-defined foreign market portfolio being the benchmark. Consequently, we can test whether the cross-section price differences are significantly correlated with firms' foreign betas. If we consider the possibility of time-varing betas, it is also desirable to test the relationship between the time-series price differences and the firms' corresponding time-varing betas. Second, from (1.25) or (1.26), we can infer some testable implications about the relationship between the number of outstanding A- and B-Shares. For example, the firms with a positive number of outstanding B-Shares and zero A-Shares should have a zero or negative beta with the foreign market portfolio being the benchmark. Hence, we can test whether the firms with no outstanding A-Shares have lower foreign betas than the firms that have not only outstanding B-Shares but also outstanding A-Shares. In addition to the two major implications above, there are also some other im-plications that may be testable, such as the relationship between the difference of share prices and the difference of outstanding shares. However, to test these impli-cations, one has to construct a non-linear regression, while there may not be any additional statistical power from such tests. Therefore, it is not so desirable to test 59 these additional empirical implications. Now we move on to discuss the test of liquidity effect. The liquidity can be mea-sured with bid-ask spread. In addition, the trading volume can also be a meaningful indicator of the liquidity, especially for large investors, bid and ask prices at a certain point of time alone cannot tell how large a discount an investor has to suffer when he must sell a large volume of shares. Therefore, the range of supporting trading volume should also be considered in the measure of liquidity, which is important for accommodating market pressure. As derived in our analysis, the differences between A- and B-Share liquidity should be positively correlated with price ratios. The higher the gap between B- versus A-Share bid-ask spread, the higher the A- to B-Share price ratios. Similarly, the trading volume should play a similar role in price differences. Other than the testable implications of our model, it is also worthwhile to conduct some tests of alternative hypotheses related to Chinese stock markets. Here is a list of examples. • Test of information asymmetry. We can use some proxies for publicity, such as size and geographic location, to test the hypothesis of information asymmetry. The higher a firm's publicity among foreign investors, the higher the B-Share price. There are some examples of this type of test techniques in existing liter-ature, such as Beiley and Jagtiani (1994) and Domowitz, Glen, and Madhavan (1997). 60 • Test of differential beliefs. This may be carried out by analyzing the impact on prices by payoff-related information, such as earnings announcements. • Test of agency problems. This can be done through tests of asset pricing models, such as the risk-return relationships. In addition, some event studies can also provide significant power in testing the agency problems. • Test of exchange rate risk. Owing to the governmental control on the convert-ibility of the Chinese currency, R M B , a special measure needs to be constructed so as to proxy for the risk of exchange rate risk. Under the plausible assump-tion that R M B is more closely correlated with other Asian currencies than US Dollars, we can proxy the risk of holding R M B with the difference between the change of R M B versus USD and the change of other Asian currencies versus USD. If such a proxy is significantly correlated with the A-minus-B share price differences in the right direction, then the exchange rate risk is priced in the Chinese stock market and can contribute to the explanation why A-Share prices are higher than B-Share prices. 1.8 Conclusion With a general equilibrium model, we have analyzed the government's incentive to discriminate between domestic and foreign investors, resulting in higher prices of A-Shares than B-Shares. Contrary to common perception, the number of investors and 61 the coefficient of risk aversion do not affect the price differences between A-Shares and B-Shares. This is because of the role of the monopolistic government. We have also offered an explanation why the size of the A-Share market is larger than the B-Share market in China, and why the A-Share market was established years before the B-Share market. Al though our analysis is only based on a simple one-period world, its implications may extend to a multiperiod case. Further, our study helps to analyze some unexplained issues in some other coun-tries such as Finland, wi th implications that are different from previous studies. Some empirical implications have also been derived from our model, such as the relationship between foreign betas and price differences, as well as relative share supplies. We have also discussed some alternative hypotheses and corresponding tests. There are further possible extensions of our model. First , it may be possible to integrate the agency problem from unbalanced compensation wi th the explanation for price differences between A-Shares and B-Shares in this chapter 1 6 . Second, the model may be applied to study the interplay between the government and investors in a multi-period framework where investors have rational expectations of future stock 16See Chapter II titled Unbalanced Compensation and Asset Prices: An Agency Asset Pricing Model from China. 62 issuances 17See Kihlstrom (1998) for a brief literature review. Basak (1996) mentioned in Kihlstrom (1998) should be a good reference. 63 Bibliography Aitken, Michael J., Alex Frino, Michael S. McCorry, and Peter L. Swan, 1997, Short Sales are Almost Instantaneously Bad News: Evidence from the Australian Stock Exchange, working paper , University of Sydney. Basak, Suleyman, 1996, A n international model of international capital market segmentation, Journal of Financial and Quantitative Analysis 31(2), 161-188. Beiley, Warren, and Julapa Jagtiani, 1994, Foreign ownership restrictions and stock prices in the Thai capital market, Journal of Financial Economics 36, 57-87. Bekaert, Geert, and Campbell R. 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Green, 1995, , Microe-conomic Theory , Oxford University Press [43] Maskin, Eric S., 1999, Recent Theoretical Work on the Soft Budget Contraint, American Economic Review 89, 421-425. 66 [44] Santos, Manuel S., and Michael Woodford, 1997, Rational Asset Pricing Models, Econometrica 65, 19-57 [45] Sarkar, Asani, Sugato Chakravarty, and Lifan Wu, 1998, Information Asym-metry, Market Segmentation, and the Pricing of Cross-listed Shares: Theory and Evidence from Chinese A and B Shares, Journal of International Financial Mar-kets, Forthcoming , [46] Shanghai Stock Exchange, 1998, Stock Exchange Fact Book [47] Sjoberg, Orjan, and Zhang Gang, 1998, Soft Budget Constraints: A n Analysis Based on a Survey of Chinese Township Enterprises, Working Paper , Stockholm School of Economics. [48] Stulz, Rene' M . , 1981, On the effect of barriers to international asset pricing, Journal of Finance 25, 307-319. 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[51] Su, Dongwei, 1999, Ownership Restrictions and Stock Prices: Evidence from Chinese Stock Markets, The Financial Review 34, 37-56 [52] Tian, George Lihui, Nov 2000, State Shareholding and the Value of Chinese Firms, Working Paper , London Business School [53] Tirole, Jean, 1982, On the Possibility of Speculation under Rational Expecta-tions, Econometrica 50, 1163-1182 [54] Tirole, J., 1988, The Theory of Industrial Organization , MIT Press, Cambridge, M A [55] Vasicek, Oldrich A. , 1973, A Note on Using Cross-Sectional Information in Bayesian Estimation of Security Betas, Journal of Finance 28, 1233-1239 [56] Wheatley, Simon, 1988, Some tests of international equity integration, Journal of Financial Economics 21, 177-212. 67 Table 1.1: Ownership Restrictions in Different Countries This table shows different ownership restictions of a number of countries that have been studied in the literature. Paper Country Domestic Investors Domestic Foreign Shares Shares Foreign Investors Domestics Foreign Shares Shares Endogenize Supply Stulz and Wasserfallen (1995, RFS) Switzerland U U R U Y Domowitz, et al (1997, JF) Mexico U U R U Y Bailey and Jagtiani (1994, JFE) Thailand U N R U N Hietala (1989, JF) Finland U N R U N Gordon and Li (1999, 2001) Y This paper (1998, 2002) China R N R U Y Fernald and Rogers (2002) Su (1999), and others N 68 Figure 1.1: The Government's Optimal Supply Schedule For any fixed amount of capital that the government must raise from Chinese stock markets, this figure gives the government's optimal supply of A- and B-Shares as a monopolistic supplier. The graph are based on numerical results calculated with the formulas in this chapter by setting the parameters as follows: a = 0.5, r = 0.05, (if = 1000, oj = 0.35pf,Pf = 743.16, p,d = 100, ad = 0.35//d,na = 10,nb = 5,and p = 0.5. These numerical results only serve as an example to show how the government's optimal supply schedule looks like. O S, _ _ s=s +s. a b <K0' V i o o o o o ^0 o * 0 JD JOT oo1 oo1 oo oo1 oo oo oo o oo 0 o ° * M*1 O&r x * * * 0 10 ** ** ** ** t** ** ** 20 30 Amount of Raised Capital (K) 40 50 69 Figure 1.2: The Case of China Price 70 Figure 1.3: The Case of Finland 71 Chapter 2 Unbalanced Management Compensation and Equity Prices: An Agency Asset Pricing Model for China 2.1 Introduction The transitional economy in China poses many challenges to economic theory, and one of the most pressing tasks is to offer explanations to puzzles in Chinese stock markets. Peng, et al (1998) show that the consensus in the A-Share market, which 72 is open to Chinese investors only, is that stock prices are higher than their intrinsic values. Such an overpricing anomaly is hard to justify with traditional asset pricing models. Moreover, it is also a puzzle in China why investors, including the largest in-vestment companies, are willing to take extremely risky positions in their investment. For instance, in 1997 the largest securities company in China, Shenym Wan'guo Se-curities Company (SWSC), invested over 60% of its equity value in Lujiazui, a single firm listed in the Shanghai Stock Exchange. Because of such puzzles, many practi-tioners and researchers in China complain about mainstream asset pricing models, and doubt whether the current financial theory can explain the pricing behaviour in Chinese stock markets. Nevertheless, there have been very few academic studies in the finance literature that rationalize these anomalies in China, especially the over-pricing of Chinese stocks. In this chapter, we argue that traditional financial theory can indeed offer an explanation for the situation in China. We accomplish this by adding two Chinese factors into asset pricing: Unbalanced Management Compensa-tion (UMC) and a no short-sales constraint. U M C refers to a situation where a manager gets more financial benefit from one unit of profit than the penalty from one unit of loss, and the no short-sales constraint refers to regulations that prohibit short sales in Chinese stock markets. U M C causes a misalignment between the interests of fund managers and fund owners, and hence results in a distortion in asset pricing. This is the agency problem to be studied in this chapter. As pointed out in Allen (2001), relative to the huge literature on agency 73 problems in the area of corporate finance, only very a few researchers have studied how agency-based asset pricing models can explain pricing anomalies. Some of the existing contributions in this area are Brennan (2000), Cuoco and Kaniel (2000), and Arora and Ou-Yang (2000). There has been even less investigation of the link between agency-based asset pricing models and bubbles. Notable exceptions are Allen (2001) and Allen and Gale (2000). In this chapter, we develop a static one-period model with U M C and a no short-sales constraint. We call this model the Agency Capital Asset Pricing Model ( A C A P M ) , and use it to justify the existence of bubbles in Chinese stock markets in a rational equilibrium. In addition to managers with U M C , managers with Balanced Management Compensation (BMC) are also included in the model. B M C managers can also represent individual investors who directly invest in the stock markets. With fixed supply of shares of a single risky asset, we derive share prices in a partial equi-librium and study the link between U M C and asset pricing. To facilitate our discussion, we define two forms of bubbles. The strong form bubble is defined by a negative Sharpe ratio. In a weak form bubble, the Sharpe ratio is positive, but smaller than what it would be in a world without U M C 1 . The existence of U M C gives rise to either a strong form of bubbles or a weak form of bubbles, depending on the number of U M C managers and the parameters in their JOur model is a static single-period one, and so the definitions here focus on the overpricing property of bubbles. 74 compensation contracts. The no short-sales constraint plays an important role in the formation of the strong form of bubbles, though it is negligible in the weak form of bubbles. Without the no short sales constraint, the strong form of bubbles cannot exist, for even a U M C manager also prefers to short sale a stock with a negative Sharpe ratio rather than purchase it. A n extension of our model to multiple assets gives implications for fund managers' portfolio choices. The results show that a U M C manager chooses to diversify in a market with a weak form of bubbles. However, when a strong form of bubbles exists, a U M C manager prefers to invest in one single asset rather than holding a diversified portfolio. Meanwhile, a U M C manager may still prefer a lesser amount of absolute risk although he chooses not to diversify. This seemingly contradictory result comes from the structure of U M C , which forces U M C managers to care about not only the total risk of his holdings, but also the risk decomposition of his holdings. We also investigate other characteristics of A C A P M , such as how aggregate util-ities of U M C and B M C managers change as the compensation structure varies. In addition, we apply our analysis to North American stock markets, and offer an expla-nation to a number of issues such as the equity premium puzzle and the conflicting and uneven evidence on the risk-return relationship in the literature. The papers by Cuoco and Kaniel (2000) and Allen and Gale (2000) are the closest 75 to ours in literature. Cuoco and Kaniel (2000) adopt a different form of asymmetric compensation, which is based on index-adjusted compensation fees, to study the pricing differences between index and non-index stocks. They do not link the agency problem from compensation with bubbles. Allen and Gale (2000) use the limited liability in bank loans, which gives rise to an agency problem similar to the one from U M C , to explain the existence of bubbles. Allen and Gale (2000) assume a risk-neutral world with one asset, and hence do not analyze either managers' portfolio choices or the interaction between a manager's personal risk aversion and the risk-distorting effect of his or her compensation contract. A more detailed comparison between our work and these studies is given in next section. Before we move on to the literature review in next section, we show here why U M C is a reasonable assumption for China. We show that the claim that U M C is common in China is supported by both academic literature and public information from Chinese stock markets. Please note that UMC managers in our model is a simplification of the diverse investors in China with de facto U M C , including managers of SOEs, corrupted officials, as well as managers of investment companies and money funds. First, the literature on the Soft Budget Constraint (SBC) indicates the existence of U M C in China. For example, Lin and Tan (1999) states "In a socialist economy, when a state-owned enterprise incurs losses, the government often provides it with additional funding, cuts its taxes, and offers other compensations. Coincidentally, the managers of an SOE (State-Owned Enterprise) also expect to receive financial 76 assistance from the State. Such a phenomenon is called the soft budget constraint (SBC)." This gives one account of SBC in China. Blayney (1999) gives another ac-count, "Misappropriation and wasting of state assets has become an all-too-common problem in China. Too often, Chinese factory managers and local government offi-cials, by a variety of stratagems, have been able to exploit loopholes in China's asset appraisal regime to transfer state assets to themselves or entities under their control." In general, a SOE manager can steal a larger portion of SOE assets in positive states than in negative states, and this explains why U M C is even worse than what the government allows. In addition to the growing literature on SBC, there are also a few papers on compensation contracts of Chinese managers, namely Shirley and X u (2002) and X u (2001). Although the focus of these studies is on the impact of performance contracts on firms' performances, Shirley and X u (2002) and X u (2001) provide information showing that performance contracts in China tend to be based on profits, but not on losses. Further, they also show that the management compensation in SOEs tends to be risk-free rate based rather than index-adjusted. Also, they find few stock options in performance contracts, although stock options are very popular in North America. This gives a reason why U M C is more serious in China than in North America, for stock options with zero or very low exercise prices are essentially balanced compensation contracts. Additional evidence for the existence of significant stock investment by SOE man-77 agers in China comes from a crackdown on such illegal and improper investments in 1997. The official announcement by the government shows how serious a problem U M C is in Chinese stock markets. We quote part of this announcement here Recently, there has been a sustained flow of capital from state-owned com-mercial banks to stock markets through a variety of channels. Some SOEs and listed companies invest in stock markets with bank loans. ... Some SOEs invest in stock markets with capital allocated for further corporate development and expansion. Such a situation not only boosts stock spec-ulations in stock markets, but also puts the state-owned capital at high risk and jeopardizes the security of state-owned assets. The illegal trading activities by SOEs and listed firms must be prohibited so as to maintain orders in stock markets. The magnitude of the impact of U M C on asset pricing also depends on the weight of institutional investors in stock markets. A researcher in the Shanghai Stock Ex-change (SHSE), Honghui Sun (1998), finds strong evidence showing that the majority of investment in stock markets is controlled by institutional investors. In short, U M C is widespread in China, and managers with unbalanced compensation play a major role in asset pricing because they control the majority of the capital invested in stock markets. The rest of this chapter proceeds as follows. Section 2.2 reviews the related litera-78 ture, and section 2.3 develops the model: A C A P M . Section 2.4 characterizes A C A P M , and section 2.5 gives numerical analysis. After the discussion on the formation of bub-bles in section 2.6, section 2.7 extends our analysis to North American stock markets, including the provision of a possible explanation for the equity premium puzzle with the unbalanced capital gains tax. Section 2.8 concludes. Appendices are provided on the assumptions concerning managers' personal investments, an extension of our model to multiple assets, and the effect of index-adjusted compensation in North America. The appendices also show the proofs. 2.2 Literature Review This chapter is related to several fields, including agency problems, management com-pensation, fund performance, bubbles and soft budget constraints. In the following, we review the related literature in different groups. 2.2.1 Agency, Incentive Compensation, and Managerial Risk Choices There has been a rich literature on principal-agent conflicts and moral hazard prob-lems resulted from limited liability and/or unbalanced compensation structure, such as Jensen and Meckling (1976), Myers (1977), Fama (1980), Jensen and Murphy (1988 79 and 1990), and Garen (1994). For example, Jensen and Murphy (1990) emphasize that it is how managers are paid that matters most, not how much managers are paid. Jensen and Murphy (1988) also discuss the understanding of the internal incen-tive structures and call for viable economic explanations. There are also a number of papers discussing optimal contracting and the effect of incentive fees on managerial risk choices, such as Carpenter (2000), Dybvig, Farnsworth, and Carpenter (2001), Ou-yang (2000), Brander and Lewis (1986), and Nohel and Todd (2000). However, the existing literature limits itself to the field of corporate finance, and few have studied the effect of management compensation in the investment industry on asset pricing. Exceptions are Brennan (2000), Cuoco and Kaniel (2000), Allen (2001), and Arora and Ou-Yang (2001). Brennan (2000) studies the effect of symmetric incentive fees based on a benchmark portfolio, and hence focuses his analysis on the pricing differences between listed and non-listed stocks as well as related issues on portfolio choices. Arora and Ou-Yang (2001) study the impact of fund management compen-sation on asset pricing, but they limit their model to linear contracts which therefore excludes the case of unbalanced management compensation. Ou-Yang (2000) studies the contracting problem between investors and portfolio managers with exogenous equilibrium prices. Cuoco and Kaniel (2000) and Allen and Gale (2000) are the closest to our work. In his presidential address, Allen (2001) points out the lack of research in the link between agency problems in the investment industry and asset pricing, and calls for 80 more work in this area. Although Allen and Gale (2000) do not discuss management compensation in the investment industry, their analysis of the credit risk is similar to our analysis of the unbalanced management compensation, and hence has an inherent link with our work. A close comparison between Allen and Gale (2000) and our work is to be discussed in details in Section 2.2.3. Cuoco and Kaniel (2000) offers the only model that directly deals with pricing effects of asymmetric incentive fees, which is comparable to U M C in this chapter. However, their work limits itself to the pricing differences between index versus non-index stocks. Like our work, Cuoco and Kaniel (2000) study the effect of asymmetric management compensation on asset pricing. The key difference between Cuoco and Kaniel (2000) and our work is the structure of compensation contracts, and hence the major issues to explain. Cuoco and Kaniel (2000) assume an index-adjusted performance fee, and focus on the difference in the pricing of index versus non-index stocks. A key limitation of their study is that they say little about the formation of bubbles, or overpricing at the market level. In our model, the compensation contract is based on a manager's riskfree-rate-adjusted performance, not his index-adjusted performance. Such an assumption is closer to the real situation in Chinese stock markets, and can justify the existence of the strong form of bubbles in a rational equilibrium, which is important for explaining puzzles in China. The techniques employed in Cuoco and Kaniel (2000) are also different from ours. Cuoco and Kaniel (2000) develop a continuous-time dynamic model to examine the 81 optimal investment by fund managers, while we carry out an analysis based on a static one-period mean-variance model. Without going through the amount of mathematics required of a continuous-time model, we are nonetheless able to explain key issues of concern and infer major implications of interest. A n advantage of employing a simple model as in our work is the benefit of concise results and clear inferences. For example, simple functional analysis alone can show key economic implications on asset pricing in our model, while Cuoco and Kaniel (2000) must resort to numerical analysis to reach conclusions of similar nature. Other than Cuoco and Kaniel (2000), few papers on asset pricing deal with the asymmetric nature of management compensation. Brennan (2000) studies the agency problem caused by symmetric compensation based on index adjusted performance, and finds supporting evidence using data from the N Y S E . He urges two types of further work: modeling manager's dynamic strategy and endogenizing the optimal compensation contract. Cuoco and Kaniel (2001) is the work aimed towards the first direction, while Carpenter (2000), Dybvig, Farnsworth, and Carpenter (2001) and Ou-yang (2001) are the work aimed towards the second direction. Our work is a study based on U M C which can link the agency problem with bubbles in China as well as other countries in a similar economic situation. There do exist a number of other papers which are close to our analysis of the risk incentive of managers' decision making, such as Brander and Lewis (1986) and Nohel and Tod (2000). These papers, though, do not study the effect of such principal-agent 82 problems in the investment industry on stock prices. In Brander and Lewis (1986), a manager with limited liabilities aims to raise the firm's profits in good states and lower the firm's profits in poor states, and make the firm's payoff riskier so as to exploit his limited liability. Nohel and Tod (2000) is close to ours in the analysis of a manager's choice among risky investments. In a static model with investments' future payoffs following a uniform distribution, Nohel and Tod (2000) study the relationship between a manager's risk-taking behaviour and different forms of compensation: fixed wage, stock option, and free stocks. They show that a manager takes excessive risk when the bonus for profits outweighs the penalty for losses. In this chapter, we not only show that a manager will exhibit risk-seeking behaviour when his compensation is sufficiently unbalanced, but also demonstrate the effect of such risk-taking behaviour on asset prices. In addition, to infer more reliable empirical implications, we use a normal distribution rather than the uniform distribution in Nohel and Tod (2000). Lie (2000)'s work is also based on the existence of the type of problem we are studying, but his work is limited to a firm's internal mechanism. Lie (2000) proposes that disbursement of excess cash can mitigate the agency problem. In a dynamic setting, Carpenter (2000) studies the effect of call options in managerial compensation on managers' portfolio choices, and infers that incentive compensation "does not strictly lead to risk-seeking". Carpenter (2000) also takes the price processes as given, and hence does not study the link between managerial compensation and asset pricing. 83 Heinkel and Stoughton (1994) study the problem of motivating managers to work harder in a multiple period setting, and find that the possibility of multiple period contracting can induce a manager to work to the mutual benefit of both the principal and the agent. Dybvig, Farnsworth, and Carpenter (2001) assume prices as given and study the optimal compensation contract. They show that a performance-based com-ponent should be included in the optimal contact, and such a component is symmetric in the first-best case, though there is no indication such a component should still be symmetric in the third-best case where agents truthfully reveal their signals. To my understanding, even these papers are not against the existence of indirect asymmetric incentive fees in the real world. For example, the multiple period contracting might be interpreted as one indirect form of incentive fee. There is also empirical evidence showing that the structure of management com-pensation does matter in reality. For example, using data of 153 firms and a sample period of 1979-1980, Mehran (1995) finds supporting evidence of incentive compensa-tion, which also suggests that the form rather than the level of compensation is what motivates managers to increase firm value. 2.2.2 SBC in Transitional Economies Recently, there has been a growing literature in the area of Soft Budget Constraint (SBC), which is a typical problem in transitional economies such as China. "The 84 challenges of the market economy in China for economic theory touch on private versus public ownership of assets and ... individualism versus the collective good ..." says Chow (1997), who advised China in the 1980's and 1990's. This points out the need for new development in theory to solve problems in transitional economies, especially the half born market economy in China. Under such a background, SBC in State-Owned Enterprises (SOEs) rises in the literature as a base for the development of some new theories. SBC normally refers to the governmental subsidy offered to SOEs when they are losing money, as well as the lack of punishment on the managers when SOEs are not performing well. Meanwhile, when SOEs do perform well, managers can legally claim a portion of the profits as bonus, and even take out more in other forms such as perks. Kornai (1980) is among the first who study the SBC problem in central-planned economies. As more and more socialist economies change to market economies, the SBC problem has attracted the attention of more and more researchers, such as Chow (1997), Jefferson (1998), Lin and Tan (1998), Lin, Cai and L i (1999), and Maskin (1999). The literature has also discussed possible ways to solve the SBC problem. In our work, the focus is to measure the impact of such a problem on the pricing behaviour in Chinese Stock Markets. 85 2.2.3 Bubbles In the existing literature on bubbles, there is a lack of models that use standard assumptions to rationalize bubbles, as described by Fanklin Allen (2001): "How can asset prices get so high? The standard asset-pricing paradigm has little to say about this. ... within the paradigm, bubbles can only arise in exceptional circumstances. However, there are many theories of bubbles with assumptions that lie outside the paradigm." This chapter is our approach to justify the existence of bubbles in a rational equilib-rium, with assumptions lying inside the paradigm. Allen (2001) emphasizes the impact of agency problem in financial institutions on the equilibrium price level in the market. He urges research in this direction, which has been largely neglected by the literature despite its importance. As Allen (2001) points out, previous attempts to explain anomalies such as bubbles have as-sumed market incompleteness, transaction costs, and other kinds of frictions or even irrational behaviours. Our work employs the standard paradigm and account for the existence of U M C in China. There is no need for any frictions. Among papers on bubbles, the model by Allen and Gale (2000) is the closest to ours. Like our study, Allen and Gale (2000) also point out the inherent relationship between an agency problem and asset pricing. In their model, they use credit risk 86 of investors, which has a similar effect on asset pricing as U M C in our model, to explain the formation of bubbles. While the apparent difference between their work and ours is the source of the agency problem, which is the credit risk in their model and the U M C in ours, the more distinctive difference lies in the following. Allen and Gale (2000) assume a risk-neutral world with a single asset that has a future payoff following an unspecified distribution on an interval, which takes the form of a uniform distribution in their numerical analysis. Hence, the model by Allen and Gale (2000) lacks implications for risk analysis, such as how the risk-aversion of an agent interacts with his risk-distorting incentive contract. In our model, we assume risk-averse individuals and a Gaussian distribution of the risky asset's future payoffs. This enables us to derive richer implications, such as why and when a risk-averse manager makes risk-seeking investment decisions for the fund under his management. In addition, we analyze U M C managers' portfolio choices in our extension to a two-asset model. Further, our model has assumptions closer to the reality in China, and hence explains the situation in Chinese stock markets better. Our model also offers a richer set of testable implications to be carried out in empirical analyses. Other than Allen and Gale (2001), there are also a number of other studies on bubbles that are related to our work. For example, Abreu and Brunnermeier (2001) show that bubbles can exist despite the presence of rational arbitrageurs as long as there is a synchronization problem, which means the arbitrageurs are unable to coordinate their selling strategies in a timely manner. This synchronization problem 87 is one form of market inefficiency. In our model, no such inefficiency of information flow is required of the stock market. Tirole (1982) concludes that no speculation can exist in rational equilibrium under his setting, and bubbles rely on the myopia of traders. Our work shows that bubbles can exist in a rational equilibrium without any myopic traders, and the key difference between our model and Tirole (1982) is the existence of U M C . 2.2.4 Chinese Stock Markets There has been growing interest in the young but rapidly expanding Chinese stock markets. Among others, the A- and B-Share price difference is one of the major topics that have attracted many researchers2. The arguments for higher A-Share prices than B-Share prices vary among different studies, such as liquidity, information asymmetry, deadweight costs, and monopolist government. We hypothesize that U M C is more unbalanced for Chinese managers than for North American managers. The link to A- and B-Share price differences come from the fact that Chinese managers cannot purchase B-Shares^. This naturally provides another angle to explain the higher 2As defined in Chapter I, Ownership Restrictions and Market Segmentation, Chinese A-Shares and B-Shares are the identical shares issued by the same Chinese firms to domestic and foreign investors respectively. 3Owing to a policy change in 2001, Chinese investors are now allowed to invest in B-Share markets subject to certain restrictions. Ever since the change, the B-Share markets have been going up a lot, and there are much smaller gaps left between A-Share and B-Share prices. .88 prices of A-Shares than B-Shares. Compared with our Chapter I, another chapter titled Market Segmentation and Ownership Restrictions, this chapter serves more as an integral complement rather than a completely different explanation. As discussed above, this chapter helps to explain why A-Share prices are higher than B-Share prices in China by adding U M C as a pricing factor. In Chapter I, we focus on the impact of the monopolist government on asset pricing. A n implicit assumption of Chapter I is that U M C does not exist in Chinese investment industry. In this chapter, we acknowledge the existence of U M C and its dramatic impact on stock prices. Meanwhile, we leave aside the government's share issuance decision in this chapter, and fix the supply so as to focus our attention on the link between U M C and asset pricing. If, rather than a partial equilibrium, a general equilibrium with endogenous supply had been used to carry out our analysis in this chapter, this chapter would have been considered as an extension of Chapter I. Therefore, the two chapters are in fact sister chapters which complement each other's analysis, not two mutually excluding theories that compete with each other. Another aspect of the Chinese stock markets has been developed by Tian (2000) who shows that the state-ownership has a U-Shape relationship with listed firms' accounting performances. This indicates a stricter control and monitoring of state-owned assets when there is a larger state-ownership. Similarly, X u and Wang (1997) provide empirical evidence that the state-ownership is adversely related to a firm's performance. They use the firms listed on Chinese Stock Markets as the sample, 89 and study the relationship between concentration of state-ownership and the firm's economic performance. This is consistent with the belief that the more concentration of state-ownership a firm has, the more likely it receives more subsidies from the government. Gao and Peng (1998a and 1998b) show that the consensus opinion of Chinese investors is that stock prices are too high relative to their intrinsic values. It is not so convincing to explain this by simply claiming that Chinese investors are born to be gamblers. In fact, Kachelmeier and Shehata (1992) conduct an interesting study and find no differences between the risk preferences of Chinese individuals and those of North American individuals. This study speaks for the advantage of our model from another angle. 2.3 Agency Capital Asset Pricing Model (ACAPM) 2.3.1 Setup We use a static one-period model to study the impact of U M C on asset pricing in China. There are nu U M C managers and nB B M C managers in the market, where the supply of a single risky asset is fixed. Here B M C refers to Balanced Management Compensation, where a manager gets the same bonus out of $1 profit as the penalty out of $1 loss. The payoff of the risky asset at the end of the period, TT, follows a 90 normal distribution, N(fi,a). To keep the model as parsimonious as possible, we assume a single risky asset throughout the main text, and leave an extension to the case of multiple assets in Appendix A.2. A l l managers are risk averse individuals with a standard C A R A utility function, —exp(-aw), where a is a positive constant and w stands for the end-of-period wealth. Each U M C manager has an identical contract, and we denote Manager k as the representative U M C manager. The size of Fund K is WK- Manager k receives a fixed amount of basic salary 8k, plus a bonus of $c5 from fund K's $1 profit, and minus a penalty of $Q for fund K's $1 loss. Here the profit and loss are riskfree rate adjusted performance, where the riskfree rate is r. For any x G let x+ = MAX{x,0} and x~ = MIN{x,0}, and write manager k's compensation contract as Wk = o~k + cgDK(TT — RP)+ + CiDk(ir — RP)~, where R = l + r, and Dk is Fund K's investment in the risky asset. Same as any other individual, manager k's objective function is to maximize his personal utility at the end of the period, and his reserve utility is assumed to be satisfied by 8k alone. In general, we assume that cg > c\ in this chapter unless otherwise specified. Meanwhile, each B M C manager also has an identical contract. We denote Man-ager q as the representative B M C manager, who controls fund Q. The size of Fund Q is WQ. Manager q gets a fixed amount of wage 5q, plus a fixed portion of Fund Q's riskfree-rate-adjusted performance. This fixed portion is set to be CQ. Denoting Fund Q's investment in the risky asset as Dq, we write manager q's compensation 91 contract as follows: w~q = Sq + CoDq(n — RP). Manager q's objective function is also to maximize his personal utility at the end of the period, and his reserve utility is assumed to be satisfied by 5q. Under this setting, managers with balanced compensation behave like investors who are investing with their own wealth, and so without loss of generality, we have only institutional investors in our model: the role of individual investors is redundant, being subsumed by the role of B M C managers. Fund managers can invest in both the riskless asset and the risky asset. In addition, we do not consider fund managers' per-sonal investment in the stock market. This assumption is consistent with regulations in China, and more importantly, our model does not lose any generality because of this assumption, for as we shall show in Appendix A.1, fund managers will not make any such investment anyway even if they are allowed to do so. The total claims on the single risky asset is normalized to one share. This share is infinitely divisible, and a portion of it is sold out as negotiable shares in the market. To be consistent with the standard terminology, we still use the plural shares when referring to the amount of demand and/or supply. Short sales are not allowed in our model, as is the real situation in Chinese stock markets. As usual, there is only one price for the risky asset since we are not studying B-Shares, Chinese shares accessible to foreign investors only, in this chapter. 92 2.3.2 Managers with Balanced Compensation At the beginning of the period, manager q, a representative B M C manager, solves the following problem: max. E{Uq(wq} = E{—exp(—awq)} (2.1) s.t. WQ = DqP + Cq (2.2) wq = Sq + cQDq(n - RP) (2.3) Dq > 0 (2.4) where equation (2.2) is the budget constraint, equation (2.3) is the compensation, contract for manager k, and equation (2.4) is the no short-sale constraint. Equations (2.1-2.4) form a mean-variance maximization problem where the ob-jective function is max acoDq(fi - RP) - \a2c2QD2qa2 (2.5) Taking first order conditions, we get manager q's demand for the risky asset O , . M A X { ^ , 0 } = ^ ^ . (2.6) Note that Dq must be no less than 0 because of the no short-sale constraint. Now we discuss whether manager q's contract can put his interests in alignment with fund q's owners. If fund q was a private fund owned by a single person who had 93 the same risk attitude as manager q, then the owner would purchase (aa2)~x (p—RP)+ rather than (c0ao2)~l (p — RP)+, and so it seems that manager q would behave in a less risk averse manner than what the fund owners desire. However, this argument is not necessarily true because fund q may be owned by many investors. If fund q has n identical owners with same risk attitudes as manager q, the investment decision of manager k is exactly as what the n owners desire if c 0 = l / ( n + l ) . 4 When n is large, it is reasonable to assume that manager q's variable wealth from his compensation is roughly at the same scale as the average equity claim per fund q's owner. In such a situation, the compensation ratio c 0 is about l / ( n + l ) , and so manager q's investment decision is in alignment with the risk attitudes of fund q's owners. The argument above shows that B M C does not cause a serious agency problem between fund owners and their manager. Alternatively, assuming relative constant risk aversion would give the same result, but it is not discussed here since the analysis above suffices. 2.3.3 Managers with Unbalanced Compensation Manager k, a representative U M C manager, solves max E{Uk(ulk} = E{—exp(—aw^)} 4Investors need to consider k's free stock options, and Co should be set at 1/(1 + n) rather than 1/n to perfectly align k's interest with fund owners. 94 s.t. WK = DkP + Ck (2.7) wk = 4 + cgDk(iv - RP)+ + ctDk(n - RP)~ (2.8) Dk > 0. (2.9) Equation (2.7) is the budget constraint, equation (2.8) is the compensation contract for manager k, and equation (2.9) is the no short-sale constraint. To solve manager k's maximization problem, we first derive Lemma 1: Lemma 1 Manager k's utility maximization problem is equivalent as the following: ~ L + L / A r* (2.io) max Dk>o h(A — ciaDka) h(—A + cgaDkcr) where A = ^ ~ R P (2.11) a Here f(x) and N(x) are, respectively, the density function and distribution function of a standard normal variable. The function h(x) is increasing, convex, approaches x as x —> co, and approaches 0 as x —> — oo. The function h(x) is called hazard rate5, and A is the Sharpe ratio. The Sharpe 5 Hazard rate is a frequently encountered term in reliability or survival theory. Its inverse, M(x) = (1 - N(x))/f(x), is the well-known Mill's ratio in statistics. 95 ratio also provides a natural metric for the strength of bubbles: the lower the Sharpe ratio, the stronger the bubbles. Taking the first order condition of the simplified maximization problem in Lemma 1, we obtain Lemma 2 Assuming Dk > 0, the first order condition of equation (2.10) lows: BgCg = BtCl where Bg = 1 - $ ( - A + cgaDka) Bi = 1 - $ ( A - ciaDka) h[x) where h(x) is as defined in equation (2.12), and A is the Sharpe ratio. In (2.13), Bg represents the marginal base of incentive compensation in states of positive performance. Bi is the counterpart of Bg in states of negative performance. Equation (2.13) indicates that a larger cg, the bonus rate for positive performance, than Q, the penalty rate for negative performance, must be met with a proportionally smaller Bg than B[. Economically, the first order condition in Lemma 2 requires that the marginal bonus from holding more of the risky asset must be equal to the marginal penalty. 96 is as foi-(2.13) (2-14) (2.15) (2.16) Equation (2.14) shows that cg is part of the expression of Bg, which fits intuition well since manager k's bonus also depends on the number of shares purchased for Fund K , and hence on the bonus rate, cg. The logic is similar for B\ and q. The transcendental equation (2.13) has no closed form solution. Therefore, we cannot get an explicit pricing function. However, we can derive an implicit pricing function from equation (2.13), and then study major issues of concern by character-izing this implicit pricing function. 2.3.4 Equilibrium Putting together the demand of U M C and B M C managers, we solve the price in a partial equilibrium with fixed supply. The market clearing condition is S = nBDq + nuDk (2.17) At the beginning of the period, if the risky asset's Sharpe ratio is negative, a B M C manager does not purchase any shares of the risky asset. Note that a manager can not take a short position owing to the no short-sale constraint. In this case, only U M C managers invest in the stock market, and the market clearing condition (2.17) reduces to Dk = S/ny- Substituting S = riuDk into (2.13), we have: (1 - $ ( A - ciaSa/nu))ci = (1 - $ ( - A + cgaSa/nu))cg, A < 0. (2.18) On the other hand, if the risky asset's Sharpe ratio is positive, the demand of 97 manager q is positive. Substituting (2.6) and (2.17) into (2.13), and canceling Dk and Dq, then rearranging, we get: ( l _ $ ( ( l + ^ ) A _ Q a 5 a / n [ / ) ) Q = ( i _ $ ( _ ( i + ^ ! ^ ) A + C g a > Scr/n t / )) C g , A > 0. c 0 nv c 0 nv (2.19) Combining equation (2.19) and equation (2.18), we get an implicit pricing function for P in the partial equilibrium: [ 1 - $ ( A + - — A + - Q a S c r M / ) ] Q = [ l - $ ( - A - ^ — A+ + cgaSa/nu)}cg (2.20) c 0 c 0 nv If we relax the assumption that Q < c 9 in the analysis above, the same results still hold as long as Dk > 0. However, if Dk = 0 because of a much larger value of Q than cff, the model shall collapse to a situation with only B M C managers left in the market, and equation (2.20) should be replaced with the following pricing function: R 2.4 Characterization of the A C A P M Traditional C A P M determines the pricing of securities under a perfect market, where no agency problems exist. By contrast, we take into account the agency problem resulted from Unbalanced Management Compensation (UMC), which makes the in-vestment decision of a fund manager different from the one fitting into the best inter-ests of fund owners. In C A P M , a risky asset's market price only depends on its risk, 98 or say the dispersion of its future payoffs. In this model, however, the market price depends on not only the dispersion of the risky asset's payoff, but also fund managers' compensation contracts. Using the implicit pricing function (2.20), we can extract an asset pricing model where the agency problem caused by U M C is fully taken account of. Such a model is named Agency Capital Asset Pricing Model ( A C A P M ) in this chapter. 2.4.1 UMC and Price First, we study how U M C affects the market price in equilibrium. We define a measure, m = cg/ci, to gauge the severity of U M C . It is clear from m's definition that the more upward skewed manager q's compensation is, the higher the value of m should be. Although there is no explicit solution to the transcendental equation (2.20), we can study how market price varies as m changes by inspecting the implicit derivative function of P with regard to ra. Without loss of generality, we hold cg as a constant and allow Q to vary in the range of (0, cg] so as to study how market price reacts when m changes. Taking derivatives of p with regard to ra, rearranging, get 99 Proposition 1 For ci G (0,cg], dP/dm > 0. Further, E 2 £ ^ _ a 5 ( T 2 P - n B C g + n u C 0 ^ m _^ x ( 2 2 2 ) PL and P —• oo as m —> oo (2.23) Proposition 1 shows that the lower the penalty rate, the higher the market price. In addition, as long as the penalty rate, Q, is small enough, P can be much higher than its intrinsic value since P —> +oo as m —> +co. This offers an explanation to why A-Share prices in China are widely considered to be much higher than their intrinsic values, and why Chinese investors still invest in such an overpricing market. B M C managers do not invest in the stock market when there is a strong form of bubbles, where Q is so low that the Sharpe ratio is negative. In China, stock markets are widely considered to be a "policy market", or "gov-ernmental market", partly owing to the fact Chinese stock markets often move up and down abruptly, and sometimes turbulently, as the government changes its policy. One reason to this phenomenon is the government's power to change the intensity of its monitoring on the investment by SOE managers and government officials. These managers and officials are the de facto U M C managers in this model, and the moni-toring on their investment in stock markets has significant impact on market prices. When the government loosens restrictions on the investment by these U M C man-agers, market prices shall go up. Or say, when m and/or nv goes up, p rises. This is 100 a scenario that rising bubbles can form in Chinese stock markets. 2.4.2 R i s k and P r i c e In this subsection, we examine how market price P varies as the dispersion of future payoffs, which is measured by a here, changes. To do so, we first take derivatives of P with regard to cr, and then get the following proposition. P r o p o s i t i o n 2 With all other parameters fixed, the relationship between P and o in equilibrium, which corresponds the risk-return relationship in the market, is as follows This proposition shows that the risk-return relationship depends on the market condition measured by the Sharpe ratio. When the Sharpe ratio is positive, the risk-return relationship is positive. This indicates that the stock market exhibits risk-averse behaviour even if there is a distortion in asset pricing from U M C , as long as such a distortion is not serious enough to cause a market return lower than riskfree rate. Therefore, a low Q relative to cg does not always cause a negative risk-return relationship. When ci is so low that the Sharpe ratio is lower than —aSoce/nu, the risk return relationship becomes negative. This is why stock market may exhibit risk-seeking (2.24) where c# is a weighted average of cg and C\. 101 behavior when U M C is severe. When 0 > A > —aSace/nu, however, risk-return relationship is positive rather than negative, despite the existence of the strong form of bubbles. Such a situation lies in the fact that managers are themselves risk-averse individuals. The investment decision of a U M C manager is equivalent to a decision of investing in Asset II, whose end of period payoff is #// = (n — RP)+ + (q/cg)(nd — RP)~, with his personal wealth. With price fixed, an increase in a has two effects on the distribution oi jtu. On one hand, it increases the expected payoff of Asset II, E{7tn} 6 . On the other hand, it also increases the dispersion of Asset II's payoff, au = y/VAR[TXH)- A U M C manager does not like the latter effect, and so he pays less for one unit of TX when the first effect cannot outweigh the latter effect. This is how P may be decreasing with regard to a even when a strong form of bubbles exists. 6Mathematically, there can be a situation when the increase in a does not increase E{TTJJ}. That is, if RP — fi is so high relative to a that E{cg(ir — RP)+} is smaller than — E{ci(n — RP)~}, a small increase in a has a negative, rather than positive, effect on the expectation of 717/. However, such a situation is not feasible in this model, for it requires the expectation of TTJI to be negative in the first place, which cannot exist in equilibrium: a UMC manager is a risk averse individual as well, and so does not buy a risky asset with a negative mean of payoff in such a situation. 102 2.4.3 Price and Demand When the risk preference in the market is distorted by U M C , one may wonder how price-demand relationship changes. Moreover, an analysis of the price-demand re-lationship is also helpful for linking this model with the one in Chapter I, Market Segmentation and Ownership Restrictions. The relationship between P and S is as follows: Propos i t ion 3 The more shares in the market, the lower the market price. That is, Noting that cv and CQ are positive, it is easy to prove that the derivative of P with regard to S is always negative. The negative sign of | ^ fits intuition well, for a lower C[ than cg can only change the slope of Price-Supply relationship, but not the sign of it. 2.4.4 Fundamental Value and Market Value (2.25) where eg is a weighted average of cg andci, andcv is a weighted average ofci/(l + ^f-) and cg/(l + CgNB c0Nu In a perfect market where a firm's market value is equal to its true value, a change in the firm's fundamental value should cause a same change in its market value. 103 However, in a market with U M C , it is obvious that a firm's market value is higher than its true value, and it is interesting to know how the market value reacts when the firm's fundamental value changes. In our model, a shock to / i is a change in the asset's fundamental value, and we examine in the following how the market price varies as the value of \i changes. P ropos i t ion 4 The market value is linear with regard to /.i, the risky asset's expected future payoff, and the coefficient is 1/R. That is, dPA 1 dpd R (2.26) This shows that the overpricing in a market with U M C managers only comes from the misvaluation of the risk component of the risky asset's future payoffs. Caution is needed in empirical tests. Although the market value changes the same amount when there is a shock to the risky asset's fundamental value, the percentage change of the market price is not the same as the percentage change of the funda-mental value. Since the market price is higher than the fundamental value in our model, the denominator is higher when calculating returns. This has an implication for the comparison between A-Share and B-Share markets: when there is news about a shock to a firm's cash flow, the abnormal return in A-Share market should have a smaller magnitude than in B-Share market. However, if the news also affects the dispersion of future payoffs, it may cause a larger change in A-Share returns than in B-Share returns. This is consistent with evidence in the literature. 104 2.5 Numerical Analysis In this section, we conduct a numerical analysis of A C A P M for better understanding of the results in the model. To study the relationship between market price and the two pricing factors — risk and U M C , we first calculate the market price in equilibrium as ci and a take on different values in corresponding ranges. Then, to compare the market shares of U M C versus B M C managers in different situations, we also calculate the demand of representative manager q and k as Q and a vary. Last, we also calculate the utility of representative manager q and k for all combinations of (Q, a), and then study how the utility of different managers is affected by U M C as well as the total risk of the asset. In this numerical analysis, we set parameters as follows: a = 0.5, S = 0.5, fi = 1100, r = 0.1, nB = nv = 25, c 0 = cg = 0.05, Sq = 5k = 1. We then change ci from 0.001 to 0.1 by a step of 0.001, and a from 50 to 350 by a step of 3. The range of penalty rate, q, includes not only values lower than cg, but also values higher than cg, which enables us to study different effects of U M C on asset pricing as the compensation is skewed in opposite directions. When Q = 0.05, it is equivalent to a market with B M C managers only. nB = nu means that the managers in the market are equally divided into the two categories, and we will change this equality later in this chapter to study the impact of the proportion of U M C managers on asset pricing. The riskfree rate, r, is set to be 10%, which is close to the interest rate in China in 105 1990s. 2.5.1 Analysis of Market Price and Compensation Ratios Using the implicit pricing function, we calculate the market price in equilibrium for different combinations of (q,cr), and present the results in Figure I. Figure I shows that the market price increases as the penalty rate, Q, decreases, as documented in Proposition 1. Meanwhile, the relationship between market price and the dispersion of the risky asset's future payoff depends on the value of Q. When Q is high, price and risk have a negative relationship, similar to the case in a standard C A P M . However, as ci becomes smaller and smaller, the price-risk curves start to bend upward. When ci is sufficiently small, price and risk have a positive relationship. The diagram shows that the risky asset's price can be higher than the present value of its future payoff discounted at the riskfree rate, which is 1000 in this analysis. This verifies the existence of the strong form of bubbles in a rational equilibrium when Q is sufficiently small. Figure IA provides cross-sectional views of Figure I by fixing a at 50, 200, and 350 respectively. These price-penalty rate curves show that the market price is increasing w.r.t. m = Cg/ci, or say decreasing w.r.t. Q. The sign of such a relationship is independent of a. The value of cr, however, does affect how fast P decreases w.r.t. Q. The higher the value of cr, the faster P increases as Q decreases. 106 Figure IB gives four price-risk curves by fixing Q at 0.001, 0.03, 0.05, and 0.1. This enables us to study the shape of price-risk curves as Q takes on different values. When Q = 0.5, the model reduces to a world where all managers have balanced compensation, and the market price is decreasing-w.r.t. a, same as in a traditional C A P M . However, when Q = 0.001 <C 0.05, the market price is strictly increasing with regard to the dispersion of the risky asset's future payoff, a. This indicates risk-seeking investment behaviour in the market. Moreover, the market price can be higher than p/R even when Q is just moderately lower than cg, as shown in the price-risk curve at q = 0.03. This is interesting, for it indicates that a small gap between cg and q in the real world can make a big difference in asset pricing. The relationship between risk and market price, however, is not so clear at q = 0.03, and a close view is provided later in Figure IC. In Figure IB, the price-risk curve at q = 0.1 shows that, when the penalty rate is higher than the bonus rate, market price is even lower than what it would be in a traditional C A P M , for the stringent penalty drives U M C managers to make more risk-averse decisions than B M C managers. This may help to show why unbalanced capital gains taxes can result in high risk premium. For a fixed level of risk, it is clear that a higher q would result in a lower price, and hence a higher return. This is why the risk premium in a world with unbalanced capital gains taxes can be higher than in a traditional asset pricing model. Such an argument may offer an explanation to the equity premium puzzle, which is claimed by many to be the #1 anomaly in asset 107 pricing. Figure IC is simply a close view of the price-risk curve at Q = 0.03. With a in the range (50,350), P reaches its maximum value of 1023.9687 at a = 260. Noting that the price is higher than 1000 throughout the region, this graph demonstrates a scenario where the market price can be decreasing with regard to the dispersion of the risky asset's future payoffs, even in a market with the strong form of bubbles. From the analysis in Proposition 2, we know that a U M C manager prefers more risk when a is less than 260 because of the distortion effect of the unbalanced compensation. As a exceeds 260, though, any additional increase in a cannot bring a large enough increase in the expectation of TTU = ( ^ - 0 . 1 P ) + + 0.03 (7f-i?P)~/0.05 to compensate its impact on the dispersion of 7f// . Therefore, the market price would fall. In short, the price-risk curve bends downward in the range a > 260 just because U M C managers are also risk-averse individuals themselves. Figure IC is also interesting for analyzing a U M C manager's choice of diversifi-cation when there are multiple risky assets available in the market. This is to be discussed further in Appendix A.2. 108 2.5.2 Analysis of Market Price and the Number of UMC Managers The number of U M C managers also affects the level of market price in equilibrium, which can help explain the formation of bubbles, as well as price differences between Chinese A-Shares and B-Shares later in this chapter. In addition to the setting where ny = ns = 25, we also calculate the market price in a different setting where ny = 10 and nB = 40. Then, we calculate the price difference between two settings, Pdiff = Pnu=25 - Pnu=io- Here Pnu=25 is the market price with 25 U M C managers, and Pnu=w is the market price with 10 U M C managers. Figure II show the results. When ci < cg, the more U M C managers, the higher the market price. When Q > cg, the price difference is the other way around. Figure IIA shows a cross-sectional view at a = 200. It offers a closer view, clearly showing that Pdiff > 0 when cg > ci, and Pdiff < 0 when cg < c\. 2.5.3 Analysis of Demand To compare the market share of each type of managers, we calculate manager k and q's demand for the risky asset in equilibrium. Figure III show the results, and the parameters are the same as in Figure I. When Q = 0.05 = cg, the demand of manager k is the same as the demand of manager q. When q < 0.05 = cg, manager k purchases more of the risky asset than manager q. When Q is so small that the market price 109 is higher than or equal to 1000, the demand of manager q is 0. Because of the no short-sale constraint, the demand of a manager cannot be negative even if q further decreases, and hence the demand of manager k stays at 0.02. On the other hand, when q > 0.5, manager k purchases less of the risky asset than manager q, for manager k faces a harsher penalty than manger q, and becomes more risk-averse. Figure IIIA is a cross-sectional view of Figure III at a = 200, and gives a clear view of the relationship between Dq and Dk. 2.5.4 Analysis of Managers' Utility It is interesting to know how a manager's utility is affected by the compensation structure at a macro level, such as whether a manager's utility in a U M C world is higher than in a traditional setting without any U M C . To investigate this, we study how the utility of different managers changes as the compensation contracts of U M C managers vary. Figure IV shows the results of our calculation, and Figure IVA is a cross-sectional view at a — 200. Manager k, a representative U M C manager, does not necessarily have a higher utility level as the penalty rate, q, decreases. This implies that U M C is not only harmful to the benefits of B M C managers and fund owners, but also harmful to U M C managers themselves at an aggregate level when q is too low. There are two effects of low q. On one hand, a very small q gives an individual manager protection against poor states; on the other hand, he also suffers from a 110 higher market price in equilibrium because of the higher demand from other U M C managers. This analysis shows that U M C can cause a typical Pareto inefficiency because of a market failure from externalities. We suggest that the Chinese government may mitigate this problem by giving SOE managers stock options with an exercise price of 0. This can reduce the ratio of cg/ci, even if it is impossible to keep SOE managers from grabbing a larger portion of profits in positive states7. 2.6 Bubbles In literature, there are two different types of definitions of bubbles. One type refers to the rising of stock prices without any fundamental justifiability and the eventual market crash, and the other type only refers to higher stock prices than intrinsic values. The first type mainly describes dynamic properties of bubbles, and the second type only gives static properties. For simplicity, we adopt the second type of definition in this chapter, and it is easy to justify the rise and fall of prices once the overpricing is explained. A C A P M helps to rationalize the existence of bubbles in China, as well as other countries with unbalanced compensation. It is shown earlier that the second type of bubbles can exist in a rational equilibrium. For the first type of bubbles, which 7Stock options are rare in State-Owned Enterprises. I l l requires rising prices in addition to the a high market price level, we can rationalize it based on results in this chapter. The analysis in last section show that market price can rise without any change of the risky asset's future payoffs. First, if m becomes higher, which means management compensation becomes more upward skewed, the price will rise, ceteris paribus. In addition, if njj becomes larger relative to ng, which means more funds in the market are managed by managers with unbalanced compen-sation, the price will also rise. Therefore, rising bubbles can be easily rationalized as long as the de facto compensation contract and/or the number of U M C managers do vary over time. Similarly, it is also easy to justify the burst of bubbles. A convenient example is a crash down on U M C by the government, which can cause bubbles to burst as long as. the government does push it hard enough. 2.7 North American Stock Markets Although the analysis above aims at an explanation to the situation in China, it can also be applied in North American stock markets to investigate certain issues, such as the equity premium puzzle and the pricing of a firm's idiosyncratic risk. In the following, we discuss some of these issues. 112 2.7.1 Capital Gains Taxes and the Equity Premium Puzzle As we have already seen, the unbalanced management compensation in China can cause a distortion in asset pricing. Similarly, the asymmetric treatment of capital gains and losses in the U.S. can also result in a distortion in asset pricing, though the effect is the other way around. The distortion of pricing caused by unbalanced capital gains taxes may offer an explanation to the well-known equity premium puzzle in American stock markets. Mehra and Prescott (1985) find that the risk premium in the U.S. stock markets is too high to be justified with a reasonable risk coefficient, which is the so called Risk Premium Puzzle or Equity Premium Puzzle (EPP) in the literature. Ever since then, many researchers in finance and economics have offered different theories to solve the puzzle. The literature on E P P largely divides into two groups. The first group belongs to the behavioural approach, which contains two subgroups. One subgroup employs a utility function different from the widely accepted expected utility theory, such as Mankiw and Zeldes (1991). The other subgroup uses other behavioural assumptions, such as myopic loss aversion in Benartzi and Thaler (1995). The second group of researchers mainly resort to market imperfections and/or frictions to explain EPP, such as information asymmetry. Despite the various explanations available, it seems that no theory has been widely accepted as satisfactory. By studying the unbalanced treatment of capital gains and losses in taxation, 113 this chapter may offer an explanation to the high risk premium from a new angle. In the United States, taxes on capital gains and losses are not balanced. Whenever an investor makes a gain in the stock market, all or part of the gain must be included in his taxable income however large the capital gain is, and the exact tax rate depends on the investor's holding period. On the contrary, when an investor suffers a loss, only up to $3,000 per year 8 can be included in his taxable income. When a loss is larger than this upper limit of $3,000, the amount exceeding this limit can only be applied to past capital gains in the last three years, if any, and possible gains in the future. Such a tax structure is not balanced because of the following reasons. First, there is a good possibility for an investor to finally end in net losses although the expected rate of return on his investment can be positive at the time of his investment. Meanwhile, the total loss is possibly to be much larger than $3,000 in a given year, especially for large investors who have significant influence on market prices. Clearly, such an investor has to suffer all his losses without an appropriate tax subsidy. However, in the case of net capital gains in the end, an investor has to give up a significant portion of his gains as taxes. Further, it is safe to assume that the richer people tend to be the elder, and hence may have a higher possibility of ending up in losses because they have a shorter life span left9. 8For a married person, the amount is even less: up to $1,500 each year. 9Assuming a standard market where the return follows a standard diffusion process, it is straight-foward to see that the variance of log(Pt/Po) is linear with regard to the length of time, t. Therefore, for t2 > i i , the possibility for the Ptl - P0 to be negative is larger than the possibility for Pt2 - Po 114 Second, capital gains taxes are paid at end of each year, while the deduction in taxes from capital losses may be years from the dates of losses even if the investor is lucky enough to gain back all his losses in the end. Such a time lap creates a significant asymmetry in capital gains taxes because of the time value of capital, for the government makes no interest payments on tax credits. This gives another reason why capital gains taxes are unbalanced. Third, some researchers have argued that the best method to deal with capital gains tax is never to realize capital gains. This argument requires a number of as-sumptions, such as no costs in extended period of short sales and the availability of perfect tax-exempt substitutes. If such assumptions do hold in reality, surely capital gains taxes would not matter not all. However, capital gains taxes do matter in the real world because of costs in short sales and other imperfections, as argued by some researchers such as Klein (2001). In short, the discussion above shows that taxes levied on capital gains are much larger than tax subsidies to capital losses. Such an asymmetry in capital gains taxes is similar to a situation analyzed in the main model of this chapter where cg < c\. Consequently, the equilibrium market prices should be lower than in a world without capital gains tax, ceteris paribus. Therefore, the risk premium in a model with capital to be negative, since the expected rate of return is positive and linear with regard to the length of time too. This is why the unbalanced capital gains tax has a more pronounced effect on people who have a shorter life span to invest. 115 gains taxes should be larger than that in a model without capital gains taxes. Since the mean excess return in Mehra and Prescott (1985) is only about 6%, it does not seem to be difficult to explain the E P P with asymmetric taxes on capital gains and losses. Klein (2001) studies the long-term return reversals with capital gains taxes. How-ever, his model does not have any direct link to the explanation of the E P P because capital gains taxes are assumed to be balanced in his model: capital losses can al-ways be included in investors' taxable income in Klein (2001). Such an assumption is obviously not consistent with the real situation in the United States. In the following, we use the analysis in the main text to study the impact of capital gains taxes on asset pricing. For simplicity, we assume that an regular investor pays a fixed tax rate, Tg, on capital gains, and receives a fixed subsidy rate, T), for capital losses. Meanwhile, there are also some tax-exempt investors whose tax rate on capital gains and losses is T0 = 0. Denoting cg = (1 — Tg) and q = (1 — TJ), we use investors facing unbalanced capital gains taxes to replace U M C managers in the main model, and the number of such investors is ny. Similarly, denoting CQ = 1 — T 0 = 1, we use tax-exempt investors to replace B M C managers in the main model, and the number of such investors is nB- Noting that cg is now lower than q, we get the counterpart of Proposition 1 as follows: P ropos i t ion 5 For Tg G (7), 1), the higher the tax rate on capital gains, the higher 116 the equity premium. That is, dP < 0 (2.27) Further, nsCg+nu as Tg —> Tt (2.28) P -> P and P —> max{ 0} as Tg 1 (2.29) P The n u above represents the number of investors with balanced tax structure, such as these tax-exempt institutions. The effective tax rate for investors with balanced tax structure, Co, should be equal to 1 in the case of tax-exempt investors. The tax-exempt investors could be non-profit organizations who do not need to pay taxes on capital gains, or individual investors who have huge tax credits. Equations (2.28) and (2.29) also fit well into intuition. Equation (A.71) indicates that the pricing in the market is just the same as in a standard asset pricing model if there are no capital gains taxes. Meanwhile, equation (A.72) indicates that only tax-exempt investors would stay in the market if the government were to take away all capital gains. Proposition 5 states that the equity risk premium is higher when Tg > Ti, than when Tg = T[. Since the major players in the U.S. markets are not all tax-exempt, it is not surprising to see a higher equity risk premium in reality than what is derived from theoretical asset pricing models where unbalanced capital gains taxes do not exist. 117 A more rigorous analysis of the link between capital gains taxes and E P P requires a multiple-period or continuous-time setting, and asks for numerical analysis with key parameters estimated from data in the real world. This is what we are working on in an independent study. 2.7.2 Index-adjusted Management Compensation In contrast to China, U.S. does not have significant problems related to Soft Budget Constraints. However, the U.S. does have different forms of asymmetry in fund managers' compensation, such as incentive fees based on index-adjusted performance. Such compensation structures in the U.S. also cause distortions in the valuation of firms' idiosyncratic risks, which is similar to the case in China, but the market risk of each firm is still priced in a similar manner as described in traditional C A P M . This gives a possible explanation to conflicting, ambiguous, and time-varying evidence on risk-return relationship in the literature. Appendix A.3 provides details. 2.7.3 Implications in Corporate Finance The analysis in this chapter also has implications in management compensation in the area of corporate finance. In the main text of this chapter, we only consider the compensation for managers in the investment industry who can make investment decisions for investors, and then study its effect on asset pricing at a macro level. We 118 have not studied how a manager's compensation may affect the value of the individual firm under his management. By switching our analysis from the macro level to the micro level, we can infer further implications from U M C in the field of corporate finance. To align the incentive of corporate managers with the interests of shareholders, it is necessary to give corporate managers large amount of stock options with very low exercising prices. Otherwise, if the exercising price is high, a manager may choose riskier projects than investors would like to see. The optimal exercising price of stock options depends on the range of risky projects available to corporate managers. If a corporate manager can choose from a wide range of risky projects, such as the CEOs of start-up and/or high-tech firms, exercising price of stock options should be very low. As shown in the numerical analysis of managers' utilities, awarding managers free stock options is an effective method that can benefit all parties involved. Relative to cash compensation, such as salary, stock options are more costly to shareholders, for a manager must be offered a compensation package with a higher market value so as to trade off the large amount of risk that the manager has to undertake from the package. Although it is reasonable to believe that such extra cost is worthwhile when designing compensation contract for high ranking managers, it may be not so optimal for low-ranking managers and employees who has little power over the choice of risky projects. This indicates that the CEOs should be given free stock options, while the employees should be given stock options with an economically 119 meaningful exercising price. In North America and Europe, stock options are widely used in the real world as an important form of compensation. By contrast, stock options is not a realistic choice in Chinese state-owned enterprises yet 1 0 However, as discussed earlier in this chapter, there is widespread U M C resulted from the soft budget constraint problem in Chinese SOEs, and such a phenomenon in the investment industry seriously affect asset pricing in Chinese stock markets. Such U M C also still has implications on the current economic performance of Chinese firms. For those big enterprises with higher percentage of state ownership, the government must be monitoring their activities more closely, and hence the performance should be good because closer monitoring results in a lower level of U M C . Meanwhile, for those enterprises with little state ownership, the owners must be monitoring the managers even more closely, and so their economic performance should be even better. However, for enterprises with medium state ownership, the monitoring of the managers should be the worst, and hence the a higher level of U M C tends to prevail. Consequently, these firms are expected to have the poorest economic performance on average. Another potential application in corporate finance is the relationship between unbalanced corporate tax and a firm's optimal capital structure. Similar to the impact 10Although a manager may receive a one-time free stock bonus at the time of IPO, stock options is not part of a regular compensation package. Further, listed firms compose only a small percentage of state-owned enterprises (SOEs), and a manager of a non-listed SOE do not have any stocks of the firm under his management. 120 of the unbalanced capital gains tax on an investor's valuation of risky assets and hence his portfolio choice, the so-believed unbalanced corporate tax also has an effect on a firm's valuation of its profits and interest expenses of debt. There is a large number of papers related to this area, and it is left to further study whether such a thought could result in some further development in the research on tax and capital structure. 2.8 Conclusion In this chapter, we have developed a simple agency capital asset pricing model, which shows that U M C , together with the no short-sale constraint, can explain the over-pricing anomaly in China, and hence rationalize the formation of bubbles. The un-balanced compensation gives managers incentives to underweight downside risk, and so creates a higher level of market price than in a world without U M C . Further, the risk-return relationship is negative when U M C is severe, which is in sharp contrast with the positive risk-return relationship in traditional capital asset pricing models. In addition, a U M C manager may choose not to diversify even if he prefers a lesser amount of absolute risk. The answer to this lies in the transformation effect of the unbalanced compensation, which renders the amount of absolute risk alone insufficient to measure the value of the risk. It is also shown that an excessively low penalty rate is not good even for U M C managers themselves, for the competition among U M C managers force themselves to 121 pay a high price for the same asset. Similar to the analysis of the U M C , unbalanced capital gains tax is also shown to have a profound impact on market prices in equilibrium, and hence offer a new explanation to the equity premium puzzle. In North American markets, the asymmetric compensation is based on index-adjusted performance, and only the risk attitudes towards idiosyncratic risk is dis-torted by such a compensation structure. Consequently, market prices in North Amer-ica should be increasing with regard to idiosyncratic risk, but decreasing with regard to market risk. 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X u , Lixin Colin, 2000, Control, Incentives and competition - The Impact of Reform on Chinese State-owned Enterprises, Economics of Transition 8, 151-173 Zhou, Chunsheng, 1999, Informational Asymmetry and Market Imperfections: Another Solution to the Equity Premium Puzzle, Journal of Financial and Quantitative Analysis 34, 445-464 126 Figure 2.1: Agency Asset Pricing Model — The Case of One Asset In this numerical analysis, we set cg = 0.05, and increase Q from 0.001 to 0.1 by 0.001, andu from 50 to 350 by 3. Market price, P, is then solved in equi-librium for each combination of (Q,CT ) , with other parameters set as follows: a = 0.5, S = 0.5, \i = 1100, r = 0.1, nB = nv = 25, c 0 = 0.05 = cg, Sq = Sk = 1. 1400 1300 o a 1200 ra 1100 1000 0.025 0.075 Std of Payoff (a) 350 0.1 0.05=Cg Penalty Rate (c) 127 Figure 2.1: A: Price-Penalty Rate Curves — Cross-sectional Views This figure is a set of cross-sectional views of Figure I by fixing a at 50, 250, and 350 respectively. Each price-penalty rate curve is obtained as the penalty rate, Q, increases from 0.001 to 0.1 by 0.001. The bonus rate, cg, is set to 0.05. Other parameters are set as follows, a = 0.5, S = 0.5, fi — 1100, r = 0.1, ng = ny = 25, c 0 = 0.05, 8q = 5k = 1. 0.075 0.05=Cg Penalty Rate (c() 0.025 128 Figure 2.1: B: Price-Risk Curves — Cross-sectional Views This figure shows the price-risk relationship in equilibrium with Q fixed at 0.001, 0.03, 0.05, and 0.1. For each fixed value of Q, a price-risk curve is obtained as the standard deviation of the risky asset's payoff, a, varies from 50 to 350. The bonus rate, cg, is set to 0.05. Other parameters are set as follows, a = 0.5, S = 0.5, fj, = 1100, r = 0.1, n B = n u — 25, c 0 = 0.05, S„ = 8k — 1-- - CpO.001 _e- c |=o.03 c,=0.05=c . _ . c=0.1 89888888 Doojoiiim3[n30ooooib 50 100 150 200 Std of Payoff (a) 250 300 350 129 Figure 2.1: C: A Special Price-Risk Curve — A Close View This figure represents the price-risk relationship in equilibrium with Q fixed at 0.03, which is a cross-sectional view of Figure I. This figure shows how the market price changes as the standard deviation of the risky asset's payoff, cr, varies from 50 to 350. The change of slope before and after the maximum point at (1023.9687, 260) has important implications about a U M C manager's risk attitude. The bonus rate, cg, is set to 0.05. Other parameters are set as follows: a — 0.5, S = 0.5, fj. — 1100, r = 0.1, nB = nu = 25, c 0 = 0.05, Sq = Sk = 1. i i 1 Maximum = 1023.9687 at a = 260 1024 1008 50 100 150 200 Std of Payoff (o) 250 300 350 130 Figure 2.2: Market Price and the Number of U M C Managers This figure shows the change in market price when the number of U M C managers increases from 10 to 25, with the sum of U M C and B M C managers fixed at 50. Specifically, denoting Pnu=25 as the market price with 25 U M C managers, and Pnu=io as the market price with 10 U M C managers, we write the price difference as Pdiff = Pnu=25 P, ny=10-In this numerical analysis, we set cg = 0.05, and increase Q from 0.001 to 0.1 by 0.001, and a from 50 to 350 by 3. Market price, P, is then solved in equilibrium with ny fixed at 25 and 10 respectively. Other parameters are set as follows: a = 0.5, S = 0.5, fi = 1100, r = 0.1, c 0 = 0.05 = cg, nB + nv = 50, Sq = Sk = 1. 0.075 Std of Payoff (a) 0.05=Cg Penalty Rate (c) 0.025 131 Figure 2.2: A: Price Difference versus Penalty Rate Curve — A Cross-sectional View This figure shows the relationship between the price difference and penalty rate with a fixed at 200. The price difference, Pdiff, is defined to be Pnu=2§ — Pnu=io, where Pnv=25 is the market price with 25 U M C managers, and Pnu=io is the market price with 10 U M C managers. The bonus rate, cg, is set to 0.05. Other parameters are set as follows, a = 0.5, S = 0.5, n = 1100, r = 0.1, TiB + nu = 50, c 0 = 0.05 = cg, Sq = 5k = 1. 251 1 1 1 0.1 0.075 0.05=Cg 0.025 0 Penalty Rate (c() 132 Figure 2.3: Managers' Demand This figure shows how the representative U M C manager q and B M C manager k change their demands under different market situations. We set cg — 0.05, and allow Q and a to vary in the range of (0.001,0.1) and (50,350) respectively. The representative managers' demand, Dq and Dk, is calculated in equilibrium with other parameters set as follows: a = 0.5, S = 0.5, / i = 1100, r = 0.1, nB = riu = 25, and c 0 = 0.05. 0.02-0.015-•a | 0.01 a a 0.005 -TD q. i D, 0 50 100 1! 200 250 300 0.075 Std of Payoff (a) 350 0.1 133 Figure 2.3: A: Managers' Demand — A Cross-sectional View This figure is a cross-sectional view of Figure III at a — 200. It shows how the demands of representative U M C manager q and B M C manager k change with a taking a fixed value at 200. We set the bonus rate, cg, to 0.05, and allow the values of Ci to vary in the range of (0.001,0.1). The representative managers' demand, Dq and Dk, is then calculated in equilibrium with other parameters set as follows: a = 0.5, S = 0.5, [i = 1100, r = 0.1, nB - nv = 25, and c 0 = 0.05. Penalty Rate (c() 134 Figure 2.4: Managers' Utilities This figure shows how the utilities of representative U M C manager q and B M C man-ager k vary under different market situations. We set the bonus rate, cg, to 0.05, and allow Q and a to vary in the range of (0.001, 0.1) and (50, 350) respectively. The representative managers' utilities in equilibrium, Uq and Uk, are calculated with other parameters being set as follows: a = 0.5, S = 0.5, fi — 1100, r = 0.1, nB = ny = 25, CQ = 0.05, and 5q = 5k = 1. -0.598 N -0.599. -0.6. >. -0.601 N •5-0.602 N o jp -0.603. , Q. N -0.604 -0.605 N -0.606 100 200 300 std (a) 0.075 0.05=Cg Penalty Rate (c() 0.025 135 Figure 2.4: A: Managers' Utilities — A Cross-sectional View This figure is a cross-sectional view of Figure IV at a = 200. It shows how the utilities of representative U M C manager q and B M C manager k change under different market situations with a fixed at 200. We set the bonus rate, cg, to 0.05, and allow the values of ci to vary in the range of (0.001,0.1). The representative managers' utilities in equilibrium, Uq and Uk, are calculated with other parameters set as follows: a — 0.5, S = 0.5, fj, = 1100, r = 0.1, nB = nu = 25, c 0 = 0.05, and 5q = Sk = 1. -0.6035 -0.604 -0.6045 ZD -0.605 -0.6055 -0.606 -0.6065 -0.607 0.1 0.075 0.05=Cg Penalty Rate (c.) 0.025 136 Figure 2.5: U M C Manager's Portfolio Choice This figure presents a numerical analysis of a representative U M C manager's (k's) portfolio choice, and the purpose is to explain why manager k may choose not to diversify even when he prefers to have a lesser amount of absolute risk. First, with ak fixed at 0.5, manager k maximizes his personal utility by choosing Dp. His solution is shown as aDp with ak = .5" in the top disgram. The equilibrium price in such a setting is as shown in the second diagram. Then, manager k is allowed to choose both Dp and ak rather than Dp alone in his utility maximization, with market price set to be the same as in the second diagram for each value of a. In such a situation, manager k's optimal choices of Dp and ak are shown in the top and third diagram respectively. The bottom diagram shows the increase in manager k's utility after he is allowed to choose ak in his utility maximization, where = £/afce[o,i] — Uak=,$. In this numerical analysis, we allow a to take values in [50, 350] while setting am = \/0.99<7 and ae V /0T02cr. In addition, we set cg = c0 = 0.05, Q S = 0.5, ix = 1100, r = 0.1 and 5q = Sk = 1. 0.03, a = 0.5, 0.0208 0.0206 C | 0.0204 a 0.0202 0.02 - D with ccke [0,1] D with a, =.5 P k 300 350 350 350 137 2 0 0 Std of Payoff (a) 350 Chapter 3 Equity Pricing in China: Empirical Tests 3.1 Introduction and Review of Literature Chinese stock markets have been developing very quickly since their establishment at the beginning of last decade, and now the combined size of Chinese stock markets in Shanghai and Shenzhen ranks among the largest in the world. As the size of Chinese economy approaches a global rank of #5, the research on Chinese stock markets is attracting more and more attention from both international researchers and global investors. While the Chinese equity market offers a fertile landscape for the testing of many financial theories, it also raises a variety of challenges to modern financial 138 theories. In this chapter, we review the existing empirical studies on Chinese stock markets. We begin with Su (1999) who uses the sample period of Apri l 1994 to September 1996 to study the relationship between beta and returns, and who finds supporting evidence for his model on price differences between A-Shares and B-Shares. His work is limited by the partiality of his model, in addition to the short sample period (less than two and a half years). Using latent variable analysis, Fung, Lee, and Leung (2000) show that A- and B-Shares issued by the same firm are segmented, and the fundamental forces that drive the movement of returns are different for the A- and B-Share markets. Further, they also show that the Shanghai Stock Exchange (SHSE) follows the Shenzhen Stock Exchange (SZSE) rather than the other way around. Their sample period is from May 1993 to June 1997, which is more than 1.5 years longer than the sample period in Su (1999), and their data come from the Taiwan Economic Journal and University of Hong Kong. Fung, Lee, and Leung (2000) focus on the empirical characteristics of Chinese stock markets only, and do not provide any model to explain the implication of segmentation of A- and B-Share markets or other characteristics tested in their study. Chakravarty, Sarkar, and Wu (1998) use both asymmetric information and market segmentation to explain why the A- and B-Share prices differ. In their sample period 139 (1994-1996), Chakravarty (1998), et al find empirical support for the asymmetric information hypothesis using data from Datastream. They develop a model based on information asymmetry and ownership restrictions, but do not endogenize the supply of shares to the market by a monopolistic government. Moreover, Chakravarty (1998), et al find that A-Share returns appear to lead B-Share return. As discussed later, this may be the result of the thin trading problem in the B-Share market. Chen, Lee, and-Tim (2001) use the illiquidity of B-Shares as the major reason to explain price differences between A- and B-Shares, and test their hypothesis with data from 1992 to 1997. Chen (2001), et al find that B-Share prices tend to move more closely with market fundamentals than do A-Share prices, consistent with the implication from our model in Stock Ownership Restrictions and Discriminatory Asset Pricing in the Chinese Equity Market (Chapter I): in Chapter I, our model shows that a shock in a firm's cash flow tends to cause a larger change in B-Share returns than A-Share returns. As we shall show, such a result may also be driven by their failure to deal with the thin trading in B-Share market. Chen (2001), et al argue against the asymmetric information hypothesis proposed by Sarkar, Chakravarty, and Wu (1998) to explain the price differences between A- and B-Shares. However, they do not provide any formal model, limiting the power of their tests. Moreover, they follow the empirical method by Domowitz, Glen, and Madhavan (1997) without paying attention to the potential distortion of firm characteristics in a panel regression with fixed effects. Hence, their conclusion about firm-characteristic 140 variables is dubious. In addition, in their tests of the liquidity hypothesis, they use the trading volume, not the bid-ask spread. As argued later in this chapter, a combination of the two proxies is necessary to give an accurate description of shares' liquidity. Su and Fleisher (1999) study and explain why volatility is different between the A-and B-Share markets. Darrat and Zhong (2000) test the random-walk hypothesis in Chinese stock markets using both the variance-ratio and model comparison methods. They conclude that the model comparison method is decisive in rejecting the random-walk hypothesis. Tian (2000) studies the relationship between state ownership and the value of listed firms in Chinese stock markets. He finds a nonlinear relationship between state ownership and corporate performance. Fernald and Rogers (1998) use data from Reuters, Bloomberg, and Internet Se-curities in their study of the sample period 1993-1997. In their theoretical analysis, Fernald and Rogers (1998) point out that domestic investors may demand a lower risk premium because of limited access to risky securities. However, they do not study how the monopolist supply by the government should affect the price differences in equilibrium. Fernald and Rogers (1998) find a negative but insignificant relationship between firms' international betas and their B- to A-Share price ratios. This result, although not so strong, is consistent with our model. Their lack of significance may come from the neglect of the thin trading problem in the B-Share market. One of the most challenging barriers in conducting research on Chinese stock 141 markets is the difficulty in collecting reliable data and dealing with the complexity of the market structure and regulations in China. With tedious and arduous efforts, we have collected what we believe to be a reliable dataset that can be applied to consider a variety of empirical issues in Chinese stock markets. Hence, one of the contributions of this chapter is the application of more accurate and reliable data. For example, in contrast to the broad-based, cross validated data used in this chapter, the data of Su and Fleisher (1999) are from a single stock dealer's house of a provincial security company in Zhejiang. Chakravarty, Sarkar, and Wu (1998) and Tian (2000) do use broader based data from Datastream. However, occasional but significant inaccuracy of Datastream data is suggested by comparing the Datastream data with those from the Shanghai Stock Exchange, where the latter are considered to be more reliable. Moreover, the data from Datastream is not complete. A further unique aspect of this chapter is that none of the studies of Chinese stock markets has previously dealt with thin-trading, a thorny issue in Chinese B-Share Markets. Since trading of B-Shares before 1999 was infrequent, a special procedure is needed when such data are used for empirical tests, as discussed in Campbell, Lo, and MacKinlay (1998). One of the most obvious problems of thin trading is the spurious auto-correlations which may drive some of the results in existing literature, such as Chakravarty, Sarkar, and Wu (1998) and Chen, Lee, and Rui (2001). On the risk-return relationship, there is a large and conflicting literature. Using either a firm/portfolio's covariance with market volatility or its own total volatility as 142 the proxy for risk, Fama and French (1973), French, Schwert, and Stambaugh (1987) and Campbell and Hentschel (1992) find the relation between risk and expected return to be positive, while Turner, Startz, and Nelson (1989), Glosten, Jagannathan, and Runkle (1993), and Nelson (1991) find the relation to be negative. Bekaert and Wu (2000) give a summary of studies in this area, and point out that the coefficient linking volatility to returns is often statistically insignificant in the literature. Based on application of the model from our Chapter II to the North American market, the ambuigity in the relationship between the total risk and expected return is not surprising. Appendix C of Chapter II shows that the assumption of U M C based on index-adjusted performance gives rise to an agency problem in North America dif-ferent from the agency problem in China. Such an agency problem in North America causes firms with larger idiosyncratic risks to be priced higher, and firms with larger market risks to be priced lower. Since a firm's total risk consists of both its market risk and idiosyncratic risk, the relationship between a firm's total risk and return is not clear. This is consistent with the conflicting literature on the risk-return rela-tionship which generally does not provide robust results, with outcomes depending on data selection, time periods, and methodology employed. A closer look at the literature indicates more consistency to the results in Appedix C of our Chapter II. Campbell, et al (2001) find a noticeable increase in the firm-level volatility relative to the market-level volatility in the U.S. market, and there has been a rapid growth of pension funds and mutual funds in the past two decades 143 as documented in Arora and Ou-Yang (2001) and Heinkel and Stoughton (1994). Considering that a larger portion of idiosyncratic risks in total risks and the increased impact of agency problem from fund management compensation can cause a shift in the risk-return relationship, it is consistent with our model to observe the shift from a positive risk-return relationship in Fama-MacBeth (1973) to the less positive and even negative relationship in recent studies such as Glosten, Jagannathan, and Runkle (1993). Later in our empirical tests, we conduct a comparison study using data from the U.S. in the sample period 1993-2000, which is the same as the time period of our Chinese data. Based on the evidence from the literature discussed above, we expect to find a less obscure relationship between firms' returns and idiosyncratic risks than some previous studies based on U.S. data before the 1990s or 1980s. In this chapter, we check whether there is a difference in the relationship between returns and idiosyncratic risk vs. market risk. This is the key that differentiates our model from the traditional asset pricing models in the U.S. Moreover, it also differentiates the de facto compensation structures in China and the U.S. The results in our tests of the risk-return relationships in China and the U.S. can serve as a natural comparison between markets with different types and degrees of agency problems from unbalanced compensation. In addition, our model and tests also indicate that different countries can have different structures of agency problems, and hence the risk and return relationship can differ. Therefore, it suggests we should be more careful about interpreting tests of 144 asset pricing theories for the U.S. stock markets with international data. For example, Bekaert and Wu (2000) reject the leverage theory for the volatility asymmetry, which is developed in the U.S., with the Japanese data. Since the financial institutions in Japan are different from the U.S., we suggest a more cautious approach of applying their methodology in U.S. data before reaching conclusion. In this study, we use panel data analysis with fixed time effects to test the cross-sectional relationship between risk and return. This method has improved efficiency over Fama-MacBeth (1973) and Ferson and Harvey (1999). This is shown both an-alytically and empirically in our study. Ferson and Harvey (1999) show that panel data analysis has improved efficiency over the Fama-MacBeth method because the estimates of coefficients are a variance weighted average rather than a simple weighted average. However, Ferson and Harvey (1999) do not consider the time effects in stock returns, which, in our opinion, must be a significant factor in stock price movements considering the substantial changes in macroeconomic variables from year to year. In fact, Fama-MacBeth (1973) do implicitly take the time effects into account, and hence their method has an edge over Ferson and Harvey (1999) in this sense. In the tests of the relationship between price ratios and proxies for different vari-ables, we use panel data analysis with fixed effects more carefully than some other papers in the literature. For example, in a panel data analysis with fixed firm effects, the coefficient of the independent variable size, as measured by market capitalization, is not really a measure for size; instead, such a coefficient is closer to a measure of 145 each firm's price changes over time. Consequently, it is natural to expect inaccurate inference about the size factor in such an analysis. This is to be discussed in detail later in this chapter. The rest of this study proceeds as follows. After introducing the testable impli-cations in Section 3.2, we describe our data in Section 3.3 and present our empirical methodology in Section 3.4. Section 3.5 provides the empirical evidence and tests of implications from Chapter I, Market Segmentation and Ownership Restrictions, and Section 3.6 gives the tests on Chapter II, Unbalanced Management Compensation and Asset Pricing. We conclude in Section 3.7. 3.2 Testable Implications 3.2.1 Implications from Chapter I In this subsection, we discuss the key implications of Chapter I, which derives an optimal supply strategy for the government and explains why the prices of A-Shares should be higher than those of B-Shares in a general equilibrium. Later in this study, we will consider the implications from inclusion of other factors documented in existing literature, such as liquidity and regime-switching risk in Chinese foreign exchange rates. In our model, the key results can be represented by equation (24) and (26) in 146 Chapter I: P a ~ P b = IT7 • \ • Mfr - (1 + r)PF) (3.1) and ( 1 - P 2 ) C . , Bf[pLf-(l + r)Pf] nb/na 2aadz/na The first equation shows that equilibrium prices of A-Shares are higher than those of B-Shares as long as firms' International Betas, PDF = SIDF^F1 , a r e positive. It should be remembered that if there was no monopolist government, then there would be no guarantee that A-Share prices would be higher than B-Share prices. In addition, equation (1) also implies that the price gaps are larger for those firms with high international betas, since the equity risk premium in the foreign market, which is equal to flp — (1 + r)PF, should be positive. Therefore, we can estimate the international betas of Chinese firms with both A- and B-Shares, and then see whether there is a positive relationship between international betas and the price gaps. Without the model, we cannot be sure whether such a positive relationship exists because of the trade off between the positive effect on prices of low international betas, and the negative price effect of the issuance of more B-Shares. In contrast, Su (1999), who claims higher price gaps for firms with higher international betas, does so without really obtaining such a clear-cut inference from his model. In our model, the relevant covariance is the covariance between firms' liquidating payoffs, not returns. For convenience of empirical tests, we can standardize equation 147 (3.1) with share prices, and then test the relationship using A- to B-Share price ratios and international betas estimated with returns. Equation (2) shows the relationship between the optimal supply of A-Shares and B-Shares in general equilibrium. As a reminder, this is a simplified scaler case for a single firm, which is in contrast to the vector case in the first equation. Such a simpli-fication is based on the assumption that there is no cross-sectional correlation between listed Chinese firms, though the testable implication inferred from this equation is expected to remain meaningful under a more general variance-covariance matrix of Chinese firms. The testable implication of the second equation can be inferred by looking at the second term on the right-hand side. This second term has the same sign as df, for jXp — (I + r)PF is positive. We begin by dividing B-Share firms into two groups: Group I, all of which have outstanding A-Shares as well, and Group II, which have no outstanding A-Shares. Equation (2) suggests that Group I should have lower international betas than those of Group II. In fact, the equation tells us that Group I's international betas should be negative or around 0. If the firms with only outstanding B-Shares were picked randomly rather than by the monopolist government, say because of capital needs for only foreign currency, there would be no implication that such a distinction would exist between the two groups. In China, there does exist a number of B-Share firms with no outstanding A-148 Shares, and many other B-Share firms with outstanding A-Shares. This offers a natural sample for us to test the implications of equation (2). 3.2.2 Implications from Chapter II Contrary to the traditional C A P M , our Agency C A P M predicts that the relationship between risk and return depends on the balance of fund managers' compensation structure: see figure 3.1. When c 2, the measure of punishment for negative perfor-mance, is small enough relative to C\, the risk and return relationship can be around 0 or even inversely correlated. This is in contrast with the always positive risk-return relationship as predicted by the traditional C A P M , which is equivalent to a special case of our Agency C A P M where c 2 = c\. We define a strong form of bubbles as the situation when prices are higher than the expected payoffs discounted at the riskfree rate. Further, we define a weak form of bubbles as the situation when the prices are higher than the expected payoffs discounted at risk-adjusted rates based on traditional C A P M . For the strong form, we check whether the positive relationship between risk and return can be rejected. For the weak form, we could check whether the risk-premium is significantly lower than in benchmark stock markets, such as the N Y S E or LSE, assuming that the equity premium is the same in countries without riskfree-rate adjusted performance fees. In this chapter, only the strong form is tested, for the result turns out to be 149 significant and makes the test of the weak form unnecessary. We also conduct an event study which can capture the existence of bubbles driven by Unbalanced Management Compensation (UMC). 3.3 Data Description Our data come from a number of sources: the Shanghai Stock Exchange, the Shen-zhen Stock Exchange, Shenyin Wanguo Securities Company, Shanghai Jiao Tong University, Wan De Consulting, and Datastream. In addition, we also use CRSP and C O M P U S T A T databases to retrieve U.S. data, such as the SP500 returns used in the comparison study on risk-return relationships. In addition, Datastream is used in retrieving part of the Chinese transaction data for comparison with our data from other resources. We also get the global market index, namely Morgan Stanley All Country Free World Index, from Datastream. Our data on Chinese stock markets include transaction data of all firms listed in the Shanghai and Shenzhen Stock Exchanges, the distribution data, and the account-ing data. The transaction data are daily, while the accounting data are annual. In China, firms do not give quarterly accounting reports, and the distribution data are annual as well. The items in our Chinese transaction database include the following: daily open, high, low, close, ask, bid and volume. The items in our Chinese distribution database 150 include the following items: cash dividends, stock dividends, stock splits, rights is-sues (with a few seasoned equity offerings as well), transferred shares, announcement dates and ex-rights dates. The items of our Chinese accounting databases include the following: revenue, earnings (before and after tax), adjusted earnings after non-operational gains or losses, total assets, equity, debt (short-term and long-term), sales, cost of sales and administration, fixed assets, inventory, turnover ratios of as-sets, and accounts receivable. Together, this provides an extremely comprehensive set of information for conducting research. Our sample period for Chinese data is from Jan 1, 1993 to Dec 31, 2000. We exclude the period before 1993 because of two reasons: the daily price limits before May 1992 and the small sample size before 1992. Specifically, before May 1992, A-Share prices could rise by a maximum of 10% each day. Consequently, there were dramatically reduced transactions in the Chinese stock markets, with either no transaction price or a maximum price under the limits for a typical SHSE firm in a typical day before May 1992. In such a situation, it is obvious that market prices recorded by the SHSE cannot reflect the true market value of the stocks, and it is meaningless to take recorded prices in this period as market clearing prices for tests of theories in Chapter II. In addition, the sample size is also very small for the period before 1992: there were only 8 A-Share firms listed in Shanghai Stock Exchange before 1992, and an even smaller number in B-Share market. In fact, the listing date of the first B-Share is 1992. 151 By contrast, stock prices from 1993 to 2000 face few binding hurdles in daily movements, and changes in stock indices also resemble much more of a random walk than a straightforward upward trend: see Figures 3.2, 3.3, and 3.4. The situation is similar in the Shenzhen Stock Exchange. However, since early 1993, both Chinese A-and B-Share markets have been expanding very quickly. By the end of 2000, there were 559 A-Series and 55 B-Series shares listed in the Shanghai Stock Exchange, and another 500 A-Series and 58 B-Series shares listed in the Shenzhen Stock Exchange. Our guidelines on the usage of Chinese databases are as follows. First, use the data from Datastream whenever feasible. In other words, we use Datastream data except where these are proven to be inaccurate. The objective of this guideline is to keep our empirical tests comparable with other people's work as much as possible. Second, when the data from different data sources conflict with each other, we use the latest ones. Such situations do arise in a few distribution data items, which is not unexpected considering the fact that several listed firms do report inaccurate numbers first and then make corrections later. Following a logic similar to the one adopted by CRSP in calculating returns for U.S. stocks, we use the transaction and distribution data collected from China to construct the Chinese database of returns in our study. To check the robustness of our tests, we repeat our tests using filtered data. For each firm-year, we first calculate the deviation of daily returns relative to market index returns, and then standardize such index-adjusted excess returns with the standard deviation in each firm-year. These are called Standardized Abnormal Returns (SARs). 152 We exclude the maximum and minimum observations in each series of SARs, and then repeat the tests with the rest of the observations. We choose this procedure to check the robustness of our tests out of two considerations. First, the existing literature has shown that empirical results are often sensitive to the exclusion of outliers, such as a study that points out that most of the explanatory power of Fama-French three factors goes away when the 1% outliers are excluded from the tests. Second, though we have made our best efforts in obtaining the most accurate and complete data for our study, there is always a concern that there may exist incidental missing information or data errors. For example, if a stock split or rights issue is missing in the distribution data file, the return of the stock on the ex-distribution date would be seriously under-estimated. In such a case, taking out the observation with the minimum SAR in the firm-year should help us to filter out outliers. Such a method is even more effective in China considering that a typical Chinese firm gives out only annual distributions. After obtaining the filtered data by excluding the annual maximum and minimum SARs, we repeat the major tests in this study to check the robustness of the results. A serious issue in the transaction data of B-Shares is the thin trading problem. It is well-known that B-Shares suffer a lack of liquidity, especially so in 1990s. The thin trading in the B-Share market results in a failure to correctly record the true prices of listed firms at each point of time, which can be illustrated by examining the first-order autocorrelations of different stock indices. As in Jorion and Schwartz (1986) who use the auto-correlations of Canadian stock indices to demonstrate the 153 thin trading problem in the Canadian Stock Market, we calculate the first-order auto-correlations in Chinese B-Share markets from 1993 to 2000. The results are presented in empirical tests later in this chapter, and they clearly indicate strong auto-correlations in B-Share indices. We also calculated the auto-correlations with the two subperiods 1993-1996 and 1997-2000, and the results are very similar. As suggested by the literature such as Scholes and Williams (1977), Dimson (1979), Fowler and Rorke (1983), and Heinkel and Kraus (1988), nonsynchronous trading in B-Share market can cause a serious errors-in-variable problem in empirical tests, especially the distortion in the estimation of market betas using the market model and OLS regressions. In this chapter, we use a method similar to Dimson (1979) to adjust our procedure for the thin trading problem in Chinese B-Share mar-kets. The details are discussed immediately below in Section 3.4.1. 3.4 Empirical Methodology 3.4.1 Thin Trading Using a procedure similar to the one proposed by Dimson (1979), we estimate a firm's international beta with the following regression: n,t = c*i + Bi,orm,t + Qi-\rm,t-\ + A . i^W+i + £i,t (3-3) 154 where ri<t is firm i's excess return relative to riskfree rate at time t, r m t t is the market excess return at the same time period, and r m } t - \ and r m t + i are the market excess returns at time t — 1 and t + 1. The estimator of firm i's international beta, Pi, is the sum of OLS estimators of Bifi, Pi,t-i, and P^t+i- Further, we also check the robustness of our results with the following adjusted beta PiMj = (A,t-i + Pi,t + A ,m) / (1 + 2p) (3.4) where p is the first-order auto-correlation of market returns. 3.4.2 Panel Data Analysis The traditional Fama-MacBeth (1973) method uses two stage regression. First, they estimate sample firms' betas and other factors, such as residual risk, using a fixed length of data, say 5 years. Second, they use these estimated factors to explain the returns of a subsequent "window" period. To do so, they run cross-sectional regressions period by period. The coefficients of each factor in the cross-sectional regressions are averaged over time, and then a t-statistic is used to test whether each factor coefficient is significantly different from zero. The Fama-MacBeth (1973) method is a useful way to determine the sign of co-efficients for factors that have to be estimated with the rolling data. On the other hand, intuitively one can also see some drawbacks of this method. First, by taking an average of the factor coefficients, the cross-sectional regression in each time period is 155 given equal weight in the t-statistics. However, the accuracy of the estimated factor coefficients are likely to differ over time. For example, in some time periods, there may be more observations than other periods, making the coefficient estimates more accurate. Also, the cross-sectional differences across different firms are bigger in cer-tain periods than other periods, and so estimated coefficients tend to be more robust against noises in certain periods. The traditional Fama-MacBeth (1973) method fails to account for these differences over time. Ferson and Harvey (1999) propose a pooled regression rather than the period-by-period cross-sectional regression in Fama-MacBeth (1973). Such a pooled regression addresses the differences in the accuracy of coefficient estimates over different time periods, and hence is more efficient than Fama-MacBeth's method in terms of het-eroskedasticity. However, to argue that their pooling method has improved efficiency over Fama-MacBeth (1973), Ferson and Harvey (1999) make an implicit assumption of no time effects, upon which we do not agree. We argue that pooled returns should have significant time effects, which can seriously change the statistics in regressions. One argument in support of the existence of time effects comes from the fact that macroeconomic variables do change over time, which affects the aggregate level of returns in the stock markets in each time period. Fama and MacBeth (1973) have implicitly taken into consideration time effects, and hence have their own advantage over Ferson and Harvey (1999) under a more realistic assumption that acknowledges the existence of time effects in stock returns. 156 To account for both the heteroskedasticity of coefficient estimates and the time effects of stock returns, we propose panel analysis with fixed time effects rather than the ones employed by Fama-MacBeth (1973) and Ferson and Harvey (1999). In the following, we show that our empirical procedure has improved efficiency over both Fama-MacBeth (1973) and Ferson and Harvey (1999). The use of panel data analysis with fixed time effects is not new1. Below we show why panel data analysis with fixed time effects has advantage over both the cross-section method by Fama-MacBeth (1973) and the simple pooled method by Ferson and Harvey (1999). We write the panel data regression with fixed time effects in the following matrix form: Y = Da + XP + e (3.5) where V = [3/i,2/2>-,yr]') a = [cti,a2, ...,ctT}', X = [Xj, 3^ 2) •••) XT\ I £ = £2, £i\ » and D = [ei, e 2 , e r ] , where et = [0[,Oj.j, l't, 0 j + 1 , 0 ^ ] ' . In addition, the variance-covariance matrix of the error term, e, is fl. JFor full references, see Hsiao (1986) and Greene (1999) who provide good reviews on literature and development in this area. 157 The panel data regression equation is equivalent to the following after a Md transformation MdY = MdXP + Mde (3.6) where Md = I - D(D'D)-lD' The intuition for the transformation is as follows. It is easy to see that Mi 0 • • • 0 0 M 2 I Md = • • 0 0 0 Mr with matrix Mt on the diagonal equal to Mt = It — j^-Ji'- Meanwhile, for a vector Zt, MtZt = Zt — zti, where zt is the mean of Zt. Therefore, the panel data regression with fixed time effects is in fact equivalent to a regression with the dependent and independent variables being first transformed to time-period mean-deviations. Such a transformation is very useful in comparing our method with the one used by Fama-MacBeth (1973). In Fama-MacBeth (1973), the following regression is run for each time period t Yt = at + Xt3 + eu (3.7) and then the time-series average of the 8 estimators is used in a t-test to determine whether 8 is different from 0. With the Mt transformation in (3.6), we can also get the following from (3.7) for each time period t MtYt = MtXt0 + MtEt (3.8) 158 It is easy to see that the estimator of 3 at time t from (3.8), bt, is in fact the same as the estimator from (3.7). From the transformed (3.6), we get the GLS estimator of 3 b= {X'MdQ-lMdX]-l[X'M'dn'lMdY} (3.9) Assuming that there is no time-series correlation in the residuals e, we can rewrite (3.9) as b = [E X[M'tn7lMtXt}-1 • [E X'tM[Vt7lMtYt] = E [E X[M'tQ,7lMtXt\-1 • [X'tM'tnTlMtXt] • bt (3.10) where bt = [XlMfa1MtXt)-\X[M'tQ.7xMtYt] (3.11) is the GLS estimate of 3t in (3.8). Since Est VAR{bt} = [X'tM't^MtXt]-1, (3.12) it is clear that the GLS estimator b is a weighted average of bt, t = 1 , T , and the weight for each period t is a multiple of the inverse variance-covariance matrix of the estimated bt. Therefore, following logic similar to Ferson and Harvey (1999), the GLS estimator b in panel data regression with fixed time effects has improved efficiency over the simple arithmetic average of bt as in Fama-Macbeth (1973) stemming from the use of the variance-covariance weighted average. 159 Now we move on to Ferson and Harvey (1999) who use a simple pooled regression. They assume Y = a0 + X6 + e (3.13) where e = [e'1,e'2,...,e'T},,E(ee') = n and Qf 0 is a constant. The GLS estimator b from specification (3.13) is b = [X'M'^-'M^X^lX'M'^n^M^Y] (3.14) where Mone = 1- ^ l ' l ) " 1 ! ' , 1 = [ l x , 1 2 , l m l , l m i , l m T ] ' . By implicitly assuming that there are no fixed time effects, Ferson and Harvey (1999) show that their pooled regression has improved efficiency over Fama-MacBeth (1973). However, with time effects being considered, the estimator in (3.14) is obvi-ously not as accurate or efficient as the estimator in (3.9) and (3.10) because of the difference between Md and Mone. The analysis above is mainly for the test of the risk-return relationship related to Chapter II. In Chapter I, we also use panel data regression with fixed firm effects. With either fixed time effects or with fixed firm effects, panel data regression requires cautious explanation of its economic meaning. In the case of fixed time effects, we have MtZt = Zt — zti for any vector Zu where zt is the mean of Zt. As discussed earlier 160 in this subsection, it is equivalent to a regression with the dependent and independent variables being first transformed to mean-deviations in each time-period. This needs special attention when one or more of the independent variables are time-specific but common among firms. For example, if one of the independent variable is the market return, which takes a single value at each time period, the transformed market return will be 0 for all observations. Therefore, a panel data regression with fixed time effects is meaningless when market return is one of the variables because of the multi-collinearity problem. For panel data analysis with fixed individual effects, the situation is similar. The regression is equivalent to one with all variables being transformed to mean-deviations of each firm/individual. If there is some variable that is firm-specific but common over time, there is also a problem from multi-collinearity. Such an issue could become more subtle when the independent firm-specific variable does vary slightly over time. For example, Domowitz, Glen, and Madhavan'(1997) use each firm's market capitalization to proxy for the size factor in their panel regression with fixed individual effects. Since a firm is not likely to issue new equity and/or incur large operating gains or losses every month, the market capitalization in the regression by Domowitz, Glen, and Madhavan (1997) should proxy more for each firm's price changes than differences of size across firms. Such subtle differences in the economic meanings of variables deserve special attention when making a choice between simple pooled panel regression and panel regression with fixed effects. 161 In the following section, we begin with the panel data regression with fixed time effects to determine the relationship between firms' betas and price ratios. Then, we use the panel regression with fixed firm effects to determine the relationship between price ratios and other factors, including regime-switching risk in the foreign exchange rate, and liquidity differences between A- and B-Shares. Lagged price ratios are used as an independent variable in the regression to keep the error term stationary. In the test of the risk-return relationship, we use panel data regression with fixed time effects in addition to the traditional Fama-MacBeth tests. 3.5 Tests of Chapter I 3.5.1 International Betas and Price Ratios Our model in Chapter I implies that the higher the international betas, the higher the A- to B-Share price ratios. To test this relationship with the Asian financial crisis and U.S. stock market boom in late 1990s in mind, we divide the full sample period into two periods: 1993-1996 and 1997-2000. The betas are estimated using the data in the first sample period, and then we use the data from second period to see whether the estimated betas can predict the differences in Price Ratios or not. On one hand, this division of the two periods is a natural choice based on our 8-years sample; on the other hand, the discussion in the subsection above shows that the betas estimated 162 from sub-period 2 may not be reliable. We use two methods to check the relationship between the betas and the price ratios so as to check the robustness of the tests. The price ratios in the following tests are the mean of all daily observations so as to reduce noise in the estimates of price ratios. First, we use the standard Fama-Macbeth test. We regress the price ratios on the estimates of betas in each year, and then see whether the coefficients of Beta are significantly positive. Table 3.4 shows significant t-statistic with a strong positive relationship between betas and price ratios. We also pooled all the data together and use the panel data regression with fixed time effects to double check the relationship. These results, shown in Table 3.5, also reveals a significant positive relationship. 3.5.2 Test of Other Factors In addition to the tests above specifically designed for testable implications of Model I, we also look at other secondary factors which may play a role in the differential pricing between A- and B-Shares. In the following, we first discuss the liquidity and regime-switching risk in China, and then present the results of our test. 163 Liquidity The lower the liquidity, the higher the required rate of return, or say the lower the price. On the other hand, the difference between A- and B-Share's market liquidity also changes the difference between domestic and foreign investors' elasticities of demand, and hence the difference between A- and B-Share supplies. This has a positive effect on the shares with lower liquidity because of a lesser amount of supply. In equilibrium, we show in Chapter I, , that the A- vs. B-Share price differences are as follows: P a " P b = W V 7 f D + ^ ^ r f ^ D F ^ i f l F - (1 + r)PF] (3.15) where TA-B is a md by md diagonal matrix, with the ith item on the diagonal being 7j b — 7 " . Here md is the number of domestic firms with both types of shares, and 7 " and 7 t 6 refers to the bid-ask spread of firm i's A-Shares and B-Shares respectively. This equation shows that smaller the bid-ask spread of B-Shares than A-Shares, the higher the price difference. This can be empirically tested with price-standardized bid-ask spreads and price ratios. In addition, the liquidity can be measured from two aspects. One is the gap between the ask and bid, as we have discussed before; the other is the dollar amount of trading volume, which measures the depth of liquidity. Bid-ask spread alone cannot tell how large the liquidity cost is for an investor who sells a not-so-small amount of shares. Therefore, we construct two measures of liquidity: one is the average gap between the daily ask and bid prices at market close time divided by closing prices, and the other is the sum of daily trading volume denominated in dollars, not the number of shares. Further, we calculate the difference between the 164 average bid-ask spread of A- and B-Shares, and the ratio of B- to A-Share trading volume2. We test whether these two measures play a significant role in determining the price ratios. In fact, in China there are no market makers. Therefore, the liquidity may be even more important than in North America. Regime Switching/Governmental Exchange Rate Risk In China, it is the government, not the market, who controls the exchange rate between Chinese Yen (RMB) and other currencies, such as USD and Euro Dollar. In general, the official exchange rate between Chinese Yen and USD may not be consistent with the exchange rate that would be determined by a free market. In such a situation, a foreign investor faces two types of exchange rate risk. First, as any other currency, there is an intrinsic exchange rate risk in R M B that comes from the uncertainty of the trade and economy. Second, there is a risk that the government may not be able to maintain the exchange rate target in the future, or the government may switch to a freely convertible currency after an unknown period. The difference between official and free-market exchange rates can undermine 2 As a measure for liquidity, trading amount measured by dollars should be more relevant than turnover ratio, for an investor normally cares most about the selling price of his own holdings, not the selling price of all outstanding shares of a firm that he invests. Therefore, we are not using the ratios of B- to A-Share turnover ratios here, though they are probably highly correlated with the ratios of trading amount used here. 165 the accuracy of A- to B-Share price ratios calculated with official exchange rates. For example, if there would be a 10% appreciation shock of USD vs. Chinese Yen based on market forces, the market value of a Chinese firm denominated in USD should decrease proportionally although the value denominated in Chinese Yen stays the same. If the official exchange rate adjusts right away to fully reflect the 10% appreciation of USD, as what the exchange rate would be in a free market, we would see no change of price ratios. However, if the official exchange rate does not adjust at all, the price ratios will be higher. To better describe the two types of risk, we denote the current official exchange rate of R M B to USD as 90, and the future exchange rate as 9\. In addition, we denote the intrinsic current exchange rate as 8'0, which is how much the exchange rate should be if the government allow R M B to be freely convertible and chooses not to interfere in the money market. As for the intrinsic future exchange rate, we denote it as 9[. Under the assumption of interest rate parity, the expectation of 8[ should be equal to 9'0. If the government was setting the exchange rate as it should be in a free market, we would have that 90 — 9'0 = 0 = E(6\ — 8[). However, we expect to see that \9Q — 9'0\ > 0 in reality. The regime-switching risk in fact refers to the risk that such a difference tend to diminish or disappear in the future, and so E(9X should be somewhere between 9Q and 9'0, or equal to 9'0. To test the null hypothesis that the government does not matter in the dynamics of real exchange rate, we can test how 166 the price ratios react to shocks of A0 = 90 — 9'0. We include the regime switching risk in our regression out of two considerations. First, it is naturally a interesting phenomenon common to many countries who do not have freely convertible currencies, and may also be a significant pricing factor in determining the price differences between A- and B-Shares. Second, it can also serve as a control variable for the possible miscalculations of real price ratios owing to the use of official exchange rates. The difficulty in testing the regime-switching risk in exchange rates lies in the unobservability of intrinsic exchange rates between Chinese Yen and U S D / H K D . The black market of currency exchange is illegal in China, and it comes as no surprise that there are no recorded exchange rates available from the black market. Further, the savings rate in China is also controlled by the government, not the market, and so the difference between USD and R M B savings rates cannot reflect the changes in intrinsic exchange rates either. Therefore, we have to look for a proper proxy for the regime-switching risk. There is a tendency that Asian currencies move together relative to USD, possibly owing to a stronger correlation among Asian economies. Therefore, the change of exchange rates between Asian currencies and USD should be a good proxy for the change of the intrinsic exchange rate between R M B and USD. What we do in the following is to first pick up a portfolio of Asian currencies, including these of Thailand, Korea, 167 Indonesia, Singapore, Taiwan, Philippine, India, and Japan, and then calculate the equal-weighted changes of this portfolio relative to USD. We use the gap between the change in official exchange rate of R M B vs. USD and the change in the market exchange rates of this Asian portfolio currency vs. USD to measure the magnitude of regime-switching risk in Chinese foreign exchange rates. To check the robustness of the measure, we also use the portfolio without Japanese Yen and see how the results respond to this. We can also try to further measure the risk of intrinsic exchange rate in China. However, we choose not to do so here. First, such a risk is common among all countries, and hence not so necessary to be investigated in this study on Chinese stock markets. Second, the variance of foreign exchange rate is relatively stable from month to month, and so unlike the regime-switching risk, it is not expected to cause much variation in price ratios. Tests To fully utilize the data sample we have and increase the power of the test, we choose to use panel analysis with fixed firm effects in our analysis here, and we have separately tested the effect of international betas on price ratios earlier in this chapter. Table 3.6 shows that the statistics of proxies for both liquidity and regime-switching risk are strongly significant and consistent with our inferences. 168 3.6 Empirical Evidence and Tests on Chapter II 3.6.1 Empirical Evidence E / P ( P / E ) Rat ios P / E ratios are widely used in the literature, both as a measure of price level and a measure of growth opportunity. However, considering the large number of Chinese firms with negative earnings, we choose to use E / P ratios, the inverse of P / E ratios. Our choice lies in the following. First, P / E ratios for firms with negative earnings do not have a consistent economic meaning so as to be pooled together with P / E ratios for firms with positive earnings, while E / P ratios are less vulnerable in this aspect and have consistent meanings for both positive and negative earnings. In fact, the statistics of pooled P / E ratios across firms and/or over time, such as the mean, do not have such a good economic interpretation as corresponding statistics of E / P ratios either. For example, if there is one single firm with a positive earning that is close to 0, which is not unusual since a significant portion of firms can even have negative earnings, then the average P / E ratios of the entire sample can be abnormally high simply because of this normal observation. Further, we wish to present the aggregate accounting performance of firms listed in Chinese stock markets, and it is important for us to include all sample firms rather than just only firms with positive earnings. From Table 3.7, we can see that E / P ratios in the Shanghai Stock Exchange are extremely low. Contrary to the small firms listed in N A S D A Q which may give 169 investors plenty of room for growth imagination, the firms listed in the Shanghai Stock Exchange (SHSE) are mainly large cap stocks that have been in operation for many years before going public. Moreover, unlike the high tech industry in N A S D A Q , most Chinese firms listed in the SHSE are grown and mature companies rather than the high tech ones that may give lots of room for growth imagination. Table 3.8 compares the E / P ratios with the interest rates on 1-year fixed term bank deposits. In China, treasury bills were not a feasible investment choice for the public until recently, and the official interest rates are the effective riskfree rates to Chinese residents. The rates are matched year to year, and the 1-year interest rate is a compounded rate of different subperiods if there are changes in the official interest rates over a certain year. From table 3.8, it is clear that the interest rate is much higher than the E / P ratio most of the time. This may be explained by two alternative hypotheses: either the high growth rate of Chinese firms or the existence of strong bubbles driven by the U M C 3 . If we accept the first hypothesis, then the risk return relationship should still be positive, as predicted by the traditional C A P M or its 3Both the mean and median growth rates of Chinese firms' earnings are believed to be too low to justify the low E / P ratios. We may present such evidence in a later revision. In fact, in the recent study by two official state-owned institutions, State Information Centre and Shanghai Securities News (2002), it is stated that the average earnings to book value ratio in Chinese stock markets for the year of 1998 to 2001 are 7.51, 8.05, 7.58, and 5.56 respectively. These numbers do not indicate any positive sign of high growth at all. Anyhow, right now we just simply give two alternative explanations, and leave the choice to the empirical tests later in this chapter. 170 variants. On the contrary, if strong bubbles do exist because of the U M C in China, we can see negative risk return relationship. In the rest of this chapter, we mainly test the risk return relationship in China, in addition to the event study on the existence and impact of the U M C in China and risk return tests in the U.S. R i s k - R e t u r n Correlat ions Before we carry out the formal analysis of the risk-return relationship in China, it is interesting just to see the correlations between risk and return in Chinese stock markets. First, we estimate the standard deviation of a firm's, say firm i's, returns in the estimation window and take it as the measure for firm i's total risk. Further, we use the following market model to decompose firm i's risk into market risk and firm-specific, or say idiosyncratic, risk. ru = at + 3rmt + eit (3.16) The coefficient Beta, Q, is the measure for market risk. The standard deviation of the residual term e is taken as the measure for firm i's idiosyncratic risk. In traditional C A P M , only a firm's market risk is priced in the stock market, and the residual risk should not matter. Consequently, the total risk is not a good measure for priced risk either. However, in the Agency C A P M developed in the chapter Unbalanced Management Compensation and Asset Pricing, it is shown that a firm's idiosyncractic risk does matter. Meanwhile, a firm's market risk matters as well, and the best measure for priced risk should be the measure of total risk. Moreover, in traditional C A P M , a firm's market risk should be positively correlated 171 with the expected rate of return. That is, the higher the risk, the higher the expected rate of return. However, in our Agency C A P M , the risk-return relationship can be negative. Before we carry out the formal tests of risk-return relationships later in this chapter, we first have a look at the correlations between the different risk measures and different return measures. Table 3.9 presents the product-moment correlations between the two measures of returns, the log excess returns adjusted by riskfree rates and abnormal returns adjusted by market returns, and various measures of risk, including total variance, beta, and residual variance. We also put in the square of 0, which is used in the literature as one of many ways to capture the non-linear relationship between risk and returns. We use a three year rolling window period to estimate the measures of risk and return, and then the returns in the subsequent period are matched with risk measures estimated previous window period for calculation of correlation coefficients. In addition to the widely used Person product-moment correlations, we also calculate nonparametric correlations including the Spearman rank correlations and Kendall's tau-b so as to capture possible non-linear relationship between risk and return. A l l results strongly indicate that there is a negative risk-return relationship in both the Shanghai Stock Exchange and the Shenzhen Stock Exchange. See table 3.10 and table 3.11 The values of the correlation coefficients are significant both statistically and eco-172 nomically. Most of the coefficients are statistically significant at a level less than 0.0001, and such a relationship is persistent as we investigate the data from different angles with various methods. Specifically, the results are robust and consistent re-gardless of the choice of sample firms (SHSE, SZSE, or both Chinese stock exchanges), the choice of cross-section unit (individual firms or portfolios sorted by rank of risk measures), the choice of benchmark index (either local exchange indices or the entire Chinese stock market index which can be either equal weighted or value weighted average of local exchange indices), the time interval of data (weekly observations or monthly observations), the updating period of beta and other risk measures (updated annually, quarterly, monthly, or even weekly), and the methods of calculating correla-tions (standard product-moment/Person correlation, rank/Spearman correlation, and other non-parametric correlations such as Kendall's tau-b). Later in Fama-MacBeth cross-sectional regression we will also show that the negative relationship is econom-ically significant. Kendall's tau-b is a nonparametric measure of association based on the number of concordances and discordances in paired observations. Concordance occurs when paired observations vary together, and discordance occurs when paired observations vary differently. The formula for Kendall's tau-b is: = Ei<jSign(xi - Xj)Sign(yj - y^) V ( T o - T i ) ( T 0 - T 2 ) where T0 = n(n - l ) /2 , Ti = Et^U - l ) /2 , and T 2 = Zfa(fa - l ) /2 . Here tt is the number of tied x values in the ith group of tied x values, fa is the number of tied y 173 values in the zth group of tied y values, / is the number of observations, and Sign(z) is defined as Sign(z) = 1 if z > 0, Sign(z) = 0 if z = 0, and Sign(z) = — 1 if z < 0. 3.6.2 An Event Study: Crack-down on UMC Managers In China, U M C takes many forms. Some are legal, such as the management compen-sation contracts of investment companies, pension funds, and consulting companies. Meanwhile, many others are illegal, such as SOE managers and government officials who invest in the stock markets with state-owned capital that is allocated for pro-ductions and operations. In addition, banks are not allowed in the stock markets either, though many of them do invest. The illegal investment in the stock markets is widespread, and hence stands as one important factor for the existence of U M C in China. The May 1997 announcement by Chinese government provides some specific information on this situation, and an excerpt of the announcement is available in Appendix B . l . In May 1997, the government announced a crack-down on illegal stock trading by managers and officials in the state-owned sectors. This offers a natural opportunity for us to conduct an event study and see whether the U M C is a significant factor priced in the stock markets. Some people may argue that the government faces a serious problem in monitoring, and so the crack-down on illegal trading may be far from so enforcing as what the government announces. We argue that, while acknowledging 174 the limit of the government's enforcing ability, such a crack-down should at least have some marginal effect on the illegal trading, and hence offers a good case to empirically investigate the existence of one type of U M C in Chinese stock markets. The Result: see table 3.12. The returns in the event window are significantly negative. This provides empirical support for the existence of U M C managers in Chi-nese Stock Markets, and such U M C managers do have an important role in Chinese asset pricing. Furthermore, the pre-event window period also shows significant nega-tive returns, which indicates leakage of the information on the crackdown before the government makes the public announcement on May 22, 1997. Some people may be concerned about the changing of parameters in the market model after the event window period. To check the robustness of our tests, we also use the after-event window period as the estimation window. The results are similar, strongly supporting the claim that there are statistically and economically significant negative market reactions up and before the announcement of the crack down on May 22, 1997. To address the issue of heteroskedacity among firms, we also use the standardized daily returns of each firm to test the significance of market reactions in the three window periods, and the t-statistics are similar. The results are not presented here because the economic meanings of such standardized mean and media are not clear. 175 3.6.3 Tests of the Risk and Return Relationship in China From Chapter II, we see that negative risk and return relationship is the sufficient condition for a strong form of bubble to exist. Such a negative relationship also indicates significant impact of U M C (unbalanced management compensation) on asset prices. In the following, we test the risk-return relationship in China using both the traditional Fama-MacBeth method and a new method with improved efficiency. Further, we also conduct the test in U.S., where the management compensation is unbalanced in a different manner. Such a different compensation structure in the U.S. offers a natural data sample for our comparison study. Fama-Macbeth Test of Risk and Return Relationship Use the standard Fama-Macbeth (1973) cross-sectional regressions to test the relationship between risk and returns. See Table 3.13. Improved Method: Panel Data Analysis with Fixed Time Effects As dis-cussed earlier in the test of Chapter I, panel data analysis with fixed time effects has improved efficiency over both Fama-MacBeth (1973) and Ferson and Harvey (1999). We conduct such a panel regression with fixed time effects, and the results are shown in Table3.16, 3.17, and 3.18. 176 From Table 3.16, first we see that there are strong time effects based on the F-test statistics. This supports our choice of panel regression with fixed time effects against Ferson and Harvey (1999). Second, the significance level of each risk measure coefficient is much stronger in this table than the counterpart in 3.13, which indicates the improved efficiency of our empirical procedure than Fama-MacBeth (1973). We see in Table 3.16 that each of the three risk measures has a significant negative coefficient when used separately in the regression. This indicates that the higher the risk, the lower the return. Moreover, the measure of total risk dominates two other risk measures: the residual risk; and the market risk (3). This is exactly as what is predicted in our model, where we state that the U M C managers do not diversify and only care about the total risk rather than the systematic risk in their valuation of the " i securities in the stock markets, i, Noting that the total risk^of each firm is in fact the sum of its market risk and idiosyncratic risk, a problermof muti-linearity probably shows up when all three risk measures are used together'in the same regression. However, we still see that TotRiskStd, the measure for total risk, remains strongly significant and still dominates two other risk measures in the all-in-one regression in Table 3.16. Meanwhile, it is not surprising to see that the significance level of the measure for total risk is not so high in the last regression of Table 3.16 as in other regressions of the same table. Table 3.17 and 3.18 present the results for the Shanghai Stock Exchange and the 177 Shenzhen Stock Exchange respectively. The results are similar, and the sign of the coefficients are still significant or consistent with Table 3.16, though the significance levels are not so strong. The reason probably lies in the loss of test power with a smaller sample size. In Table 3.16, we also see that the loading for the measure of market risk, B, is over 1% for the entire sample of listed Chinese firms. This indicates that an aggregate Chinese investor is willing to sacrifice more than 1% of return in a typical month to hold a stock with exactly the same level of risk as the market index. Some people may be concerned that the market return may be negative in our sample period, and hence contribute to the negative risk return relationship. This can be addressed by the following two arguments. First, the market return in the sample period is strongly positive in both the Shanghai Stock Exchange and the Shenzhen Stock Exchange. In fact, the market indices have risen around 100% in our sample period, and even more considering the cutting off the first three years as the initial estimation window period. Therefore, such an argument of the conditional market movement can only strengthen our results. Second, we have used fixed time effects in our model, which can absolve the impact of the market-level return variations over time. To check the robustness of our tests, we have also used different market indices in the tests, including the local indices in each stock exchanges and the equal-weighted 178 and value-weighted indices of the local market indices. The results are persistent. 3.6.4 Tests of the Risk-Return Relationship in the U.S.: A Comparison Since the fund management compensation problem in China is different from that in the U.S., U.S. data sample is a natural source for a comparison study. Using the same sample period as that of Chinese data set, which is 1993-2000, we replicated all the tests on risk-return relationships using U.S. data sample. We choose SP 500 firms as our U.S. data sample in the comparison study. In addition to the obvious fact that SP 500 firms are the most representative firms in the U.S. and have been chosen as data sample in various empirical tests, there are additional reasons why this sample is chosen in our study. First, the universe of firms available in CRSP includes a large number of small firms with thin trading, and the estimates from firms with thin trading may cause special problems in the statistical inferences, such as Heinkel and Kraus (1988) who show that thin trading can markedly affect the significance level of empirical tests. In the meantime, no Chinese A-Shares suffer from thin trading problem in our sample period. Even not in a specific situation as in our comparison study, some people choose to drop firms with thin trading in their data sample. With the consideration of thin trading's impact on test results, SP 500 is a better candidate for our comparison 179 study than the total universe of CRSP firms. Second, Chinese firms listed in A-Share markets are uniformly "large" firms. Based on P P P or G N P per capita, the smallest firms listed in China are comparable with, or even larger than, the smallest firms in SP 500. Therefore, using SP 500 firms can also help to control for the size effect. Third, there is a question about which index is the best proxy for index-adjusted performance calculated in the industry. SP 500, in our opinion, is a very good choice because of its historical notability in the industry and its reputation in terms of representation and scientific construction. SP 500 also has the advantage of acces-sibility to the people in the industry, and other academic indices such as CRSP N Y S E / N A S D A Q / A M E X Value-Weighted Indices may not be so likely to be widely adopted by the mutual funds in setting up the compensation contracts for their man-agers. Moreover, this may also interacts with the fact that a variety of different mutual funds exist in the real world, many of which aim at only a subset of stocks, such as big cap vs. small cap. In such a situation, their benchmark in compensation should be an index close to the subgroup of stocks that they can invest, and hence the decomposition of idiosyncratic risk and systematic risk should be based on cor-responding sub-index rather than the market index of the entire U.S. equity market. By looking at the SP 500 firms only, we can alleviate the need for an extra process to determine different benchmark indices for different firms. 180 There are frequent changes in the list of SP500 firms from year to year, mainly resulting from the change of firm sizes. Therefore, the active members of SP500 may be subject to a size survivorship bias which means firms that are successful and growing tend to stay or join SP500. To at least partially adjust for this survivorship bias, we include all firms that ever show up in SP500 during the 1993-2000 period in our entire sample period. This adjustment also makes our sample firms more comparable with the situation in China, where few firms are ever delisted though only big and successful state-owned enterprises (SOEs) tend to be listed in the stock markets. The statistics in our study show that the beta-return relationship is W E A K L Y positive in the U.S.. This is not surprising considering the weak empirical support for C A P M in the past and the special situation (the conceived bubbles in the stock market) in the U.S. in the past several years. Further, our tests show that the relationship between residual risk and return is more than weakly negative. This is not consistent with traditional C A P M , which states that residual risk does not matter, but consistent with our agency model where the fund managers' compensation has a huge impact on asset pricing in stock markets. For details, please see the appendix of one chapter in this thesis titled Unbalanced Management Compensation and Asset Pricing. 181 Fama-Macbeth Test of Risk and Return Relationship We first use the tra-ditional Fama-MacBeth (1973) method and find the consistent evidence supporting negative residual risk-return relationship. See table 3.19. The statistics are not signif-icant, though. The lack of power in Fama-MacBeth method, in addition to the short time period in our sample, may give an explanation to the low level of significance. Improved Method: Panel Data Analysis with Fixed T ime Effects See ta-ble 3.20. Note: In analysis, we used both individual and portfolio data to test the models so as to get stronger robustness in our results. On one hand, our tests based on portfolios makes the results comparable with the tests in the literature where port-folios are the popular choice; on the other hand, our tests based on individual firms addresses the problems arisen from portfolio formation, such as the over-rejection of models discussed in Berk(2000). The tables presented here are based on individual firms' returns and risks only, for the results based on portfolios are similar. Both the coefficient for the residual risk, or say idiosyncratic risk, and the coeffi-cient for the total risk are on the boundary of being significant at a 10% level when B is included as the other independent variable. This gives strong support to our model. The negative coefficient of total risk in the first and fifth regression in the table is con-sistent with the evidence that idiosyncratic risk is taking up a much larger portion of total risk than the systematic risk, as documented in Campbell, et al (2001). Despite the high correlation between total risk and residual risk implied from the regressions, 182 total risk still has a positive coefficient when the only other independent variable is residual risk. This further corroborates our explanation that the negative coefficient of total risk in the first and fifth regression solely comes from its high correlation with residual risk. In the seventh regression, all three risk measures are included in the regression, and the results are less stable because of a problem of multi-collinearity: total risk is in fact the sum of residual risk and market risk. 3.7 Conclusion In this study, we have found supporting evidence for both Chapter I and Chapter II. On Chapter I, we fist find that the A-to-B price ratios are significantly larger than one, and it holds for every subperiod and every single firm. Second, firms with only B-Shares have significantly lower international betas than firms with both types of shares, and the betas of B-Share only firms are negative, though not statistically significant. Third, international betas have significantly positive impact on price ratios, and this supports the key inference from our model. Further, we also find that the liquidity and exchange rate risk also play significant roles in asset pricing. Regarding implications of Chapter II, we have found supporting evidence from the event study for the existence of the Unbalanced Management Compensation in Chinese stock markets. More importantly, our tests also show that the risk-return relationship in China is negative, which is in sharp contrast with the traditional 183 C A P M but consistent with our Agency Capital Asset Pricing Model ( A C A P M ) . We also call this A C A P M the Chinese version of C A P M , though our A C A P M can be modified to apply in the North American stock markets as well. In addition, we also find a negative idiosyncratic risk and return relationship in North American stock markets, though the market risk and return relationship stays in the positive range. Such results are consistent with the application of our model to the U.S. stock markets, as discussed in the appendix of the chapter titled Unbalanced Management Compensation and Asset Pricing. In the design of our empirical study, we employ an empirical procedure with theoretically improved efficiency over Fama-MacBeth (1973) and Ferson and Harvey (1999), and find such a procedure does provide more significant statistics in the empirical tests. Meanwhile, we have also conduct the tests using the more traditional methods, and the results are robust and consistent. We also adjust our empirical procedure to deal with the thin trading in the Chinese B-Share market. The thin trading problem is largely neglected in existing literature of empirical studies on Chinese stock markets, and such a neglect can cause serious distortion in many aspects of empirical tests and give rise to spurious results. In addition, we also use the panel data analysis with fixed effects more carefully than some previous studies. There is a variety of other tests which may shed more light on other secondary 184 implications of our model in Chapter I and Chapter II, and we mainly carry out the tests of the key implications in this study. Further, there are also many other interesting empirical topics in Chinese stock markets, such as tests of agency problems, a search for the empirical pricing factors in China, and tests of implications from behavioral finance models. 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This figure gives cross-sectional views of the Figure I in Unbalanced Management Compensation and Asset Pricing. For each fixed value of q, a price-risk curve is obtained as the standard deviation of the risky asset's payoff, cr, varies from 50 to 350. The bonus ratio, cg, is set to 0.05. The values of other parameters are set as follows, a = 0.5, S = 0.5, p = 1100, r = 0.1, nB = nu = 25, c 0 = 0.05, 7 ( ? = 7 f c = 1. i 1450F 1400h 1350 1300h £ 1250 a> o £ 1200 CD X. k. CO E 1150 1100 1050 1000 950 - - c,=0.001 - Q - c,=0.03 c,=0.05=c . _ . c,=0.1 g (e8888888B888B8888888888e nnnramooaooa BEEBBb 50 100 150 200 Std of Payoff (a) 250 300 350 192 Figure 3.2: SHSE A- and B-Share Index Level and Returns in 1992 This figure shows the Shanghai Stock Exchange A-Share and B-Share index returns in 1992. The top graph is the time series of daily index levels, and the bottom two graphs are the time series of index returns for A-Share index and B-Share index respectively. A-Share index and return show that A-Share prices in the Shanghai Stock Exchange more than double after the removal of daily price movement limits in May 1992. They also indicate that A-Share price movements before the removal of the daily price limits are not random; instead, prices just go up along a straight line most of the time during the pre-removal period. Consequently, A-Share prices in 1992. cannot reflect the true market values in equilibrium, nor could A- to B-Share price ratios re-flect the true gaps between domestic and foreign investors' valuation of Chinese firms. tn i < U J Vi x 2000 1800 1600 1400 1200 1000 800 600 400 200 A-Share Index B-Share Index |_ 120 <S 140 12/31/91 06/31/92 H50 40 12/31/92 12/31/91 12/31/91 06/31/92 12/31/92 06/31/92 Date 12/31/92 193 Figure 3.3: SHSE A- and B-Share Index Level and Returns during 1993-2000 This figure shows the Shanghai Stock Exchange A- and B-Share index lev-els and returns from 1993 to 2000. The top graph is the time series of daily index levels, and the bottom two graphs are the time series of index returns for A-Share index and B-Share index respectively. Relative to the 1992 price movement in Shanghai Stock Exchange, as shown in Figure 3.2, the stock prices in the period from 1993 to 2000 resemble more of a random walk. 2500 f 2 2000 A-Share Index 12/31/94 12/31/96 12/31/98 B-Share Index 120 20 12/31/00 c CD CC X a> •o 12/31/94 12/31/96 12/31/98 12/31/00 12/31/94 12/31/96 Date 12/31/98 12/31/00 194 Figure 3.4: SZSE A- and B-Share Index Level and Returns during 1993-2000 This figure shows the Shenzhen Stock Exchange A- and B-Share index lev-els and returns from 1993 to 2000. The top graph is the time series of daily index levels, and the bottom two graphs are the time series of index returns for A-Share index and B-Share index respectively. Relative to the 1992 price movement in Shanghai Stock Exchange, as shown in Figure 3.2, the stock prices in the period from 1993 to 2000 resemble more of a random walk. i A-Share Index B-Share Index 200 12/31/94 12/31/96 12/31/98 12/31/00 12/31/94 12/31/96 12/31/98 12/31/00 12/31/94 12/31/96 12/31/98 12/31/00 Date 195 Figure 3.5: The Development of A- vs. B-Share Markets This figure presents the historical development of Chinese stock markets. Here we use the cumulative numbers of shares issued in A- and B-Share markets by assuming that the number of A-Shares issued before 1990 is 0, noting that no B-Shares were issued before 1990, and the first Chinese stock exchange, SHSE, was estabished in December 19, 1990. The figure looks similar when we ue the R M B amount of shares issued rather than the numbers of shares. 196 Table 3.1: The Statistics of A- to B-Share Price Ratios This tables presents the price ratios of Chinese firms with outstanding A- and B-Shares, which are identical shares issued to domestic and foreign investors by the same Chinese firms with the only difference being the ownership restrictions. The P95, P5, and median are respectively 95%, 5%, and 50% percentiles of price ratios. T-statistics are against the null hypothesis that the mean of price ratios is equal to 1, and it is obvious that all T values indicate rejection of this null hypothesis at any commonly used significance level. The time period is from January 1, 1993 to December 31, 2000. Sample Mean Median Std P95 P5 T N CHINA (1993-2000) 4.74 4.01 3.29 10.69 1.22 434.41 146237 SHSE (1993-2000) 5.69 4.85 3.67 12.27 1.76 336.27 69119 SZSE (1993-2000) 3.88 3.18 2.63 8.82 1.05 304.10 77118 Sample Year Mean Median Std P95 P5 T N 1993 4.15 3.77 1.67 6.97 2.19 133.64 5027 1994 2.46 2.11 1.53 5.52 0.89 98.50 10747 1995 3.52 3.14 1.92 7.40 1.14 154.45 13890 z 1996 3.52 3.10 1.77 6.77 1.32 184.55 16889 X f "\ 1997 3.14 2.72 1.72 6.68 0.97 178.05 20506 1998 6.38 5.75 3.50 12.98 1.70 229.62 22348 1999 6.99 6.45 3.82 13.97 1.38 241.42 23729 2000 5.23 4.96 2.69 10.25 1.37 252.16 25765 1993 5.06 4.79 2.14 8.94 2.19 82.35 1888 1994 3.17 2.72 1.68 6.29 1.25 99.88 6004 < 1995 4.28 3.96 1.85 7.80 1.90 156.86 7800 O 1996 4.37 4.14 1.78 7.42 1.95 173.75 8462 z < 1997 4.04 3.79 1.81 7.53 1.64 164.74 9632 X CO 1998 7.91 7.55 3.64 14.46 2.80 190.41 10081 1999 8.31 7.86 3.79 15.30 3.05 200.06 10776 2000 6.12 5.60 2.93 11.75 1.62 186.84 11467 1993 3.60 3.46 0.95 5.45 2.20 153.86 3139 1994 1.56 1.48 0.56 2.50 0.77 68.68 4743 Z UJ 1995 2.54 2.02 1.53 5.76 0.99 78.50 6090 X N 1996 2.66 2.42 1.28 5.02 1.07 119.11 8427 z UJ 1997 2.35 2.27 1.17 4.23 0.68 120.57 10874 I CD 1998 5.12 4.75 2.82 9.94 1.36 162.09 12267 1999 5.89 5.30 3.48 11.85 1.17 159.81 12953 2000 4.51 4.44 2.23 8.38 1.31 187.95 14298 197 Table 3.2: Auto-correlations of A- and B-Share market index returns This table shows that there are significant auto-correlations in B-Share index returns, while the auto-correlations of A-Share index returns are very small and insignificant. We have also checked the auto-correlations for the subperiods 1993-1996 and 1997-2000, and the results are similar. A Share B Share Index Return Index Return Pearson Auto Corr -0.0030 0.2054 Correlation P-Value 0.8897 <0.0001*" Spearman Auto Corr 0.0027 0.2159 Correlation P-Value 0.9038 <0.0001*** Kendall's Auto Corr 0.0030 0.1576 tau-b F'-Value 0.8390 <0.0001*** 5 lU X CD I ~ t ~ - 2 0 8 6 75 c o ra Z Pearson Auto Corr -0.0204 0.1889 Correlation P-Value 0.3524 <0.0001*** Spearman Auto Corr -0.0344 0.1693 Correlation P-Value 0.1166 <0.0001*** Kendall's Auto Corr -0.0245 0.1190 tau-b P-Value 0.0940 <0.0001*** 2086 Pearson Auto Corr -0.0026 0.1741 Correlation P-Value 0.9050 <0.0001*** Spearman Auto Corr 0.0147 0.1804 Correlation P-Value 0.5013 <0.0001*** Kendall's Auto Corr 0.0129 0.1309 tau-b P-Value 0.3800 <0.0001*** 2086 * Significant at 0.05; " Significant at 0.01; *** Significant at 0.001. 198 Table 3.3: International Betas and Issuance of A- vs. B-Shares This tables shows the difference between the mean of international betas between two groups of firms: group I, firms with both A- and B-Shares, and group II, firms with only outstanding B-Shares. The t-tests in both the subperiod 1993-1996 and the entire sample period show that the mean of group I is significantly larger than the mean of group II. Meanwhile, the mean of group I remains larger in the subperiod 1997-2000, though the statistics are not as strong. This is not surprising considering the boom of US stock markets in late Iflflfls and the Asian financial crisis from 1997. These two events, which should be treated as outliers, strongly biase the estimated international betas of Chinese firms in the subperiod 1997-2000 towards negative values. Consequently, the power of the test of the mean differences between groups can be significantly reduced by such a distortion in estimation. , J*??'*, .T"". Differ.!*. Mean m Std Dev 8 Std Err A N 5 F-test *~ T-test (ProbT) 0.7197 1.3137 56 -0.313 1.3802 6 1.82 (0.0367) 1.0331 1.3194 1.10 (0.7381): Pooled T-test 0.1755 0.5635 0.5667 Mean -0.343 -0.475 0.1317 o Std Dev 0.5368 0.6722 0.5637 o a Std Err 0.0576 0.1503 0.1398 CM i!•» N 87 20 £ F-test 1.57 (0.1670): Pooled T-test T-test 0.94 (ProbT) (0.1741 ) Mean -0.163 -Q.453 0.2892 o Std Dev 0.4526 0.6399 0.4918 § Std Err 0.0485 0.1431 0.122 £ N 87 20 S F-test 2.00 (0.0328J~Satterthwalte T-test T-test 1.91 ( ProbT) (0.0339 ) Note: F-test Is the test against the null hypothesis ol equal variances, and T-test Is against equal means. The choice of pooled t-test or Satterthwaite t-test is based on the result ol F-test at a signlticance level of 1 0 % . 199 Table 3.3: International Betas and Issuance of A- vs. B-Shares This tables shows the difference between the mean of international betas between two groups of firms: group I, firms with both A- and B-Shares, and group II, firms with only outstanding B-Shares. The t-tests in both the subperiod 1993-1996 and the entire sample period show that the mean of group I is significantly larger than the mean of group II. Meanwhile, the mean of group I remains larger in the subperiod 1997-2000, though the statistics are not as strong. This is not surprising considering the boom of US stock markets in late 1990s and the Asian financial crisis from 1997. These two events, which should be treated as outliers, strongly biase the estimated international betas of Chinese firms in the subperiod 1997-2000 towards negative values. Consequently, the power of the test of the mean differences between groups can be significantly reduced by such a distortion in estimation. Group I (with outstanding A Shares) Group II (with no A Shares) Difference (Group I - Group II) 3-1996 Mean Std Dev Std Err N 0.7197 1.3137 0.1755 56 -0.313 1.3802 0.5635 6 1.0331 1.3194 0.5667 cn CT) F-test T-test ( ProbT) 1.10(0.7381) : Pooled T-test 1.82 ( 0.0367 ) 7-2000 Mean Std Dev Std Err N -0.343 0.5368 0.0576 87 -0.475 0.6722 0.1503 20 0.1317 0.5637 0.1398 cn cn T — F-test T-test ( ProbT) 1.57 (0.1670) : Pooled T-test 0.94 (0.1741 ) 3-2000 Mean Std Dev Std Err N -0.163 0.4526 0.0485 87 -0.453 0.6399 0.1431 20 0.2892 0.4918 0.122 cn cn T -F-test T-test ( ProbT) 2.00 (0.0328) : Satterthwaite T-test 1.91 (0.0339) Note: F-test is the test against the null hypothesis of equal variances, and T-test is against equal means. The choice of pooled t-testMfRatterthwaite t-test is based on the result of F-test at a significance level of 10%. Table 3.4: International Betas and Price Differences: Fama-MacBeth T-Test This table presents the adapted Fama-MacBeth t-test of the relation between firms' international betas and A- vs. B-Share price differences. The top half of the table presents the annual cross-sectional regression of price differences on each firms' inter-national betas. The price differences are the averages of each firm-year from 1997 to 2000, and the betas are estimated with data from 1993 to 1996. The second stage of the test is to pool together the estimates of international betas' coefficents, and then use the t-test to check whether the coefficients overs year are significantly different from 0 or not. Estimator Std Err T Prob CO I § o CO m CO CO £ CO D) CO CU O DC o 1997 0.2865 0.1453 1.97 0.0539 1998 0.3361 0.2640 1.27 0.2086 1999 0.6025 0.2417 2.49 0.0159 2000 0.4968 0.2020 2.46 0.0173 i i-Mean 0.4305 Fama-lacbeth Test Std T 0.1457 5.91 ProbT 0.0097 200 Table 3.5: International Betas and Price Differences: Panel with Fixed Effects This table presents the adapted Fama-MacBeth t-test of the relation between firms' international betas and A- vs. B-Share price differences. The top half of the table presents the annual cross-sectional regression of price differences on each firms' inter-national betas. The price differences are the averages of each firm-year from 1997 to 2000, and the betas are estimated with data from 1993 to 1996. The second stage of the test is to pool together the estimates of international betas' coefficents, and then use the t-test to check whether the coefficients overs year are significantly different from 0 or not. Beta R-Square DFE F-Statistic (P-value) cu Coefficient 0.4305 Full Sampl Std Err T Prob 0.1085 3.9700 0.0001 0.4187 211 45.43 (<0.0001) Shanghai Coefficient Std Err T Prob 0.1657 0.1414 1.1700 0.2438 0.4684 115 33.32 (<0.0001) Shenzhen Coefficient Std Err T Prob 0.3136 0.1222 2.5700 0.0119 0.5309 91 32.13 (<0.0001) 201 Table 3.6: Factors in Pricing Differences: Panel with Fixed Effects This table presents the adapted Fama-MacBeth t-test of the relation between firms' international betas and A- vs. B-Share price differences. The top half of the table presents the annual cross-sectional regression of price differences on each firms' inter-national betas. The price differences are the averages of each firm-year from 1997 to 2000, and the betas are estimated with data from 1993 to 1996. The second stage of the test is to pool together the estimates of international betas' coefficents, and then use the t-test to check whether the coefficients overs year are significantly different from 0 or not. Pratio _Last Spread _Diff Amount BtoA Diff CrrRet R-Square DFE Coefficient 0.8910 3.6378 -0.0362 1.9058 nil Sampl Std Err T 0.0067 133.64 0.5412 6.72 0.0087 -4.18 0.4580 4.16 0.8542 4929 u. Prob <.0001 <.0001 <.0001 <.0001 Coefficient 0.8759 5.9592 -1.5334 3.2904 Shanghai Std Err T Prob 0.0100 87.99 <.0001 0.9923 6.01 <.0001 0.2418 -6.34 <.0001 0.7560 4.35 <.0001 0.8321 2377 Coefficient 0.8977 1.6910 -0.0322 0.7416 Shenzher Std Err T Prob 0.0088 102.49 <.0001 0.5790 2.92 0.0035 0.0072 -4.45 <.0001 0.5286 1.40 0.1608 0.8541 2548 202 Table 3.7: The Statistics of E / P Ratios in China This tables presents the E / P ratios of Chinese firms, and the time period is from January 1, 1993 to December 31, 2000. Firms with negative earnings are also included in the data sample. The data presented are filtered by cutting off the top and bottom percentiles. The unfiltered data have very close values of means and medians, though their maximum and minimum observations have much larger absolute values than the filtered data here. Sample Mean Median Std P95 P5 Range N CHINA (1993-2000) 2.92% 2.58% 5.39% 8.79% -2.74% 82.56% 4833 SHSE (1993-2000) 3.10% 2.58% 6.02% 7.74% -1.44% 80.28% 2506 SZSE (1993-2000) 2.72% 2.56% 4.62% , 9.79% -3.92% 67.48% 2327 Sample Year Mean Median Std P95 P5 Range N 1993 3.51% 3.40% 1.59% 6.22% 1.35% 11.66% 162 1994 5.68% 5.14% 3.58% 12.16% 1.20% 31.86% 275 1995 4.87% 4.28% 5.20% 14.17% -1.28% 53.09% 302 <: z 1996 2.52% 2.98% 3.18% 5.50% -2.61% 33.54% 487 X r "j 1997 3.25% 2.78% 7.20% 10.16% -2.26% 82.56% 769 1998 3.39% 3.95% 5.39% 8.65% -6.73% 64.24% 800 1999 1.80% 2.11% 3.36% 5.36% -4.26% 35.71% 912 2000 2.14% 1.38% 6.32% 6.51% -2.66% 80.92% 1126 1993 2.98% 2.79% 1.32% 5.16% 1.17% 6.84% 88 1994 4.57% 3.79% 3.28% 10.57% 0.86% 26.78% 157 < 1995 4.08% 3.89% 4.31% . 10.11% 0.17% 53.09% 172 - 1 -o 1996 2.82% 3.16% 2.93% 6.01% 0.24% 29.61% 271 z < 1997 4.07% 2.84% 9.09% 16.72% -0.17% 80.03% 380 X CO 1998 3.24% 3.69% 4.44% 8.03% -3.34% 61.95% 400 1999 1.81% 2.09% 3.04% 4.82% -2.91% 32.95% 455 2000 2.83% 1.40% 8.13% 10.91% -2.10% 75.55% 583 1993 4.15% 4.33% 1.65% 6.60% 1.90% 11.13% 74 1994 7.17% 6.90% 3.43% 13.21% 2.30% 21.82% 118 z LU 1995 5.93% 5.10% 6.04% 14.62% -3.28% 37.71% 130 X N 1996 2.16% 2.51% 3.44% 5.32% -3.46% 33.54% 216 Z LU 1997 2.45% 2.68% 4.54% 10.04% -4.77% 44.91% 389 X cn 1998 3.54% 4.28% 6.19% 9.38% -8.48% 64.24% 400 1999 1.79% 2.11% 3.65% 5.77% -4.86% 35.71% 457 2000 1.39% 1.33% 3.27% 6.21% -3.29% 42.68% 543 203 Table 3.8: The Comparison Between E / P Ratios and Interest Rates in China This tables compares the mean and median of E / P ratios in Chinese stock markets with the corresponding 1-year interest rates of bank deposits. The time period is from January 1, 1993 to December 31, 2000. Firms with negative earnings are also included in the data sample. 12.00% 10.00% 2 6.00% 4.00% 2.00% 0.00% 1994 1995 1996 1997 1998 1999 Year 204 Table 3.9: Pearson Correlations Between Risk and Return in China This tables presents the correlations between realized returns and estimated risk measures of Chi-nese firms listed in both the Shanghai Stock Exchange and the Shenzhen Stock Exchange. The statistics are based on monthly observations, and the time period is from January 1, 1993 to December 31, 2000. Sample Risk Measure Type AR LnRet Corr -0.0622 -0.0322 Total Risk P-Value <.0001 <.0001 Corr -0.0288 -0.0511 Full Residual Risk P-Value <.0001 <.0001 Corr -0.0902 -0.0532 Beta P-Value <.0001 <.0001 Corr -0.0826 -0.0491 Beta Square P-Value <.0001 <.0001 Corr -0.0981 -0.0230 Total Risk P-Value <.0001 0.0098 'ca Corr -0.0215 -0.0363 Residual Risk P-Value 0.0016 <.0001 c 03 Corr -0.0931 -0.0292 -C CO Beta P-Value <.0001 0.0011 Corr -0.0900 -0.0274 Beta Square P-Value <.0001 0.0022 Corr -0.0185 -0.0466 Total Risk P-Value 0.0604 <.0001 c cu Corr -0.0453 -0.0711 sz N Residual Risk P-Value <.0001 <.0001 c cu Corr -0.1028 -0.0808 cn Beta P-Value <.0001 <.0001 Corr -0.0926 -0.0725 Beta Square P-Value <.0001 <.0001 22850 12563 10287 205 Table 3.10: Spearman Correlations Between Risk and Return in China This tables presents the correlations between realized returns and estimated risk measures of Chinese firms listed in both the Shanghai Stock Exchange and the Shenzhen Stock Exchange. The statistics are based on monthly observations, and the time period is from January 1, 1993 to December 31, 2000. Sample Risk Measure Type AR LnRet N Corr -0.0855 -0.0486 Total Risk P-Value Corr <.0001 -0.0401 <.0001 -0.0578 Full Residual Risk P-Value Corr <.0001 -0.0834 <.0001 . -0.0557 22850 Beta P-Value Corr <.0001 -0.0834 <.0001 -0.0557 Beta Square P-Value <.0001 <.0001 Corr -0.1106 -0.0389 Total Risk P-Value <.0001 <.0001 Corr -0.0322 -0.0430 _cz a> Residual Risk P-Value 0.0003 <.0001 12563 CO Corr -0.0959 -0.0240 CO Beta P-Value Corr <.0001 -0.0959 0.0072 -0.0240 Beta Square P-Value <.0001 0.0072 Corr -0.0534 -0.0692 Total Risk P-Value <.0001 <.0001 c CD Corr -0.0520 -0.0772 - C N Residual Risk P-Value <.0001 <.0001 10287 C CO Corr -0.0740 -0.0890 .c CO Beta P-Value <.0001 <.0001 Corr -0.0740 -0.0890 Beta Square P-Value <.0001 <.0001 206 Table 3.11: Kendall's tau-b Between Risk and Return in China This tables presents the nonlinear correlation measure, Kendall's tau-b, between realized returns and estimated risk measures of Chinese firms listed in both the Shanghai Stock Ex-change and the Shenzhen Stock Exchange. The statistics are based on monthly observations, and the time period is from January 1, 1993 to December 31, 2000. Sample Risk Measure Type AR LnRet N Corr -0.0573 -0.0341 Total Risk P-Value Corr <.0001 -0.0272 <.0001 -0.0388 Full Residual Risk P-Value Corr <.0001 -0.0561 <.0001 -0.0372 22850 Beta P-Value Corr <.0001 -0.0561 <.0001 -0.0372 Beta Square P-Value <.0001 <.0001 Corr -0.0738 -0.0270 Total Risk P-Value <.0001 <.0001 'o3 Corr -0.0218 -0.0287 Residual Risk P-Value 0.0003 <.0001 12563 c 03 Corr -0.0643 -0.0158 sz CO Beta P-Value Corr <.0001 -0.0643 0.0078 -0.0158 Beta Square P-Value <:oooi 0.0078 Corr -0.0366 -0.0483 Total Risk P-Value <.0001 <.0001 CD Corr -0.0353 -0.0520 SZ N Residual Risk P-Value <.0001 <.0001 10287 c Corr -0.0498 -0.0601 SZ CO Beta P-Value <.0001 <.0001 Corr -0.0498 -0.0601 Beta Square P-Value <.0001 <.0001 207 Table 3.12: Event Study of the Crack-Down on U M C in May 1997 This tables presents the market reaction to the crack-down on various forms of unbalanced man-agement compensation in May 1997. It shows that the market prices dropped significantly upon the announcement of the crack-down by.the government. The test is based on daily returns, and the four window periods are as follows: base window (-221,-22), pre-event window (-21, -2), event window (-1,9), post-event window (1,20). The mean returns of the base window is compared with the means of all other window periods to determine whether there are significant market reaction around the announcement. The gap between the base window and the event window, called the pre-event window here, is the buffer zone to account for potential release of information on the announcement to the market. The test is also carried out with the 200 daily observations after the post-event window period, and the results are similar, strongly supporting the claim that there are strong negative market reaction on and before the announcement. Base Pre-Event Event Post-Event Window Window Window Window Mean 0.0033 -8.80E-04 -0.068 0.0006 CD Q. Std Dev 0.0415 0.0499 0.0399 0.0367 Std Err 0.0002 0.0006 0.0015 0.0004 E re Diff -0.0042 -0.0709 -0.0026 CO N 68600 6860 686 6860 Li- F-test unequal equal unequal T-test -6.66 -44.58 -5.62 ProbT <.0001 <.0001 <.0001 Mean 0.0027 -2.00E-03 -0.064 -0.0001 Std Dev 0.0384 0.0484 0.0422 0.0334 ra Std Err 0.0002 0.0008 0.0021 0.0005 .e o> Diff -0.0049 -0.0665 -0.0028 c ra N 40400 4040 404 4040 . c CO F-test unequal unequal unequal T-test -6.19 -31.56 -4.99 ProbT <.0001 <.0001 <.0001 Mean 0.0041 1.00E-03 -0.073 0.0017 Std Dev 0.0455 0.0521 0.0359 0.0409 c CD Std Err 0.0003 0.001 0.0021 0.0008 .C N Diff -0.0031 -0.0772 -0.0024 C CD N 28200 2820 282 2820 -C CO F-test unequal unequal unequal T-test -3.09 -35.87 -2.97 ProbT 0.002 <.0001 0.003 Note: F-test is the test against the null hypothesis of equal variances, and T-test is against equal means. The choice of pooled t-test or Satterthwaite t-test is based on the result of F-test at a significance level of 10%. 208 Table 3.13: Fama-MacBeth Regression Coefficients in China This is a test of the risk coefficients when in cross-sectional regression of returns on each risk measures. The.data are monthly observations from the full sample period. The negative risk premium for Beta in the full sample is slightly over 1% per month on average, which is not only statistically significant, but also economically impressive. Total Risk Residual Risk Beta Number of Observations Mean Median t-value alpha -0.1228 -0.1142 -2.64 0.0106 60 Mean Median t-value alpha -0.1433 -0.1611 -2.00 0.0497 60 Mean Median t-value alpha -0.0300 -0.0129 -2.24 0.0288 60 Mean Median t-value alpha -0.0971 -0.0637 -2.11 0.0393 -0.0079 -0.0009 -0.75 0.4591 60 Mean Median t-value alpha -0.1437 -0.1190 -2.40 0.0194 -0.0046 -0.0455 -0.05 0.9604 60 Mean Median t-value alpha -0.1512 -0.1669 -2.29 0.0255 -0.0306 -0.0102 -2.40 0.0195 60 Mean Median t-value alpha -0.0965 0.0415 -0.79 0.4314 -0.0411 -0.1004 -0.28 0.7800 -0.0174 0.0039 -1.08 0.2844 60 209 Table 3.14: Fama-MacBeth Regression Coefficients in SHSE This is a test of the risk coefficients when in cross-sectional regression of returns on each risk measures. The data are monthly observations from the full sample period. The negative risk premium for Beta in the full sample is slightly over 1% per month on average, which is not only statistically significant, but also economically impressive. Total Risk Residual Risk Beta Number of Observations Mean Median t-value alpha -0.1077 -0.0921 -3.28 0.0018 60 Mean Median t-value alpha -0.1324 -0.0859 -2.34 0.0229 60 Mean Median t-value alpha -0.0168 -0.0166 -3.00 0.0040 60 Mean Median t-value alpha -0.1155 -0.0920 -2.92 0.0049 0.0048 -0.0009 0.52 0.6070 60 Mean Median t-value alpha -0.1382 -0.1204 •2.28 0.0260 0.0092 0.0206 0.10 0.9184 60 Mean Median t-value alpha -0.1355 -0.0925 -2.39 0.0202 -0.0179 -0.0218 -3.18 0.0024 60 Mean Median t-value alpha -0.1475 -0.1084 -1.00 0.3220 0.0179 0.0256 0.11 0.9152 0.0003 0.0041 0.02 0.9820 60 210 Table 3.15: Fama-MacBeth Regression Coefficients in SZSE This is a test of the risk coefficients when in cross-sectional regression of returns on each risk measures. The data are monthly observations from the full sample period. The negative risk premium for Beta in the full sample is slightly over 1% per month on average, which is not only statistically significant, but also economically impressive. Total Risk Residual Risk Beta Number of Observations Mean Median t-value alpha -0.0537 -0.0345 -1.26 0.2123 60 Mean Median t-value alpha -0.1282 -0.0520 -1.54 0.1294 60 Mean Median t-value alpha -0.0101 -0.0026 -1.05 0.2957 60 Mean Median t-value alpha -0.0576 -0.0072 -0.75 0.4577 0.0076 -0.0064 0.32 0.7529 60 Mean Median t-value alpha -0.0611 -0.0223 -1.12 0.2692 -0.0572 -0.0180 -0.53 0.5998 60 Mean Median t-value alpha -0.1386 -0.1144 -1.68 0.0975 -0.0058 0.0004 -0.61 0.5415 60 Mean Median t-vaiue alpha 0.0014 0.0629 0.01 0.9931 -0.1116 -0.0291 -0.59 0.5556 -0.0254 0.0016 -0.66 0.5109 60 211 Table 3.16: Panel Data Analysis with Fixed Time Effects in China This table shows the coefficients and related statistics from the panel data regression with fixed time effects in China, including the firms listed in both the Shanghai Stock Exchange and the Shenzhen Stock Exchange. The sample time period is from January 1, 1993 to December 31, 2000. The F-statistics in the last column of the table are the results of F-tests in each regression against the null hypothesis of no fixed time effects, and the null is being rejected in all regressions at a significance level a (alpha) < 0.0001. The dependent variable in the regression is the log returns of each firm, and the dependent variable ranging from each risk measure alone and different combinations of the three risk measures. The rest of the table should be self-explanatory. Total Residual Beta R-DFE F-Value Risk Risk Square (alpha) Coefficient -0.13193 243.91 (<0.0001) std err t-value 0.0138 -9.59 0.3879 22774 alpha <.0001 Coefficient -0.13408 241.17 (<0.0001) std err t-value 0.0252 -5.33 0.3861 22774 alpha <.0001 Coefficient -0.01737 241.40 (<0.0001) std err t-value 0.00268 -6.49 0.3865 22774 alpha <.0001 Coefficient -0.10502 -0.01508 240.82 (<0.0001) std err t-value 0.0257 -4.09 0.00273 •5.51 0.3870 22773 alpha <.0001 <.0001 Coefficient -0.12867 -0.00097 242.68 (<0.0001) std err t-value 0.0182 -7.07 0.00354 •0.27 0.3879 22773 alpha <.0001 0.7845 Coefficient -0.13915 0.021555 242.88 (<0.0001) std err t-value 0.0174 -8 0.0318 0.68 0.3879 22773 alpha <.0001 0.4976 Coefficient -0.13827 0.020959 -0.0002 241.69 (<0.0001) std err t-value 0.0239 •5.8 0.0336 0.62 0.00375 -0.05 0.3879 22772 alpha <.0001 0.5333 0.9569 212 Table 3.17: Panel Data Analysis with Fixed Time Effects in the SHSE This table shows the coefficients and related statistics from the panel data regression with fixed time effects in the Shanghai Stock Exchange. The sample time period is from January 1, 1993 to December 31, 2000. The F-statistics in the last column of the table are the results of F-tests in each regression against the null hypothesis of no fixed time effects, and the null is being rejected in all regressions at a significance level a (alpha) < 0.0001. The dependent variable in the regression is the log returns of each firm, and the dependent variable ranging from each risk measure alone and different combinations of the three risk measures. The rest of the table should be self-explanatory. Total Residual Beta R-DFE F-Value Risk Risk Square (alpha) Coefficient -0.13173 125.10 (<0.0001) std err t-value 0.0208 •6.33 0.3717 12494 alpha <.0001 Coefficient -0.1549 124.28 (<0.0001) std err t-value 0.0351 -4.41 0.3707 12494 alpha <.0001 Coefficient -0.0173 124.40 (<0.0001) std err t-value 0.00405 -4.27 0.3706 12494 alpha <.0001 Coefficient -0.14865 -0.01655 124.45 (<0.0001) std err t-value 0.0351 -4.23 0.00405 •4.09 0.3715 12493 alpha <.0001 <.0001 Coefficient -0.11972 -0.00412 124.96 (<0.0001) std err t-value 0.0253 -4.74 0.00491 -0.84 0.3717 12493 alpha <.0001 0.401 Coefficient -0.118 -0.04008 124.79 (<0.0001) std err t-value 0.0255 -4.63 0.043 -0.93 0.3717 12493 alpha <.0001 0.351 Coefficient -0.08731 -0.06716 -0.00735 124.62 (<0.0001) std err t-value 0.0341 •2.56 0.0474 -1.42 0.00541 -1.36 0.3718 12492 alpha 0.0104 0.1563 0.1743 213 Table 3.18: Panel Data Analysis with Fixed Time Effects in the SZSE This table shows the coefficients and related statistics from the panel data regression with fixed time effects in the Shenzhen Stock Exchange. The sample time period is from January 1, 1993 to December 31, 2000. The F-statistics in the last column of the table are the results of F-tests in each regression against the null hypothesis of no fixed time effects, and the null is being rejected in all regressions at a significance level a (alpha) < 0.0001. The dependent variable in the regression is the log returns of each firm, and the dependent variable ranging from each risk measure alone and different combinations of the three risk measures. The rest of the table should be self-explanatory. Total Residual Beta R-DFE F-Value Risk Risk Square (alpha) Coefficient -0.0449 156.74 (<0.0001) std err t-value 0.0213 -2.1 0.4762 10219 alpha 0.0353 Coefficient -0.06547 155.73 (<0.0001) std err t-value 0.0389 -1.68 0.4761 10219 alpha 0.0924 Coefficient -0.00721 155.25 (<0.0001) std err t-value 0.00426 -1.69 0.4761 10219 alpha 0.0909 Coefficient -0.00583 -0.00583 154.42 (<0.0001) std err t-value 0.00439 •1.33 0.00439 •1.33 0.4762 10218 alpha 0.184 0.184 Coefficient -0.03657 -0.00269 155.20 (<0.0001) std err t-value 0.0271 -1.35 0.00542 •0.5 0.4762 10218 alpha 0.1776 0.619 Coefficient -0.04126 -0.00882 155.71 (<0.0001) std err t-value 0.0324 -1.27 0.0591 •0.15 0.4762 10218 alpha 0.2031 0.8814 Coefficient -0.02212 -0.02689 -0.00378 154.06 (<0.0001) std err t-value 0.0446 -0.5 0.0658 -0.41 0.00603 •0.63 0.4762 102127 alpha 0.6195 0.6827 0.5312 214 Table 3.19: Fama-MacBeth Regression Coefficients in the U.S. This is a test of the risk coefficients when in cross-sectional regression of returns on each risk measures. The data are monthly observations from the full sample period. The negative risk premium for Beta in the full sample is slightly over 1% per month on average, which is not only statistically significant, but also economically impressive. Total Risk Residual Risk Beta Number of Observations Mean Median t-value alpha 0.00067 0.1394 0.01 0.99446 60 Mean Median t-value alpha -0.01369 0.14055 -0.14 0.88928 60 Mean Median t-value alpha 0.00197 0.00399 0.36 0.7219 60 Mean Median t-value alpha -0.0234 0.06615 -0.26 0.79866 0.00271 0.0009 0.74 0.46353 60 Mean Median t-value alpha 0.23491 0.37176 1.24 0.27979 -0.25146 -0.4126 -1.58 0.11942 60 Mean Median t-value alpha -0.029 0.05268 -0.34 0.73242 0.00262 0.00578 0.65 0.51733 60 , Mean Median t-value alpha 0.29744 0.4758 1.05 0.29652 -0.31774 -0.59878 -1.25 0.21778 -0.00043 -0.00817 -0.07 0.94211 60 215 Table 3.20: Panel Data Analysis with Fixed Time Effects in the U.S. This table shows the coefficients and related statistics from the panel data regression with fixed time effects in the U.S. The data sample are these firms that are included in the SP 500. To be consistent with the sample period in China, we use the CRSP data of the SP 500 firms from January 1, 1993 to December 31, 2000. The F-statistics in the last column of the table are the results of F-tests in each regression against the null hypothesis of no fixed time effects, and the null is being rejected in all regressions at a significance level a (alpha) < 0.0001. The dependent variable in the regression is the log returns of each firm, and the dependent variable ranging from each risk measure alone and different combinations of the three risk measures. The rest of the table should be self-explanatory. Total Risk Residual Risk Beta R-Square DFE F-Value (alpha) Coefficient -0.01664 103.35 std err 0.0158 0.1465 35628 t-value •1.05 (<0.0001) alpha 0.2924 Coefficient -0.02147 103.31 std err 0.0172 0.1465 35628 t-value -1.25 (<0.0001) alpha 0.2107 Coefficient 0.000684 103.62 std err 0.0011 0.1465 35628 t-value 0.62 (<0.0001) alpha 0.532 Coefficient -0.0303 0.0014 103.18 std err 0.0186 0.0012 0.1466 35627 t-value -1.63 1.21 (<0.0001) alpha 0.1041 0.2261 Coefficient -0.0319 0.0019 103.13 std err 0.019 0.0013 0.1466 35627 t-value -1.68 1.45 (<0.0001) alpha 0.0928 0.1466 Coefficient 0.035 -0.05809 103.31 std err 0.0598 0.065 0.1465 35627 t-value 0.58 -0.89 (<0.0001) alpha 0.5589 0.3712 Coefficient -0.038 0.00619 0.001992 103.12 std err 0.0874 0.0858 0.00174 0.1466 35626 t-value -0.44 0.07 1.15 (<0.0001) alpha 0.6638 0.9425 0.2518 216 Appendix A Appendix of Chapter II A . l Managers' Personal Investment In the main text of this chapter, it is assumed that managers are not allowed to make any personal investment in the market. This is solely for ease of presentation, and such an assumption does not affect any results in the model. In this appendix, we explain why it is so: managers do not invest in the stock market with their own money even if they are allowed to do so, under the plausible condition that U M C managers have a larger bonus rate, cg, than penalty rate, Q . 217 A.1.1 Setup To consider the potential interaction between manager k's personal investment and his compensation contract, we set manager k's personal wealth at the beginning of the period as W'k, and manager q's as Wq. The stock market is competitive, as assumed in the main text of this chapter, and every manager takes the market price as given without considering the impact of his own investment decision on the market price. Different from the main model where a manager only maximizes his personal utility from the consumption of his end-of-period compensation, in this appendix a manager maximizes his utility from the consumption of both his compensation and personal wealth. Everything else in this appendix is as defined in the main model of this chapter. A. 1.2 Managers with Balanced Compensation At the beginning of the period, the representative manager, q, makes simultaneous investment decisions for Fund Q and his own endowed wealth, W'q. The assets avail-able for investment are the riskfree bonds and the single risky asset. Manager q's utility maximization problem can be written as follows: max E{Uq(wq"} = E{—exp(—awq/')} (A. l) Dq,Cq,Dq,,Cq, 218 s.t. Wq = DqP + Cq (A.2) Wql = Dq,P + Cq, (A. 3) wq = Sq + c0Dq(K - RP) (A.4) Wg> = Dq>(nd — RP) + RWq> (A.5) Wqii — Wq + Wqi (A.6) Dq > 0; Dq, > 0 (A.7) where Dq is the number of shares that Fund Q purchases, and Dq> is the number of shares that manager q purchases with his own personal wealth; Cq and Cq> are, re-spectively, the amount of bonds purchased with money from Fund Q and manager k's personal wealth; wq is manager q's compensation at the end of the period, wq> is the payoff on manager q's personal investment, and wq» is the total income of manager q from both his management compensation and his personal investment. Equation (A.2) is fund q's budget constraint from Fund Q, equation (A.3) is the budget con-straint from manager k's personal investment, equation (A.4) is the compensation contract for manager k, equation (A.5) is the end-of-period payoff of manager q's personal investment, equation (A.6) is manager k's total wealth at the end of the period from both his compensation and his personal investment, and equation (A.7) is the no short-sale constraint in the stock market. Please note that CQ denotes the portion of fund q's investment payoff that goes to manager q's compensation. 219 Substituting (A.2), (A.3), (A.4), and (A.5) into (A.6), canceling Cq, Cq>, Wq, and Wq<, we get: wq„ = {Dq/ + c0Dq)(7rd - RP) + RWq, + Sq (A.8) From the equation above, we can see that manager q's problem is equivalent as choosing an optimal level of D*q+q, = (Dq> + c0Dq) to maximize his personal utility. For a given price P, manager k can tolerate a certain amount of risk in exchange for a portion of the risky asset's payoff fr, assuming the expected rate of return fi/P — 1 is higher than the riskfree rate r. Once manager k's optimal consumption is achieved at a certain level of D*+ ,, he is indifferent to whatever combination of Dq> and Dq as long as the sum of Dq> and c0Dq is equal to D*+ In other words, manager q does not care whether the risk he undertakes comes from his personal investment or from his compensation contract, providing the total amount of absolute risk stays at the optimal level. In such a situation, it is reasonable to assume that manager q chooses to focus on his job as the manager of Fund Q, and follow the rule of no personal investment by fund managers in the stock market. Such an action by manager q is in alignment with the interests of fund q's owners. A.1.3 Managers with Unbalanced Compensation For manager k, he faces the following problem: max E{Uk{wk"} = E{—exp(—awk")} (A.9) 220 s.t. DkP + Ck (A.10) Dk'P + Ck> (A.11) 4 + cgDk(7r - RP)+ + ciDk(7t - RP) (A.12) >kl{nd-RP) + RWk, (A.13) Wk" wk + Wk' (A.14) Dk > 0; Dk, > 0 (A.15) where Dk is the number of shares that Fund Q purchases, and Dk> is the number of shares that manager k purchases with his own personal wealth; Ck and CV are, respectively, the amount of bonds purchased with money from Fund Q and manager k's personal wealth; wk is manager q's compensation at the end of the period, wk' is the payoff on manager q's personal investment, and wk" is the total income of manager k from both his management compensation and his personal investment. Equation (A.10) is fund q's budget constraint from Fund Q, equation (A.11) is the budget constraint from manager k's personal investment, equation (A.12) is the compensation contract for manager k, equation (A.13) is the end-of-period payoff of manager k's personal investment, equation (A.14) is manager k's total wealth at the end of the period from both his compensation and his personal investment, and equation (A.15) is the no short-sale constraint in the stock market. In the compensation contract (A.12), cg and Q are, respectively, the bonus and penalty rate for manager k. 221 Substituting (A.10), ( A . l l ) , (A.12), and (A.13) into (A.14), canceling CK, CK>, WK, and WK>, we get, wk„ = (It - RP) + caDk{7r - RP)+ + ctDk(nd - RP)' + RWK, + 8k (A.16) Rewriting the equation above, yields, wk„ = Dk,{K - RP) + cGDk[(ir - RP)+ + (ci/cg)(itd - RP)~] + RWK, + 6k (A.17) Noting that the third and fourth terms on the right hand of (A.17) are constants, we infer that manager k's problem is equivalent as choosing an optimal portfolio of two risky assets, whose random payoffs are TTI = (TT-RP) (A.18) and nII = (7r-RP)+ + (cl/cg)(irD-RP)-. (A.19) Both assets have a price of 0. Since cg > ci, it is clear that Asset I is preferred over Asset II, and this is a First Degree Stochastic Dominance, for 7f// = ff/ 4- (Q — cg)/cg(7Td — RP)- and (Q — cg) jcg[r: — RP)~ > 0. Thus, any investor with a continuous utility function that is increasing with regard to wealth prefers Asset II over Asset I, and so manager k surely chooses to put all of his endowed wealth into the bonds market, noting that short sales are not allowed in the market. 222 A.1.4 Conclusion From the analysis in this appendix, we can conclude that neither manager q or man-ager k chooses to invest in stock markets with their own personal wealth even if they are allowed to do so, as long as short sales are not allowed. For manager q, the representative B M C manager, he cannot gain anything by switching the risk between his own investment and his compensation contract, and so it is reasonable for him to choose to follow the rule and make no investment with his own wealth. For manager k, the representative U M C manager, it is strictly preferred not to buy any stocks with his own money, for it is always better off for him to hold nu, the equivalent of undertaking risk from his compensation, rather than 7T/, the equivalent of undertak-ing risk from his personal investment. Therefore, limiting managers from making any personal investment in the stock market does not affect the results in our model, and so this chapter does not lose any generality from this assumption. 223 A.2 An Extension to Multiple Assets To study the portfolio choice of managers, we replace the assumption of one single risky asset in our main model with an assumption of two risky assets. With this extension to two assets, we can study managers' optimal portfolio choices and examine how the unbalanced compensation can affect managers' portfolio holdings. A.2.1 Setup There are two risky assets in the stock market, whose end-of-period payoffs are ffi and TT2 respectively, jr-y = jrm + e~i, and Jt2 = Ttm + £2, where 7fm ~ N (/-£m, c^J and £\,£2 ~ A /'(^o, t To)- 1^ a n o - 2^ are identical independent variables, and they are independent of fcm. The price of asset I is Pi, and the price of asset II is P2. Under such a setup, asset I and asset II must have the same price in equilibrium. Otherwise, all managers will purchase more of the asset with a lower price, and hence push its price up. This logic holds no matter managers exhibit risk-averse or risk-seeking behaviour. Therefore, we can denote the price of asset I and asset II at the beginning of the period with the same symbol: P = P i = P2. This setup enables us to focus on the major issue of concern: whether a manager has the incentive to diversify when making portfolio selection for the fund under his management. For a portfolio of a unit of asset I and I — a unit of asset II, it follows a normal 224 distribution JV(/i p, <72), where \xp — pm + (a + (1 — a))po — Pm + a n d a p = <jp + (a 2 + (1 — a) 2)c7o. Taking affi + (1 — a)7f2 one portfolio asset, a manager needs to choose a, which determines the percentage of each risky asset in his portfolio, and Dp, the number of such portfolio to purchase. The price of this portfolio is aP+ (1 - a)P = P. Everything else in this appendix are just as specified in the setup of the main model. A.2.2 Managers with Balanced Compensation Manager q, a representative manager with balanced compensation, faces the following maximization problem: max E{Uq(vjq} = E{—exp(—awq)} Dq^p ,CXq jCq s.t. Wq = DqtPP + Cq (A.20) wq = 8q + c0Dq,p[aQTT;i + (1 - aq)jt2 - RP] (A.21). Dq,p > 0, 0 < aq < 1 (A.22) Where equation (A.20) is the budget constraint, equation (A.21) is the compensation contract for manager q, and equation (A.22) is the no short-sale constraint. Manager q can invest in bonds and a portfolio of the two risky assets in stock market, and he 225 maximizes his personal utility with regard to his end-of-period wealth by allocating fund Q between bonds and a portfolio of the two risky assets. From the standard literature, we know that manager q will choose a well diver-sified portfolio for Fund Q. In addition, manager q will not invest in the market if there are strong bubbles in the market. A.2.3 Managers with Unbalanced Compensation Manager k, a representative manager with unbalanced compensation, faces the fol-lowing maximization problem: max E{Uk(wk} = E{—exp(—awk)} S.t. Wk = DktPP + Ck (A.23) Wk = fa + cgDkiP[akTTi + (1 - ak)jt2 - RP}+ + C[Dk,p[akTTi + (1 - a f c)7f 2-(&i^4~) DktP > 0, 0 < ak < 1 (A.25) Where equation (A.23) is the budget constraint, equation (A.24) is the compensation contract for manager k, and equation (A.25) is the no short-sale constraint. Manager k can invest in bonds and a portfolio of the two risky assets in stock market, and he maximizes his personal utility with regard to his end-of-period wealth by allocating fund K between bonds and a portfolio of the two risky assets. 226 Manager k's utility maximization problem is equivalent as follows: max / ( A p ) ( - ^ - + I ^ T ) (A.26) 0/=,P>o,o<afc<i p h(lp) h(gvy where A p = ^p R P (A.27) lp = A p - ctaDk:Pap (A.28) gp = - A p + cgaDk}Pap (A.29) ° v = \Jo-l + (al + (1 - aky)ol . (A.30) Here f(x) and N(x) are, respectively, the density function and distribution function of a standard normal variable. As shown earlier, function h(x) is increasing, convex, approaches x as x —> oo, and approaches 0 as x —> — oo. Compared with equation (2.10), manager k's simplified objective function in the main model where only one risky asset is available, equation .(A.26) has one more multiplicative term: / (A p ) . The corresponding term in the main model, /(A), does not show up in the simplified objective function (2.10) because A does not contain any decision variables in the single asset model, and so it can be regarded as a positive constant and taken away from the simplified maximization problem (2.10). However, in this model with multiple assets, ak is both a decision variable and a component of A p , which makes the term /(A p ) an indispensable part of the objective function (A.26). 227 Taking the first order condition of equation (A.26) w.r.t. Dkj), yields: Bg<pcg = BitPci (A.32) where Bg,p = l-$(gp) (A.33) BliP = l - * ( i p ) (A.34) *(x) = r f r (A-35) h(x) where lp, gp, and h(x) are as defined in equation (A.28), (A.29), and (2.12). We can see that this result is similar.to Lemma 2. Taking the portfolio as one-asset, we can derive properties of the market similar to those in the main model where there is only one risky asset. The more interesting part in this multiple asset model is the implication on a . manager's portfolio choice. Assuming the boundary condition "0 < ak < 1" is not binding, and taking first order condition of (A.26) w.r.t. ak, we get g - / ( A p ) { ( A ^ ( ^ + ^ ) + ^ > X , h ( 4 - l ) - c s ( ^ - l ) ] } (A.36) where II = f(Ap)(-l/h(lp)-l/h(gp)) (A.37) , A y dAp (RP - pp)(4ak - 2)CT02 M a - = dc7k= 2c-— ( A - 3 9 ) 228 From equation (A.32), the first order condition with regard to DktP, we know that the second term in the middle of equation (A.36) can be cancelled off. Therefore, the first order condition with regard to ak collapses to / ( A p ) ( A X ( ^ + ^ f ) = 0 (A.40) Since /(Ap) > 0 and c ' "ff p f p + C g ^ p f P > 0, (Ap)^ must be equal to 0. From equation (A.38 ), we infer that ak = l/2 when A p = (fj.p - RP)/ap ^ 0. To verify whether ak = 1/2 is the optimal portfolio weight that maximizes man-ager k's utility, we examine the sign of in equation (A.36) as ak takes different values in the range of [0,1]. When A p > 0, g < 0 for ak G (1/2,1], and g > 0 for ak G [0,1/2). Therefore, ak = 1/2 maximizes manager k's personal utility when A p > 0. This means that when there are no strong bubbles in the market, manager k chooses a well diversified portfolio though he purchases more market shares than manager q, a representative manager with balanced compensation, does. However, when A p < 0, g- > 0 for ak G (1/2,1], and | j j < 0 for ak G [0,1/2). In this case, the constraint 0 < ak < 1 is binding, and manager k chooses either ak = 0 or ak = 1 for Fund K's investment portfolio so as to maximizes his own personal utility. This means that manager k holds only one risky asset when the strong form of bubbles exists in the market. 229 A.2.4 A Numerical Explanation In section 2.3.3 where there is only one risky asset, we find that the market price can be decreasing with regard to risk at certain circumstances even when the stock market is in the stage of strong bubbles. This seems to be not so consistent with the inference we have just obtained in the above, which states clearly that U M C managers always choose not to diversify in a market with strong bubbles. The explanation to this lies in the different characteristic between the risk of a diversified portfolio and the risk of a single asset. Under the strong form of bubbles, asset II, 7 T / / as defined in equation (A. 19), has a higher expectation when manager k chooses a single asset rather than a well diversified portfolio. Therefore, although U M C managers may prefer not to have a larger amount of absolute risk, he still prefers to hold a single asset rather than a diversified portfolio owing to a higher level of expected payoff for holding the same amount of absolute risk. To better explain this, we carry out a numerical analysis and present the results in Figure V . In this analysis, the values of parameters are set as follows: a = 0.5, S = 0.5, \± = 1100, r = 0.1, nB = ny = 25, c 0 = cg = 0.05, and Sq = 5k = 1. Also, we set Q = 0.03. To study how the market price changes at different risk levels, we set am = \/0.99CT and ae = \/0.02<7 while allowing a to take values from 50 to 350. Under such a setting, the standard deviation of the portfolio, ap, is just equal to a when we fix the value of ak at 0.5. Here the value of ae is set to be very small relative to crm so that the choice of ak only changes the value of ap a little bit. We allow 230 a to take values between 50 and 350 so as to study a manager's portfolio choice at different risk levels, at some of which the price-risk relationship take different signs from at others. In the first stage of the analysis, we force both U M C managers and B M C managers to hold a well diversified portfolio with ak being fixed at 0.5. The choice of Dp, though, is left to the managers. This is in fact equivalent to the case where only one risky asset is available in the market. We solve out the market price, P, which is as shown in the second diagram from the top in Figure V . Clearly, P is higher than 1000 for all values of a, and P is decreasing with regard to a in the range of [260, 350]. The demand of manager k in equilibrium, Dp, is presented in the top diagram as the line "Dp with ak — 0.5". The demand of manager q in equilibrium is obviously 0 since P > 1000 = f.i/R, which means there are strong bubbles in the market. In the second stage of the analysis, we allow the managers to choose not only Dp, the demand of the entire portfolio, but also a, the components of the portfolio. The market price, however, is fixed to be the same as in the second diagram for each value of a. Under such a setting, we calculate the optimal choice of Dp and ak simultaneously by the representative U M C manager k, and present the results as the line " D p with ak G [0,1]" in the top diagram and the straight line in the third diagram respectively. We can see that the value of ak is always 0 no matter the value of a is above or below 260, which means that U M C manager k chooses not to diversify throughout the range of a G [50,250]. Manager k's demand for the entire 231 portfolio is, however, not always higher than his demand when ctk is fixed at 0.5. Denoting -D P | Q f c -5 as manager k's demand when ak is fixed at 0.5, and £>Piafce[o,i) as manager k's demand when ak is a free choice between 0 and 1, we can see that Dp,ak€[o,i] > Dpiak=0,5 when a < 260, and -D p, a f c e[ 0,i] < DP)Qk=0.5 when a > 260. Since a smaller demand by each U M C manager would cause the equilibrium market price to fall, this is why equilibrium market price in the range of a e [260, 350] decreases as risk increases, noting that ap is larger when ak changes from 0.5 to 0. In short, in the range of cr 6 [260, 350] with c/ being fixed at 0.03, manager k chooses not to diversify because TTJJ has a higher level of expectation when the port-folio is not diversified, and the equilibrium market price decreases with regard to a because manager k prefers to have a lesser amount of absolute risk. The negative relationship between P and a is consistent with manager k's choice of no diversifica-tion. A.2.5 Conclusion From the analysis in this appendix, we conclude that a manager with unbalanced compensation chooses to diversify his portfolio if and only if no strong bubbles exist in the market. When the price is not higher than the risk-neutral price, p/(l + r), manager k does diversify in his portfolio selection though he demands more of the risky assets than manager q because of his lower penalty rate, Q. However, when 232 market price is higher than the risk-neutral price, manager k does not diversify in his portfolio selection. Instead, he puts all of his money in one single asset so as to take full advantage of his low penalty rate. This has important implication in the empirical tests of risk-return relationship. In a market with no strong bubbles, returns are still determined by risky assets' market risk as long as a well diversified market portfolio is available, similar to the case in standard capital asset pricing models. On the contrary, in a market with strong bubbles, returns are no longer determined by the market risk alone, but by the risky assets' total risk instead. 233 A.3 Index-Adjusted Incentive Compensation in North America In North America, the structure of management compensation is different from that in China. First, it is index based. Second, short sales are allowed. The monitoring of managers is much more effective in North America than in China, and so the problem of U M C is far from such a serious problem in North America as in China. However, certain form of unbalanced compensation still exists in North America as well. Generally speaking, the popular incentive fees in North America is based on index-adjusted performance rather than riskfree-rate-adjusted performance. Such index based incentive fees may come directly from compensation contract, or indirectly from other means such as convex relationship between money under management and performance. From now on, we tend to use "asymmetric compensation" to refer to such unbalanced compensation based on index-adjusted performance, and the purpose is just to make it easier to identify what type of un-balanced compensation we are discussing. Recently, there have been very a few studies on the asymmetric compensation in North America. Cuoco and Daniel (2001) use two stocks in their model to analyze the difference between the pricing of index stocks and non-index stocks, with one stock being set as the index and the other being set as an non-index asset. In reality, however, it is likely that a manager's security selection would be more or less restricted 234 to the securities within the benchmark index. Therefore, it would be of practical interest to look into the impact of such asymmetric compensation on the pricing of different components of the index itself, rather than on the pricing of stocks outside the index. In this appendix, we study the impact of management compensation on the pricing of an asset's different parts of risk, namely the market risk and idiosyncratic risk. As usual, market risk refers to the portion of a risky asset's risk that cannot be diversified away in the market, and idiosyncratic risk refers to the portion of risk that is unique to a risky asset and can be diversified away in the market portfolio. Our analysis is also more tailored to empirical tests as well. Brennan (2000) also studies the asymmetric compensation in North America. Different from Cuoco and Daniel (2000), Brennan uses a one period static model rather than a continuous-time model. Brennan also focuses his study on the difference in the pricing of index versus non-index stocks. A.3.1 Setup There are n risky assets in the market, whose end-of-period payoffs are as follows. TT = 0TTm + £ where TXm and all elements of £ are independent of each other, with 7fm ~ N(fxm, CT^J and ii ~ N(0,af),Vi 6 [1, ...,n]. We normalize the vector of Q such that each asset 235 has a beta of 1, and then get = + £i ~ Nipi^al-ra2)^ ie [l,...,n] (A.41) The utility function of each manager is still assumed to be an exponential function of C A R A type. Such a type of function enables us to focus on the risk analysis without interference of wealth effect. It also makes the results much nicer because of the separability of unrelated risk components. The compensation contract for manager q, a representative manager with bal-anced compensation, is wq = Sq + cp9qn + c0(6'qjv - 9qPitm) and the compensation contract for a representative U M C manager, k, is wk = Sk + cp8'kn + cg(9'kn - 9'Jnm)+ + C[{8kn - 9k(3jrm)-In the above, a manager's compensation includes a fixed amount of wage, a propor-tional fee based on the size of the fund, and an incentive fee based on market-adjusted performance. 9 is a vector of investment in each asset. A.3.2 Discussion Substituting (A.41) into the compensation contracts, we get wq = 6q + cp9'qBirm + (cp + c0)(9'qe) 236 and wk = Sk + cp6'Jnm + (cg + cp)(9'ke}+ + (c, + cp)(6'ks)- (A.42) For manager q, his incentive fee is proportional, and so the second variable part of his compensation, (cp + c0){9'qe), has a mean of 0 regardless of the variance. As a risk-averse individual, manager q does not like the second part, and he must choose to diversify in his portfolio choice so as to minimize the risk undertaken. As a side note, it is assumed that the idiosyncratic risk of each asset can be completely diversified. If the ability to diversify was limited in this model, even symmetric compensation alone would also lead to some form of distortion in the market, such as underinvestment by fund managers. However, the situation is different for manager k because of the unbalanced com-pensation based on market-adjusted performance. The market-based incentive com-pensation for manager k includes the last two terms on the right side of equation (A.42), which can be regarded as a special risky asset and called nk here. For asset 7rfc, its mean is non-zero. When cg > ci, the expectation of itk is positive, and its value is increasing at the variance of 9'ki. Such a situation is similar to the analysis in the main text of this chapter, where the riskfree-adjusted incentive fee causes a distortion in the risk attitude of the representative U M C manager. Here the indi-vidual risk of an asset, ii, becomes desirable because of the asymmetric incentive fee based on market-adjusted performance. The smaller Q + cp is relative to cg + cp, the more desirable the idiosyncratic risk of a risky asset is to manager k. This causes a 237 distortion in the risk attitudes of manager k towards the risk of each asset, which in turn has an impact on the pricing of risky securities in equilibrium. In a standard risk-averse world without agency problem caused by incentive com-pensation, the normal notion is that a risky asset's price is determined by its market risk, with its idiosyncratic risk being irrelevant By contrast, a risky asset's idiosyn-cratic risk does matter in this model and can be priced in equilibrium. In fact, when ci + cp is smaller enough relative to cg + cp, there can be a positive relationship between a risky asset's idiosyncratic risk and its price. Meanwhile, the market risk of each asset is still undesirable as usual, for the incentive fee here only distorts the risk attitude towards the idiosyncratic risk com-ponent, not the market risk component. This is a key difference between the pricing behaviour in this model of North American securities markets and in the model of Chinese stock markets in the main text. It indicates that the different pricing of mar-ket risk in China and North America. In Chinese stock markets, only a firm's total risk matters, no matter it is market risk or idiosyncratic risk. Further, the risk can be positively related with price in China because of the unbalanced management com-pensation and the no short-sale constraint. In North America, however, the market price is negatively related with risk, though the idiosyncratic risk may be positively related with market price owing to the risk distortion from asymmetric compensation based on index-adjusted performance. This is very important for empirical tests. 238 A .4 General Equilibrium In Chapter I, Market Segmentation and Ownership Restrictions, we explain how the discrimination among different groups of investors by the monopolistic government can result in a lower price of B-Shares than A-Shares. In this chapter, we study the impact of Chinese managers' unbalanced compensation on asset pricing, which can also partially explain why A-Share prices can higher than B-Share prices. We now discuss how two chapters would be related in a.general equilibrium. The model in Chapter I is partial in the sense that it does not consider Unbalanced Management Compensation (UMC), which is widespread in Chinese stock markets. Meanwhile, the model in this chapter is also partial because it is only a partial equilibrium with exogenous supply. A general equilibrium would consider both the monopolistic government on the supply side and the U M C on the demand side. The required mathematical analysis would be too complex in the general model to solve it here, but it is worth speculating on the form of a more general equilibrium here. General equilibrium involves both domestic investors and foreign investors, who are investing in A-Share market and B-Share market respectively. In the main text of this chapter, we are only studying the situation in A-Share market, and we do not add a subscript A or D to the parameters related to A-Share market. For consistency of notation, we keep all parameters defined earlier in this chapter without adding subscripts. Meanwhile, we do add subscripts to new parameters first defined in this 2 3 9 subsection, especially these parameters related to B-Share market and foreign market. We first add foreign investors and a monopolistic supplier, the Chinese govern-ment. We then solve their problems and characterize a general equilibrium with both monopolist supplier and U M C managers. A.4.1 Foreign Investors With short sales allowed, the impact of unbalanced compensation on asset prices is limited. Meanwhile, unbalanced compensation is also much milder due to significant stock option compensation, active monitoring of fund/company owners, and an overall more sensitive compensation system. Therefore, it is reasonable to claim that U M C is negligible in highly developed capital markets relative to the situation in Chinese stock markets, though we do not deny that a certain form of asymmetric compensation may exist in international capital markets as well. For ease of analysis and without loss of generality, here we assume U M C does not exist in the foreign market. The analysis remains similar if we relax this assumption to a setting where a milder U M C exists in the foreign country than in China. The number of foreign investors is ny, and there is only one risky foreign asset in the foreign market. The foreign asset's liquidating payoff at the end of the period is Ttf ~ N(f.Lf, uj), whose covariance with TT is o\j, and the price at the beginning of the period is given as Pj. Each foreign investor, endowed with an initial wealth of Wj 240 at the beginning of the period, can invest not only in the Chinese market, but also in the foreign market. The bond market is perfectly integrated between China and the foreign country. Each foreign investor, with a C A R A utility function with regard to end-of-period wealth expressed as — exp{—avjf}, allocate his endowed wealth, Wf, among the foreign risky asset, the Chinese asset, and riskfree bonds at the beginning of the period. The objective is, as usual, to maximize his end-of-period utility. The number of shares of the Chinese asset issued to foreign investors is SB- AS mentioned earlier, the shares issued to Chinese investors are called A-Shares, and the shares issued to foreign investors are called B-Shares. Under such a setup and following the steps in the Chapter titled Market Segmen-tation and Ownership Restrictions, one can get the following B-Share price for any given SB: P b = H ~ aSB(r2(l - P%)/nf - 0df{fif - RPf) R 2 2 where P d f = and Bdf = ^ . A .4.2 Domestic Investors, Monopolistic Government and the Equilibrium Domestic investors are just like the investors in the main model of this chapter, or say the U M C and B M C managers. We can simply put the main model, which has been analyzed earlier in this chapter, into this model as the analysis about domestic 241 investors. The government is the single supplier of Chinese shares in the market, and acts as a monopoly. In such a situation, the government has the incentive to discrimi-nate between different groups of investors whenever they have different elasticities of demand, as discussed in another chapter titled Market Segmentation and Ownership Restrictions. Formally, we write such a principal in the following statement. Statement 3 Differential pricing is the optimal choice of the monopoly government if and only if the price elasticity of demand for Chinese shares is different between domestic investors and foreign investors. From (2.25), (A.43), and e^Si) = - ^ V ^ p , the definition of price elasticity of demand, we can see that foreign investors' elasticity of demand is different from Chinese (domestic) investors's elasticity of demand. Therefore, based on the state-ment above, Chinese government has the incentive to impose ownership restrictions and discriminate between domestic and foreign investors. As for the relationship between A-Share and B-Share supply in the market, we can infer the following result. Under the conjecture j£(S) < — |§§(>?), the optimal supply of A- and B-Shares are still positively correlated. A sufficient condition for §^r(S) < —\%{S) is j£(S) < 0, which means the marginal impact on A-Share price by increasing supply decreases as the absolute level of A-Share supply increases. 242 A .5 Proofs A.5.1 Properties of Several Mathematical Functions Property 1 Define h(x) = f(x)/(l — N(x)), where f(x) and N(x) are, respectively, the probability density function and cumulative distribution function of a standard norm,al variable, then h'(x) > 0, h"(x) > 0, h(x) —> x as x —> oo, h(x) —• 0 as x —> —oo Proof: Hazard rate function, h(x), is well-known in Reliability Theory. See Statistics references for details of proof. Proof Complete. Property 2 Define $(x) = x/h(x), where h(x) = f(x)/(l - N(x)) as defined in Property 1, then $(x) < 1, and V(x) = > 0. Proof: Define M(x) = l/h(x), then dM{x) dx h'(x) WW < 0 Meanwhile dM{x) dx 1 - N(x) x -N'(x)f(x)-[1-N(x)]f'(x) lf(x))2 and substitute f'(x) — —xf(x) and N'(x) = f(x) into above, we have 0 > dM{x) = -\f(x)}2-[l-N(x)}[-xf(x)} dx [ / i » ] 2 = -l + x[l-N(x)]/f(x) (A.44) 243 Since <J>(x) = x/h(x) = x[l - N(x)}/f(x), so $(x) < 1. Next we prove ty(x) = d^d^ > 0. From h'(x) > 0 and h(x) —> x as x —> oo, we can infer that /i'(x) —> 1 as x —> oo. Since h"(x) > 0, /i'(x) is increasing with regard to x, and so 0 < h'(x) < 1 Vx < co. Therefore, 1 > $(x) > h'(x)$(x) (A.45) Taking derivative of 3>(x) w.r.t. x, get T . . <9$(x) 1 , x Since /i(x) > 0 from definition and 1 — h'(x)j^pj > 0 from equation (A.45), we have \I/(x) > 0. Proof Complete. A.5.2 Proof of Lemma 1 Proof: Assuming a random variable x follows a normal distribution N(/j,,a2), we get f ° ° 1 ( x - M ) 2 Ex>o{ex} = / e x - = ^ e - ^ H d x (A.46) 70 V27T<7 1 f°° 1 7o 1 ^ _ „ ^ _ , ( T 2 x + 2 M ( 7 2 + ( 7 4 _ 2 M < r 2 _ C T 4 2 ^ rfx ^ T T C T u+**/2 f°° 1 - ( - " T 2 ) 2 ^ a ; - M - g 2 = e^+a 1 1 I . , e i? 2 < / 2 7 T C T CT e^/2 j _ L e - 4 dz where N(-) is the cumulative distribution function of a standard normal vari-able. 244 Similarly, we get Ex<0{ex} = f° e x - L - e - i ^ ) dx = 1 2 N {-^ - a) (A.47) 7_oo \/2ira cr Since E{Uk(wk} = E{-exp(-awk)} = E{-exp{-a[6k + cgDk{fk - RP)+ + ClDk(lr - RP)~}}} = -e~a5k E{-acgDk{TT - RP)+ - actDk(n - RP)"} = -e-aSk E^RP>0{exp{-acgDk(H - RP)+}} -e-aS» E^RP<0{exp{-aClDk(iv ~ RP)-}}, (A.48) and 7 f — RP follows a normal distribution N(u — RP, a2), we get the following result by substituing (A.46) and (A.47) into (A.48) E{Uk(wk)} = -e-aS* {/(A)( 1 + 1 )} h(A — ciaDka) n( — A + cgaDka) where f(x) and N(x) are, respectively, the density function and distribution function of a standard normal variable, and A = ^ — — (A.49) cr « . ) - (A.50) Further, e~aSkf(A) is positive, and / (A) is independent of Dk, so is equivalent to miwE{Uk(wk} -1 -1 max — — ——r + Dk>o h(A — c\aDka) h(—A + cgaDka) Proof Complete. 245 A.5.3 Proof of Lemma 2 Proof: Define Mill's Ratio ... , 1-N(x) then rewrite objective function (2.10) as max - M ( A - ciaDka) - M ( - A + cQaDka) (A.51) Noting that M'(x) = xM(x) — 1, taking first order condition of (A.51) w.r.t. Dk, yields [ - l + ( A - q a P f ctT ) M ( A - C i a D f c ^ = 0 Rearranging, get [1 - $ ( - A + c9aD f ccr)]c5 = [1 - $(A - ciaDka)]ci where <J>(x) = h(x) Proof Complete. 246 A . 5 . 4 P r o o f of P r o p o s i t i o n 1 First, many results later in this section are quite cumbersome in notation, and so for simplicity, we define a list of short notations as follows. IA-9 A-IA+ 9A+ Cg/O C//o NB/u = (1 + Ci/0NB/U)A ~ ciaSa/nu = -(l + Cg/0NB/u)A + CgCiSa/nu = A — ciaSa/njj = (1 + Ci/0NB/U)A - ciaSa/nu c 0 Ei c 0 nB (A.52) (A.53) (A.54) (A.55) (A.56) (A.57) (A.58) Now we give a brief proof for Proposition 1. Proof: For q G (0, cg], we have dP _ a 1 - $(gA-) + {-Cg/QNB/UA + cgaSa)^{lA-)/m2 dm ~ R (1 + Q / O A V / W A - ) + m(l + Cg/0NB/u)*(gA-) when A > 0, and, when A < 0, dP cr 1 * G ? A + ) + ^ g « ^ A + ) > q > 0 (A.59) dm R V(IA+) + m<b{g&+) (A.60) where tf (x) = d$(x)/dx > 0 (A.61) 247 Further, from the implicit pricing function, we have u - —Zg—aSa2 P - nBcg+nuc0 a s m ^ l (A.62) R and P —> oo as m —> oo (A.63) Proof Complete. .5.5 Proof of Proposition 2 Proof: When the values of m and a satisfy the inequality —A — aSacg/nrj < 0, P is strictly decreasing with regard to CT. Mathematically, | -A-aSac./nu Q A > Q ^ = (A-64) Meanwhile, when m and CT satisfy —A — aSacg/nu > 0, P is increasing with regard to CT. Mathematically, dP = - A - a5CTc,/n^ Q _ <9CT Here = c^ ( f f A _) + c 2 ^ ( l A - ) C" cg(l + CG/0NB/u)^(gA^ + Cl(l + CL/0NB/u)^(l^) ' 1 and C9~ cgnSA+)+clnA+) • (A-67) where <&(•) is as defined in (A.61). In addition, we have q < CQ < cg and Q/(1 + CI/QNb/u) <Cv< cg/(l + CG/0NB/U). Proof Complete. 248 A.5.6 Proof of Proposition 5 Proof: For cg 6 [0, Q], the lower the value of m = c g / q , or say the higher the capital gains tax, the lower the market price, or say, the higher the Equity Premium. Mathematically, dP/dm > 0, for OP a 1 - $(<7A-) + (-Cg/0NB/UA + cgaSa)^{lA-)/m2 dm, R(l + Cl/0NB/u)$(lA-) + m(l + Cg/0NB/U)*(g±. when A > 0, and, when A < 0, > 0 (A.68) BP _ ffi-*(0A+) + ^ * ( i A + ) CnO-ScT . V l l j . ] > 0 (A.69) dm R ^(lA+) + m^(gA+) where tf (x) = d${x)/dx > 0 (A.70) Further, it is straightforward that c^co aS(J2 D , n B C g + n u C 0 ^ m ^ x (A.71) and R P - » m a x { ^ , 0 } a s m - » 0 (A.72) Proof Complete. 249 Appendix B Appendix of Chapter III B.1 The 1997 Announcement of Crack Down On May 22, 1997, the Securities Commission of the State Council, the People's Bank of China and the State Economic and Trade Commission issued a regulation to pro-hibit State-owned enterprises from speculating on the stock market and to ban listed companies from using bank credit capital and funds raised from stock issuance to spec-ulate in stocks. The following is our translation of part of the original announcement published in China Security News, the state-owned official newspaper for securities news. This translation is the closest English version of the original one to the best of our understanding. The announcement itself may also offer a glimpse of the rampant U M C problems in Chinese stock markets. 250 SOEs and Listed Companies Prohibited from Stock Speculation by the SRC and Other State Regulation Agencies Securities Regulation Commission of the State Council (SRC), The People's Bank of China, and the Economic and Trade Commission collec-tively issue an order to stop State Owned Enterprises (SOEs) and Listed Companies from speculating in the stock markets. They point out that Chinese securities markets are still in the early stage of development, and there are serious problems of rampant speculation and violations of secu-rities regulations. To secure the social stability and maintain the healthy development of socialist market economy, it is a paramount task of the regulation agencies to crack down on illegal stock trading and suppress the over speculation in stock markets. Recently, there has been a sustained flow of capital from state-owned commercial banks to the stock markets through a variety of channels. Some SOEs and listed companies invest in the stock markets with bank loans. Some listed companies speculate in stock m,arkets with capital raised from stock markets, which is supposed to be used in corporate operations and productions. Some SOEs invest in stock markets with capital allocated for further corporate development and expansion. Such a situation not only boosts the stock speculations in security markets, but also puts the state-owned capital at high risk and 251 jeopardizes the security of state-owned assets. The illegal trading activi-ties by SOEs and listed firms must be prohibited so as to maintain orders in the stock markets. Without such a prohibition, Chinese stock markets cannot function well as the fund-raising channel for SOEs, or facilitate the transition of Chinese economy to a healthy market economy. The following rules must be followed: ... The details of the rules above will be. clarified and carried out by cor-responding departments of the State Council. 252 

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