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Essays on institutional investors and asset pricing Zhang, Tianyao 2019

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ESSAYS ON INSTITUTIONAL INVESTORS AND ASSET PRICINGbyTianyao ZhangB.Math, University of Waterloo, 2013B.B.A., Wilfrid Laurier University, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Business Administration)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)July 2019© Tianyao Zhang, 2019The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the dissertation entitled:Essays on Institutional Investors and Asset Pricingsubmitted by Tianyao Zhang in partial fulfillment of the requirements forthe degree of Doctor of Philosophyin Business AdministrationExamining Committee:Ron Giammarino, Business AdministrationCo-supervisorAdlai Fisher, Business AdministrationCo-supervisorMurray Carlson, Business AdministrationSupervisory Committee MemberRalph Winter, Business AdministrationUniversity ExaminerVadim Marmer, Vancouver School of EconomicsUniversity ExaminerAdditional Supervisory Committee Members:Russell Lundholm, Business AdministrationSupervisory Committee MemberSupervisory Committee MemberiiAbstractIn this thesis, I study the asset pricing aspect of institutional investors and their ability to providefinancial services to households. The thesis consists of three essays.In the first essay, I theoretically investigate how institutional investors with different holdinghorizons allocate capital and the related asset pricing implications. I propose a model in whichsome institutions have shorter holding horizons, defined as short-term institutions, than other in-stitutions, i.e. long-term institutions. The optimal portfolio of short-term institutions tilts towardsspeculative stocks that experience more volatile future demand shocks, which create transient trad-ing opportunities. The current demand from short-term institutions increases the prices of thesespeculative stocks and reduces their buy-and-hold returns, making them less desirable for long-term investors. The model provides predictions relating a stock’s short-term institutional owner-ship, trading opportunity, and expected return.In the second essay, I test the predictions of the first essay. Empirically, short-term institutions,identified as high-turnover institutions, invest more in stocks with higher CAPM beta, higher id-iosyncratic volatility, and lower buy-and-hold abnormal returns. The difference in the buy-and-hold abnormal return between stocks with least and most short-term institutional investors is morethan 3% per year. Stocks with more short-term institutional investors also provide more tradingopportunities, allowing short-term institutions to make more trading profits. Their trading prof-its increase with market sentiment. This essay demonstrates that the desirability of investing inspeculative stocks depends on an institution’s holding horizon.The third essay examines the well-established negative relation between expense ratios andfuture net-of-fees performance of actively managed equity mutual funds. I show that this rela-tion is an artifact of the failure to adjust a fund’s performance for its exposures to the profitabilityand investment factors. High-fee funds exhibit a strong preference for stocks with low operatingprofitability and high investment rates, characteristics associated with low expected returns. Aftercontrolling for exposures to profitability and investment factors, I find that high-fee funds signif-icantly outperform low-fee funds before fees and perform equally well net of fees. These resultssupport the theoretical prediction that skilled managers extract rents by charging high fees.iiiLay SummaryThis thesis contains three essays that study institutional investors. In the first and second essays, Itheoretically and empirically investigate how institutional investors with different holding horizonsallocate capital. I show that short-term institutions allocate more capital to speculative stocks inorder to make more trading profits. The demand from short-term institutions reduces the buy-and-hold returns of speculative stocks, making them less desirable to long-term institutions. My secondessay confirms the main empirical predictions of the first essay. In the third essay, I examine thefee-performance relationship among actively managed mutual funds. The puzzling negative fee-performance relationship found in the prior literature can be resolved by controlling a mutual fund’sexposures to profitability and investment factors in the performance evaluation. After controllingfor these two factors, I find that high-fee mutual funds deliver better performance before fees,consistent with the theoretical prediction of an efficient asset management industry.ivPrefaceThe first two essays of this thesis (Chapters 2 and 3) are based solely on my own research. Thethird essay (Chapter 4) is based on the joint work with Dr. Mikhail Simutin (University of Toronto)and Dr. Jinfei Sheng (University of California, Irvine). In the joint project, all authors worked onevery aspect of the project and were in close collaboration in each stage. We contributed equallyin the project.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Institutional Holding Horizon and Portfolio Choice: Theory . . . . . . . . . . . . . 32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Theoretical results and predictions . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Trading Opportunities and the Portfolio Choices of Institutional Investors . . . . . 273.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Hypothesis development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3 Data, measurement, and motivating evidence . . . . . . . . . . . . . . . . . . . . 313.4 Empirical findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Cheaper is Not Better: The Superior Performance of High-Fee Mutual Funds . . . 624.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64vi4.3 Mutual funds fees and investment styles . . . . . . . . . . . . . . . . . . . . . . . 664.4 Mutual fund fee-performance relation . . . . . . . . . . . . . . . . . . . . . . . . 684.5 Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.6 Robustness and additional results . . . . . . . . . . . . . . . . . . . . . . . . . . 734.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92A Appendix to Chapter 2: Proof of Propositions . . . . . . . . . . . . . . . . . . . . . 99B Appendix to Chapter 3: Variable Definition . . . . . . . . . . . . . . . . . . . . . . 112C Appendix to Chapter 4: Variable Definition . . . . . . . . . . . . . . . . . . . . . . 113viiList of Tables3.1 Summary statistics of institutions. . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2 Summary statistics of stocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3 The cross section of short-term ownership. . . . . . . . . . . . . . . . . . . . . . . 503.4 Portfolio sorts based on ex ante short-term ownership. . . . . . . . . . . . . . . . . 513.5 Cross-sectional abnormal returns of stocks. . . . . . . . . . . . . . . . . . . . . . 523.6 Asymmetry in return predictability. . . . . . . . . . . . . . . . . . . . . . . . . . . 533.7 The cross section of trading profits of institutions. . . . . . . . . . . . . . . . . . . 543.8 Trading profit of institutions with medium holding horizon. . . . . . . . . . . . . . 553.9 Time varying trading profit: sentiment index. . . . . . . . . . . . . . . . . . . . . 563.10 Time varying trading profit: IPO return. . . . . . . . . . . . . . . . . . . . . . . . 573.11 Trading profits of institutions excluding micro-cap stocks. . . . . . . . . . . . . . . 583.12 Trading profit of institutions controlling for additional factors. . . . . . . . . . . . 593.13 Trading profit of institutions excluding the dotcom bubble. . . . . . . . . . . . . . 603.14 Cross-sectional abnormal return and liquidity risk. . . . . . . . . . . . . . . . . . . 614.1 Summary statistics for fund and portfolio characteristics. . . . . . . . . . . . . . . 794.2 Fund fees and characteristics of stock holdings. . . . . . . . . . . . . . . . . . . . 804.3 Mutual fund fee-performance relation: Panel regressions. . . . . . . . . . . . . . . 814.4 Fund fees and loadings on the investment (CMA) and profitability (RMW) factors. 824.5 Fee-performance relation and different fund characteristics. . . . . . . . . . . . . . 834.6 Fund fees and characteristics of stock holdings: Investor sophistication. . . . . . . 844.7 Fund fees and the valuation cost of stock holdings. . . . . . . . . . . . . . . . . . 854.8 Textual analysis of mutual fund prospectus. . . . . . . . . . . . . . . . . . . . . . 864.9 Robustness check about fund fees and characteristics of stock holdings. . . . . . . 874.10 Robustness of the mutual fund fee-performance relation: additional models . . . . 884.11 Robustness of the mutual fund fee-performance relation: non-linearity test . . . . . 89viiiList of Figures2.1 Cross-sectional effect of speculative demand . . . . . . . . . . . . . . . . . . . . . 222.2 Economies with different fractions of short-term arbitrageur . . . . . . . . . . . . 232.3 Economies with different degrees of short selling constraint . . . . . . . . . . . . . 242.4 Economies with different degrees of limit to arbitrage. . . . . . . . . . . . . . . . 252.5 Asymmetrical response to speculative demand shock. . . . . . . . . . . . . . . . . 263.1 Average institutional turnover ratio vs. stock characteristics. . . . . . . . . . . . . 443.2 Average institutional turnover ratio by sector. . . . . . . . . . . . . . . . . . . . . 453.3 Asymmetry in return predictability. . . . . . . . . . . . . . . . . . . . . . . . . . . 463.4 Buy-and-hold return and rebalanced return. . . . . . . . . . . . . . . . . . . . . . 474.1 Characteristics of stock portfolios of funds charging different fees. . . . . . . . . . 764.2 Fund fees and time series dynamics of fund portfolio characteristics. . . . . . . . . 774.3 Mutual fund fee-performance relationship. . . . . . . . . . . . . . . . . . . . . . . 78ixAcknowledgementsI am greatly indebted to many people during my years in the Ph.D. program at the University ofBritish Columbia. First and foremost, I would like to thank Ron Giammarino (my co-supervisor),Adlai Fisher (my co-supervisor), and Murray Carlson (supervisory committee member) for theirteaching, guidance, and support. They have always inspired me to think deeper about the economicforces behind a phenomenon. They have also guided me to the right direction at many criticaljunctions of my Ph.D. study. Their support and encouragement are instrumental in helping mefinish this thesis and advance my career.Besides my committee members, I also benefited tremendously from faculty members at UBC,who have always kept their doors open. I thank Lorenzo Garlappi, Jack Favilukis, Kai Li, Car-olin Pflueger, Ali Lazrak, Jan Bena, Hernan Ortiz-Molina, Elena Simintzi, Will Gornall, MarkusBaldauf, Georgios Skoulakis, Alberto Teguia, and Russell Lundholm for their thoughtful feedbackabout my research and sound advice at various stages of my study. I would also like to thank myco-author Mike Simutin from the University of Toronto for his wisdom and encouragement.At UBC, I am very fortunate to be surrounded by a group of passionate peers, from whom Ihave learned so much. A special thanks goes toward Jinfei Sheng, with whom I worked on manyinteresting projects and traveled to many conferences together. I would also like to thank TingXu, Guangli Lu, Kairong Xiao, Charles Martineau, Alex Corhay, and Sheng-Jun Xu for countlesstimes of help.I cannot complete my Ph.D. journey without the companionship of my friends. I would like tothank Jason Li, a dear friend since high-school, for helping me settle down in Vancouver when Ifirst came to this city. I would also like to thank fellow students in HA 391, who have made mylife on campus much more enjoyable.I would like to acknowledge the financial support provided by UBC and the Social Sciencesand Humanities Research Council of Canada.Finally, I want to say “thank you” to my parents. They have sacrificed so much for me andgiven me so much. No words can express my gratitude to their unconditional love. I dedicate thisthesis to them.xThis thesis is dedicated to my mother and father.xiChapter 1IntroductionThis thesis is a collection of three essays that study different aspects of institutional investors. In-stitutional investors are organizations that pool capital and invest in securities on behalf of house-holds. They play two important functions in the economy. First, institutional investors are domi-nant players that determine the prices of many assets in the financial market. Second, institutionalinvestors are providers of asset management services to households. Researchers in the field offinance are deeply interested in studying how institutional investors set asset prices and whetherthey provide valuable services to households. The ensuing chapters contribute to the understandingof these aspects.Chapter 2 of the thesis theoretically investigates how an institutional investor’s ability to tradefrequently determines its portfolio choice and the related asset pricing implications. Institutionalinvestors differ significantly in how frequently they trade, which translates into different holdinghorizons. Some institutions trade in and out of their positions frequently, while others practicelong-term buy-and-hold strategies. In terms of portfolio choice decisions, institutions with differentholding horizons prefer to invest in different types of stocks. Based on these observations, I developa theoretical model to understand this phenomenon. My model answers both the portfolio choicequestion and the asset pricing question in a single framework. On the one hand, the model givesrise to predictions on how an institution’s holding horizon affects its portfolio choice given thedynamics of stock returns. On the other hand, the model shows how stock returns are determined inan economy with both long-term and short-term institutions acting optimally. An important resultis that stocks that provide more trading opportunities are held by more short-term institutions,whose demand reduces the buy-and-hold returns of these stocks. The model provides testablepredictions relating a stock’s short-term institutional ownership, trading opportunities, and buy-and-hold returns. The model also gives rise to various other empirical predictions.Chapter 3 of the thesis empirically tests the predictions of the model developed in Chapter 2.The empirical focus of the chapter is on the cross-section of stocks. I show that in the cross section,short-term institutional investors prefer to invest in younger and more volatile stocks, despite thesestocks having lower buy-and-hold alphas, e.g. CAPM and Fama and French (1993) three-factoralphas. I also show that from stocks that short-term institutions overweight, short-term institutionsgenerate more trading profit, which cannot be replicated by long-term institutions. These findingsare consistent with the theoretical predictions of Chapter 2. Stocks in the cross section have differ-1ent amounts of trading opportunities. Short-term institutions overweight stocks that provide moretrading opportunities, bidding up their prices. Subsequently, short-term institutions make moretrading profits from these stocks by selling them at better prices. Long-term institutions optimallyunderweight stocks with more trading opportunities, because these stocks have lower buy-and-holdreturns. By examining stocks that short-term institutions prefer to hold, I can identify the ones thatprovide more trading opportunities.Chapter 4 of the thesis is based on my joint work with Jinfei Sheng and Mikhail Simutin,which focuses on the value of institutional investors to households. It investigates the effectivenessof different benchmark models in evaluating the performance of active mutual funds. A previouslydocumented puzzle in the mutual fund literature is why funds that charge higher fees do not de-liver better before-fee performance than funds charging lower fees (see, Carhart, 1997;Wermers,2000;Fama and French, 2010). This negative fee-performance relationship is in stark contrast withthe rational benchmark model of Berk and Green (2004). The puzzle raises serious concerns forthe efficiency of the mutual fund industry and has promoted many investors to avoid high-fee mu-tual funds. In Chapter 4, we show that this puzzle is largely an artifact of the failure of traditionalasset pricing models, e.g. CAPM, Fama and French (1993) Three-Factor, and Carhart (1997) Four-Factor, to account for the lower expected return of certain types of stocks, namely stocks with highasset growth rate and low profitability. Using the recently developed Fama and French (2015)Five-Factor model, we demonstrate that high-fee funds perform significantly better than low-feefunds before deducing fees and perform equally well after fees.All three essays are written to be self-contained. I provide a more detailed exposition of theresearch question, literature review, and research methodology in the introduction section of eachessay separately.2Chapter 2Institutional Holding Horizon and PortfolioChoice: Theory2.1 IntroductionAfter decades of rapid growth, institutional investors currently manage more than 70% of the U.S.equity market (Ben-David et al., 2019). Despite being labeled as a single group, their investmentstrategies differ significantly along many dimensions. One striking difference is their holdinghorizon or, equivalently, how frequently they trade. On one end of the spectrum, pension fundsand index funds buy and hold each stock for a long period of time. On the other end, active mutualfunds and hedge funds have short holding horizons and trade frequently. The holding horizonamong institutions of the same legal class also varies substantially.Financial economists have long been puzzled by the heterogeneity of investment strategiesadopted in the real world (Sharpe, 1991; French, 2008). Many asset pricing models imply that in-vestors follow similar strategies, such as buying and holding the market portfolio (Sharpe, 1964).Why would some institutions trade frequently, while others practice long-term investing? Do insti-tutions with higher trading frequencies face a different investment opportunity set from institutionsthat just buy and hold? What is the market equilibrium when both long-term and short-term insti-tutions co-exist and interact with each other? The answers to these questions are not only relevantto the management of trillions of dollars, but also shed light on the determination of asset prices.This chapter develops a model to address these questions. I consider long-term institutions asinvestors that are constrained to buy and hold, such as passive investors, while short-term institu-tions are ones that can trade frequently, i.e. active investors.1 My model answers both the portfoliochoice question and the asset pricing question in a single framework. On the one hand, the modelgives rise to predictions on how an institution’s holding horizon affects its portfolio choice giventhe dynamics of stock returns. On the other hand, the model shows how stock returns are deter-mined in an economy with both long-term and short-term institutions acting optimally. The modelis useful in analyzing a series of questions about the relationship between a stock’s expected return1Some prior literature assumes that short-term investors are forced to liquidate for exogenous reasons, for example,Amihud and Mendelson (1986), Froot et al. (1992), and Cespa and Vives (2015).3and its institutional ownership structure. The model is also useful in designing benchmark indexesfor different types of institutional investors.One direct application of the model is to provide a rational explanation of a recent empiricalpuzzle. In particular, Borochin and Yang (2017) and Lan et al. (2015) document that stocks pri-marily held by short-term institutional investors have lower buy-and-hold abnormal returns thanstocks with more long-term institutional investors. Their interpretation is that long-term institu-tions have better information about the long-run performance of stocks, while short-term institu-tions lack such information. Hence, long-term institutions are able to consistently pick high-returnstocks, whereas short-term institutions end up holding low-return stocks. If this is the case, it isstill puzzling why short-term institutions do not tilt their portfolios toward high-return stocks bymimicking the strategy of long-term institutions, given that the holdings of long-term institutionsare publicly observable.2 My model resolves this puzzle. It shows that even if short-term insti-tutional investors understand that long-term institutions overweight high-return stocks, short-terminstitutions are still willing to overweight low-return stocks. In other words, the empirically ob-served asset allocation decision of long-term and short-term institutions is a rational equilibriumoutcome.The main elements of the model are the presence of speculative demand shocks that drive stockprices away from their fundamental values and limits to arbitrage that allow mispricing to exist inequilibrium. When a speculative demand shock causes a stock to be mispriced, short-term andlong-term institutions respond to the shock differently. Short-term institutions can make tradingprofits from the shock by rebalancing their portfolios at once, while long-term institutions just buyand hold. When there are limits to arbitrage, especially short-selling constraint, it is optimal forshort-term institutions to overweight stocks with greater exposures to speculative demand shocksin advance.The theoretical literature since Miller (1977) has demonstrated that in the presence of short-selling constraints, when mispricing happens, a stock becomes on average overpriced.3 As high-lighted by Scheinkman and Xiong (2003), the occurrence of mispricing allows the existing ownersof a stock to sell it at a favorable price, similar to exercising a resale option. Short-term institutionsbenefit more from the resale option than long-term institutions. Hence, in equilibrium, short-terminstitutions are willing to pay a premium for stocks with larger exposure to speculative demandshocks comparing to long-term institutions.2Institutional investors have to disclose their equity positions within 45 days of each calendar quarter end. Privateinformation about a company’s long-term performance, if it exists, will become public when long-term institutionalinvestors reveal their holdings.3Studies that explore the implications of short-selling constraint on mispricing include Harrison and Kreps (1978),Abreu and Brunnermeier (2002; 2003), Duffie et al. (2002), Scheinkman and Xiong (2003), Hong et al. (2006),Stambaugh et al. (2015), and Hong and Sraer (2016).4The asset pricing effect of the excess demand from short-term institutions is to raise the pricesof speculative stocks, reducing their long-run buy-and-hold returns. It appears that short-terminstitutions invest more in low-return stocks, when, in fact, they are prepared to sell these stocks inthe likely event of a price appreciation driven by future speculative demand. The commonly usedmethod of comparing stock-picking skill based on the covariance of an investor’s portfolio weightsand the buy-and-hold returns of stocks does not fully capture the investor’s trading profit. This islikely to bias against short-term institutions due to the negative correlation between a stock’s buy-and-hold return and trading opportunity. Short-term institutions tilt more towards stocks with moretrading opportunities and lower buy-and-hold returns.I build a parsimonious model to illustrate the mechanism and to formulate additional predic-tions. I model stocks with heterogeneous exposure to the speculative demand from noise traders,who cause stock prices to deviate from their fundamental values. In the model, I assume that long-term institutions construct their portfolios before noise traders arrive and are unable to rebalancein the interim period. Only short-term institutions trade against noise traders, while long-term in-stitutions buy and hold their positions. Short-term institutions’ ability to trade comes at the costof a lump-sum investment in the beginning of the model. A fraction of institutions endogenouslychoose to pay for such ability.My model provides several empirical predictions, relating an asset’s expected return, ownershipstructure, volatility, and trading profit. In particular, consistent with the existing evidence, stockswith more short-term institutional investors have lower buy-and-hold abnormal returns. My modelshows that these stocks are more likely to become mispriced. When they become mispriced, theyare more likely to be overpriced because of the short-selling constraints. Short-term institutionsmake more abnormal returns through active trading. The model predicts that their trading profitslargely come from stocks they ex ante overweight. Thus, in equilibrium, it appears that the morethey invest in a stock, the more profit these institutions generate from trading that stock. Thisprediction does not contradict the intuition that more competition leads to lower profit, because inthis setting, more competition is associated with more trading opportunities.The model also highlights the different impact of long-term and short-term institutional demandon stock returns. When exogenous shocks cause long-term or short-term institutions to invest morein a stock, both types of institutions increase the stock’s current price and reduce its future return.However, exogenous increase in long-term demand also increases the stock’s future return volatil-ity, while exogenous increase in short-term institutional demand reduces volatility. The opposingeffects on return volatility help to distinguish whether certain type of institutions improve or harmmarket price efficiency. These predictions can be tested with instruments that cause exogenousvariations in short-term or long-term ownership of a stock. Finally, my model provides economy-wide predictions. It shows that the dispersion in short-term institutional ownership across stocks5is positively associated with the dispersion in the expected stock returns and the level of presenceof trading opportunities in the economy. These predictions can be tested over time or in differentmarkets.2.1.1 Literature reviewThis chapter builds on the insights developed in the literature on speculation and limits to arbitrage.The central theme of this literature is that rational arbitrageurs face costs, risks, or other constraintsthat prevent them from immediately trading away any price inefficiencies. Pioneering studies inthis area include Miller (1977), Harrison and Kreps (1978), De Long et al. (1990), and Shleiferand Vishny (1997). More recent studies that emphasize the role of short-selling constraints inexplaining the dynamics of mispricing include Abreu and Brunnermeier (2002; 2003), Duffie et al.(2002), Scheinkman and Xiong (2003), Brunnermeier and Nagel (2004), Hong et al. (2006), andNutz and Scheinkman (2018). Nagel (2005), Stambaugh et al. (2012; 2015), and Hong and Sraer(2016) investigate how short-selling constraints are related to well-known asset pricing anomalies.I add to this literature by modeling sophisticated investors with heterogeneous trading capacitiesand deriving predictions relating their demand to stock returns. My model is useful in connectingthe theory of constrained arbitrage with empirical data on the holdings of institutional investors.This chapter also relates to the theoretical literature on active investing. Sharpe (1991) suggeststhat in total, active investors must hold the market portfolios, which means that the aggregate ofactive investors cannot beat the market. Stambaugh (2014) studies the time-series trend of theamount of active investing in the US and highlights the fact that the presence of noise trading isan important determinant of the scale of active institutional investors. Pástor et al. (2017) studiesthe time series relationship between a mutual fund’s turnover ratio and its future performance.They find that the more a fund manager trades, the more abnormal return he or she generatessubsequently. This paper contributes to the literature by showing that when noise traders andshort-selling constraints are present in the market, neither active nor passive institutions wouldhold the market portfolio. Active institutions would want to tilt towards stocks with more noisetrading.Finally, this chapter contributes to the growing literature that investigates the heterogeneouspreferences among institutional investors. Basak and Pavlova (2013) present a model to illustratethat when institutions care about their performance relative to a certain index, they overweightassets that constitute their benchmark index. Hanson et al. (2015) show that traditional banksprefer to hold illiquid assets with low risk because they qualify for deposit insurance, while shadowbanks prefer to own liquid assets because they are subject to runs. Amihud and Mendelson (1986)show that when investors are forced to hold a stock short-term, these short-term investors preferto hold stocks with lower bid-ask spreads. Pastor et al. (2017) studies how size and investment6skill of a mutual fund relate to its portfolio liquidity. My paper contributes to this literature bydemonstrating that institutions with different holding horizons prefer to invest in different types ofstocks depending on the stock’s exposure to speculative demand shocks.2.2 ModelIn this section, I develop a parsimonious model to study the mechanism that drives the asset allo-cation of short-term and long-term institutions. The model also allows me to investigate the for-mation of asset prices, which provides several empirical predictions relating a stock’s short-termownership to its expected return, return predictability, and trading opportunities.2.2.1 Model setup: assetsThe economy has three dates: t =0, 1, and 2. There are N risky securities, indexed by i= 1, 2, ..., N,with a final pay-off vi2 realized at t = 2. There is one risk-free security with risk-free rate normal-ized to 0. The supply of every risky security is fixed to be 1 at t = 0, and the supply of the risk-freesecurity is perfectly elastic. The model does not feature any private information. Uncertaintieswith respect to the risky pay-off are resolved in the last period.In the baseline model, risky assets in the cross section are ex ante identical in all aspects withone exception. I assume that risky securities differ in their exposure to speculative demand shocks.At t = 1, a group of uninformed investors, which I call noise traders, arrive with a random demandui for stock i. I refer to ui as a speculative demand shock, since it is unrelated to the fundamentalvalue of the stock. I assume ui to be normally distributed with mean zero and variance σ2ui [i.e. u∼N(0,σ2ui)]. The volatility σui is stock specific and measures the intensity of the potential speculativedemand shock to stock i. In the model, the covariance structure of speculative demand shocks doesnot affect the equilibrium, since institutional investors are assumed to be risk neutral. Investigatingthe effect of correlated speculative demand shocks in a risk-averse setting is an interesting area offuture research.Noise traders in this model, sometimes also known as liquidity traders, provide a reason forinstitutions to trade. Without them, the static allocation at t = 0 is Pareto optimal and no tradeoccurs at t = 1. The presence of noise trading is a standard modeling technique in studies ofmispricing and is a realistic feature of the stock market. Several authors model the behavior ofnoise traders based on micro-founded behavioral biases, such as overconfidence (Daniel et al.,1998), bounded rationality (Hong and Stein, 1999), style investing (Barberis and Shleifer, 2003),and overextrapolation (Alti and Tetlock, 2014).My cross-sectional predictions are based on variations in a stock’s exposure to speculative de-mand shocks. It is natural to imagine that different stocks have different degree of noise trading.Empirical evidence indicates that certain types of stocks are more prone to speculation. For ex-7ample, Barber and Odean (2007) find that stocks more in the news or stocks with more extremereturns attract more trading from retail investors, who are commonly considered as noise traders.Baker and Wurgler (2006) argue that companies whose valuation are highly subjective are moreaffected by investor sentiment.2.2.2 Model setup: institutional investorsThe economy has a unit mass of ex ante identical and risk neutral institutional investors. At t = 0,before trading begins, institutions decide whether they want to be a long-term investor or short-term arbitrageur. Long-term investors can only trade at t = 0 and must hold their positions untilt = 2; short-term arbitrageurs can trade at both t = 0 and t = 1. By default, every institution starts asa long-term investor. To become a short-term arbitrageur, an institution must incur an up-front costof c at t = 0. I use λ ∈ [0,1] to denote the fraction of institutions that are short-term arbitrageurs.This fraction is endogenous to the model and reflects the trade-off that institutions make betweeninvesting in the trading capacity and potential trading profit.One strand of theoretical literature that studies short-term investors, e.g. Froot et al. (1992),Cespa and Vives (2015), often assumes that short-term investors have to sell, because for exoge-nous reasons these investors have to exit the market before the asset pays off. My model is differ-ent. I assume that long-term institutions cannot change their positions in the interim period due tolimited trading capacity. There are several reasons to model long-term institutions this way. First,institutional investors, especially those with a large number of positions under management, mighthave limited resources to constantly monitor every position. This assumption of limited ability,or lack of attention, is well-rooted in the theoretical literature on rational inattention (e.g. Sims,2003; Abel et al. 2007; 2013; Kacperczyk et al., 2016). Alternatively, long-term institutions can beinterpreted as passive investors that trade infrequently. In practice, many institutions explicitly orimplicitly track indexes. These institutions only rebalance their portfolios when the index makesadditions or deletions. Popular indexes, such as those of Standard & Poor’s and FTSE Russell, onlychange their underlying composition infrequently. Thus, a short-term arbitrageur in this model hasa superior investment technology than a long-term institution, because the short-term arbitrageurcan trade in every period. The cost is the up-front investment in the trading capacity. Examples ofsuch up-front investments are hiring traders and developing systems to facilitate trading.In the model, all institutions also incur a quadratic holding cost when investing in risky securi-ties. If an institution holds xi shares of stock i, it must pay the following cost per periodQ(xi) =q2x2i x≥ 0θq2 x2i x < 0(2.1)This function captures the cost of investing through intermediaries. Similar to idiosyncratic risk8in a risk averse setting, this cost function introduces a limit to arbitrage. With this cost function,an institution is unwilling to invest in unlimited number of shares in a stock for a tiny amount ofperceived mispricing. Under this assumption, positive abnormal returns could exist in equilibrium.The use of quadratic holding cost is standard in the literature as in Nutz and Scheinkman (2018).Risk neutrality combined with quadratic holding cost allows me to derive many propositions inclosed-forms. If I assume institutions to be risk averse, the model’s predictions are qualitativelythe same, but I lose analytical tractability.Another important feature of this function is the asymmetry in the cost of maintaining a longposition and a short position. This asymmetry is captured by the parameter θ > 1. In practice,shorting a stock is more difficult than purchasing or selling a stock because of the additional costand complexity, such as, security lending fees, regulatory risk, and operational risk. As docu-mented by Almazan et al. (2004), a large fraction of institutions restrain from selling stocks short.The theoretical literature that models short-selling constraints often assumes that all, or a fractionof, agents cannot sell stocks short. I model short-selling constraints as having a higher cost wheninstitutions carry negative positions. The effect of this assumption on asset prices is mathematicallyequivalent to assuming a fraction of institutions that cannot sell stocks short.Under these assumptions, the objective function of a long-term institutions at t = 0 can bewritten asUL = maxxLi0≥0E[N∑i=1xLi0(vi2− pi0)−N∑i=12Q(xLi0)](2.2)where xLi0 is the number of shares that long-term institutions invest at t = 0. Similarly, the objectivefunction of short-term arbitrageurs can be written asUS = maxxSi0,xSi1(pi1)1∑t=0E[N∑i=1xSit(pit+1− pit)−N∑i=1Q(xSit)](2.3)where xSi0 is the number of shares that short-term institutions invest at t = 0 and xSi1(pi1) is thedemand function of short-term institutions at t = 1, specifying the number of shares to investdepending on the price of the stock at t = 1. I make an additional assumption that long-terminstitutions cannot sell stocks short at t = 0. This assumption is not crucial for the predictions ofthe model, but it simplifies the proofs. This assumption means that a stock’s short-term ownershipis bounded at 1 at the beginning of the model, which applies to most stocks empirically. For themajority of analysis in this chapter, I assume that equilibrium short-term ownership at t = 0 is lessthan 1 for all stocks. Thus, both short-term and long-term institutions hold a positive number ofshares in each stock at t = 0, which is close to empirical observations.92.2.3 Ex ante short-term ownershipThe focus of the model is to explain the initial asset allocation of short-term and long-term insti-tutions. Throughout this chapter, I define a stock’s ex ante short-term ownership as the number ofshares held by short-term institutions at t = 0, which I denote as κi for stock i, i.e.κi ≡ λxSi0 (2.4)where λ is the fraction of short-term institutions and xSi0 is the number shares they invest in stock iat t = 0. The market clearing condition at t = 0 implies that for each stock iλxSi0+(1−λ )xLi0 = 1 (2.5)since the supply of each stock is assumed to be 1 at t = 0. The ex ante long-term ownership instock i is thus 1−κi. The mechanism that drives the difference in asset allocation between long-term and short-term institutions is short-term institutions’ ability to trade in the interim period. Theexpected return from investing in a stock at t = 0 will be different depending on the stock’s tradingopportunity at t = 1, which I formalize in the next section.2.2.4 Trading and resale optionAt t = 1, for each stock i, noise traders want to buy ui shares, where ui ∼ N(0,σ2ui). Note that thesupply of shares at t = 1 is κi, which is the number of shares that short-term arbitrageurs haveobtained from t = 0. Long-term institutions do not trade at t = 1, so the shares that they own areout of the market. When the speculative demand ui from noise traders is smaller than κi, the totalnumber of shares that short-term arbitrageurs have obtained from t = 0, short-term arbitrageurscan meet speculative demand by simply selling their stocks. If the noise demand ui exceeds κi,short-term institutions must borrow additional shares to clear the market. The optimal demandfrom short-term institutions at t = 1 is the followingxSi1(pi1) =E[vi2]−pi1q E[vi2]≥ pi1E[vi2]−pi1θq E[vi2]< pi1(2.6)The demand function for buying is different from short-selling due to the asymmetry in short-selling cost θ . Based on the market clearing condition,u+λxSi1 = κi (2.7)10simple derivation implies the market clearing price for stock i at t = 1 ispi1 =E[vi2]+qλ (ui−κi) ui < κiE[vi2]+θqλ (ui−κi) ui ≥ κi(2.8)The market price at t = 1 is positively related to noise-trader demand. If noise demand is more thanκi, which is the supply of shares at t = 1, the price increases at a faster rate with ui to compensatefor the additional short-selling cost. Equation (2.8) can be re-written aspi1 = E[vi2]+qλ(ui−κi)+ (θ −1)qλ max(ui−κi,0) (2.9)Equation (2.9) clearly indicates that pi1 contains an option-like pay-off, max(ui−κi,0), which isreferred to as a resale option by Scheinkman and Xiong (2003). I denote the expected value of thisresale option as C(κi,σui). Similar to a call option, C(κi,σui) decreases in κi and increases in σui.2.2.5 Equilibrium asset allocationThis section solves for the equilibrium asset allocation in the model. Holding the fraction of short-term institutions constant at λ , the next proposition specifies the ex ante short-term ownership κifor stock i.Proposition 1. Let λ be the fraction of institutions that are short-term institutions. When stock i’sspeculative demand volatility σui ≤ σmax, stock i’s ex ante short-term ownership κi, defined as thetotal number of shares owned by short-term institutions at t = 0, solves the following equationκi = λ +(1−λ )(θ −1)2C(κi,σui) (2.10)where4C(κ,σ)≡ E[max(u−κ,0)] = σ2√2piσ2e−κ22σ2 −κ(1−Φ(κσ))(2.11)Furthermore, the solution to equation (2.10) exists and is unique. When σui > σmax, stock i’s exante short-term ownership κi is 1, where σmax solves the equation1 = λ +(1−λ )(θ −1)2C(1,σmax) (2.12)The proof is in Appendix.4Function Φ denotes the cumulative distribution function of a standard normal random variable.11Proposition 1 states that for any given fraction of short-term institutions, an equilibrium inthe asset market always exists and is unique. This proposition also specifies the two componentsthat determine the ex ante short-term ownership. The first component is the fraction of short-terminstitutions in the economy, denoted as λ . In a frictionless economy where every institution holdsthe market equally, every stock’s short-term ownership should equal to the fraction of short-terminstitutions in the economy. The equilibrium fraction λ can be considered as a benchmark levelof short-term ownership. The second component, the more interesting one, is related to the resaleoption. Positive value of the resale option gives short-term institutions an additional incentive tobuy the stock ex ante. This proposition highlights the role of short-selling cost in determiningthe ex ante asset allocation among different institutions. The asymmetry in short-selling cost (i.e.,θ > 1) is a necessary condition for the ex ante short-term ownership κ to deviate from frictionlesslevel λ . If there is no additional cost, then selling overvalued stocks is as profitable as buyingundervalued ones, which removes the incentive for short-term institutions to accumulate positionsin advance. Equation (2.10) is important for many analysis in subsequent sections.2.2.6 Endogenous choice to invest in the ability to tradeThis section presents the solution to the equilibrium fraction of short-term institutions. In equilib-rium, the additional utility derived from trading at t = 1 must at least compensate the up-front costc for short-term institutions. Hence, institutions choose to become short-term arbitrageurs whenUS−UL ≥ c. The utility of each type of institution also changes with the fraction of short-terminstitutions in the market. The next lemma specifies this result.Lemma 2. The utility of every long-term institution increases with the fraction of short-term insti-tutions λ , while the utility of every short-term institution decreases with λ .The proof is in Appendix.As more institutions choose to become short-term investors in the economy, their ability to takeadvantage of the noise trader demand is reduced by competition with each other. In other words,increases in λ dampens the effect of speculative demand on stock prices and reduces the profit ofshort-term institutions, which can be easily seen from equation (2.9). Therefore, higher λ lowersthe average utility of short-term institutions. The effect of λ on the utility of long-term institutionsis interesting. The utility of long-term institutions depends on the average buy-and-hold return of12each stock. The long-term buy-and-hold return of each stock can be written asE[vi2]− p0 = q− q(θ −1)2 C(κi,σui) (2.13)Since increase in the fraction of short-term institutions λ increases every stock’s short-term owner-ship κ , which reduces the value of their resale options C, more short-term institutions in the marketincreases the long-term return of all stocks, thus increasing the utility of long-term institutions. Thenext proposition proves the existence and uniqueness of the equilibrium in the model.Proposition 3. An equilibrium in this model is defined as the fraction of short-term institutions,λ , the portfolio weights of long-term and short-term institutions at t = 0 and t = 1, and the priceof each stock at t = 0 and t = 1. For any up-front cost c, an equilibrium exists and is unique. Theequilibrium fraction of short-term institutions is always greater than 0.The proof is in Appendix.From Proposition 1, the equilibrium in holdings and prices in the security market is unique forany fraction of short-term institutions λ . The equilibrium fraction of short-term institutions de-pends on the difference in utility between the two types of institutions. This difference approachesinfinity as the fraction of short-term institutions approaches 0. Therefore, for any up-front costc, there is always a positive number of institutions that choose to become short-term arbitrageurs.This proposition highlights the incentive for institutions to become a short-term arbitrageurs. Whenthe additional utility from trading exceeds the up-front cost, more institutions will become short-term arbitrageurs, instead of long-term investors. This fraction λ can also be interpreted as theamount of arbitrage capital in the economy.2.3 Theoretical results and predictionsThis section assesses the equilibrium relationship among institutional investors’ asset allocation,expected stock return, and trading opportunities from the lens of the model developed in the pre-vious section. The model produces both cross sectional and time series predictions. In addition,I investigate the response of stock return to shocks from speculative demand and to shocks frominstitutional ownership. These predictions could further substantiate the model’s underlying mech-anism.132.3.1 Cross sectional relationshipThe main theoretical result is to characterize the cross sectional relationship between short-termownership and the expected stock return. The next proposition summarizes this prediction.Proposition 4. Holding the fraction of short-term institutions λ constant, stock i’s ex ante short-term ownership κi increases with its speculative demand volatility σui. The stock’s expected long-term return, E[vi2− pi0], decreases with σui.Proof is in Appendix.In essence, this proposition states that everything else equal, stocks with more exposure tospeculative demand shocks will be more held by short-term institutions, which also implies thatstocks with lower buy-and-hold returns will also be more held by short-term institutions. The intu-ition of this result is that a stock’s exposure to speculative demand reduces its long-term expectedreturn, because the resale option created by the speculative demand shock increases the demandfrom short-term institutions, who drive up the stock’s price at t = 0.A direct implication of this proposition is that short-term institutions invest more in stockswith lower buy-and-hold returns, while long-term institutions overweight stocks with higher buy-and-hold returns. However, short-term institutions are not irrational. In fact, the interpretationis the opposite. Because short-term institutions can trade in the interim, their demand is lesssensitive than long-term institutions to the stock’s long-run buy-and-hold return. Although short-term institutions invest more in low-return stocks, they make additional returns from trading. Thenext proposition summarizes this result.Proposition 5. Define an institution’s trading profit RTi from stock i as the difference between itstotal return with trading and buy-and-hold returnRTi ≡ xi0(pi1− pi0)+ xi1(vi2− pi1)− xi0(vi2− pi0) = (xi1− xi0)(vi2− pi1) (2.14)Long-term institutions’ trading profit is zero from each stock. Short-term institutions have posi-tive trading profit in expectation. Their expected trading profit from stock i increases in stock i’sspeculative demand volatility σui.The proof is in Appendix.This proposition states that short-term institutions generate additional returns from trading.Their trading skill can be captured by comparing their rebalanced return with the return they would14obtain had they practiced a buy-and-hold strategy. Empirically, the literature decomposes a man-ager’s skills into a style-picking component and a stock-picking component (e.g., Daniel et al.,1997; Wermers, 2000). This model provides a theoretical foundation for the empirical distinctionbetween style picking and stock picking. The initial demand x0 can be interpreted as an institu-tion’s choice of style, while subsequent trading is driven by its stock-picking ability within thestyle. This model helps to explain how institutions pick style. Long-term institutions overweightthe style or the type of stocks with higher buy-and-hold returns, whereas short-term institutionschoose styles based on whether they can generate trading profit. The style associated with higherexposure to speculative demand offers more trading opportunities to short-term institutions .Figure 2.1 plots the results of the cross-sectional analysis, where the x-axis is the noise demandvolatility σu. In panel A, the y-axis is the ratio between initial short-term institution demand xS0 andlong-term institutional demand xL0 . A ratio of 1 means both short-term institutions and long-terminstitutions hold the same number of shares. The figure shows that as σu increases, short-terminstitutions start to raise their demand for the stock. The convex shape of the curve indicatesthat when σu becomes large enough, the additional demand by short-term institutions increasesdrastically. Panel B plots the expected buy-and-hold return, E[v2− p0], as a function of σu. Itshows that the buy-and-hold return declines with σu. The shape of the curve is a reverse image ofPanel A. Panel C plots the trading profit of short-term institutions, which increases with σu.2.3.2 Comparative statics analysisThis section performs comparative statics analysis by changing parameters of the model, such as c,θ , and q. These parameter changes can be interpreted as different economic settings. For example,economies with different levels of c corresponds to economies with different cost of becomingshort-term arbitrageurs or with different amount of arbitrage capital. Economies with different θcorresponds to economies with different degrees of short-selling constraints. And different levelsof q corresponds to economies with different degrees of limit to arbitrage or risk aversion amonginstitutional investors. The predictions of the model can be tested in the US equity market acrosstime. Over the past four decades, the landscape of the investment community has changed dra-matically with increasing amount of sophisticated institutional investors entering the market, e.g.hedge funds. Development in trading technologies and market micro-structure could also haveshifted the parameters of the model. Alternatively, the predictions can also be tested across dif-ferent markets. For example, in emerging and less developed markets, both the entry cost andtrading parameters are different from more advanced economies. Therefore, these predictions canbe tested among different countries (i.e. emerging market vs. developed market) or different asset15classes (i.e. equity vs. bond).Proposition 6. An increase in the cost of becoming a short-term institution c will reduce thefraction of institutions that are short-term, leading to an increase in the cross-sectional dispersionof ex ante short-term ownership, an increase in the dispersion of expected return across stocks,and an increase in the expected trading profit of short-term institutions.The proof is in Appendix.This proposition specifies the effect of changes in the fraction of short-term arbitrageurs in theeconomy on various equilibrium quantities. Naturally, increase in the cost of becoming a short-term arbitrageur reduces the fraction of short-term arbitrageurs in the economy. This results in anincrease in the cross sectional variations in the stock’s short-term ownership and in the cross sec-tional variation in the stock’s expected return. The intuition is that as arbitrageur capital becomesscarce. Short-term arbitrageurs will take on more extreme positions, overweighting more specula-tive stocks and underweighting less speculative stocks. This results in an increase in the variationin the expected return across stocks. In addition, a decline in the fraction of short-term institutionspredicts an increase in their trading profit. Figure 2.2 plots the results of different fractions ofshort-term institutions in the economy.Proposition 7. An increase in the short-selling constraint θ , holding constant the fraction of short-term institutions, will lead to an increase in the cross-sectional dispersion of short-term ownershipand an increase in the dispersion of expected return across stocks.The proof is in Appendix.Increasing in the short-selling constraint θ has similar effects as decreasing the fraction ofshort-term arbitrageurs λ . Short-term institutions take more extreme positions ex ante, which driveup the cross-sectional dispersion in expected returns. Figure 2.3 plots the results for economieswith different short-selling constraints. The figure also shows that the trading profit of short-terminstitutional investors also increases with θ .Proposition 8. An increase in the overall holding cost parameter q will leave short-term ownershipunaffected, but will increase the dispersion of the expected return and increase the expected tradingprofit of short-term institutions.The proof is in Appendix.16The parameter q, although acting a limit to arbitrage, does not affect the asset allocation be-tween long-term and short-term institutions, which can be seen from the equation (2.10). However,changes in q will change the cross-sectional variation in expected return and in the average trad-ing profit of short-term institutions. As q increases, limit to arbitrage becomes stronger, whichmagnifies the effect of short-term institutional demand on expect return and the trading profit thatshort-term institutions are able to generate. Figure 2.4 plots the results for economies with differentlevels of q.2.3.3 Dynamic response to shocks in institutional and speculative demandThe previous sections specify equilibrium relationship of the model. To further shed light onthe mechanism and to distinguish from alternative hypothesis, this section studies the dynamicresponse of stock return after an exogenous shock to institutional demand or speculative demand.For reasons outside of the model, institutional investors could exogenous change their demand fora stock. For example, a change of a stock’s index membership could result in a sudden increase indemand for the stock by long-term indexers. A shock to the reputation of an institutional investor(e.g. as in the market timing scandal) could lead to a sudden withdraw of funds, which trigger alarge selling by affected institutional investors. After these institutional demand shocks, the modelprovides the following prediction.Proposition 9. An exogenous increase to short-term institutional demand at t = 0 will increaseshort-term ownership κ , decrease the stock i’s buy-and-hold return E[v2− p0], decrease stock i’snon-fundamental volatility Var(p1− p0), and decrease the trading profit that short-term institu-tions generate from stock i. An exogenous increase in long-term institutional demand at t = 0 willdecrease short-term ownership κ , decrease the stock i’s buy-and-hold return E[v2− p0], increasestock i’s non-fundamental volatility Var(p1− p0), and increase the trading profit that short-terminstitutions generate from stock i.The proof is in Appendix A.Exogenous increase in both long-term or short-term institutional demand would increase theprice of the stock, which cause a decrease in the stock’s buy-and-hold return. This is the directprice impact from institutional demand. However, long-term and short-term institutional demandhave different effect on the stock’s volatility. Exogenous increase in long-term holding increasesthe stock’s future volatility due to a reduced number of shares available to meet speculative de-mand. On the contrary, exogenous increase in short-term holding decreases the stock’s future17volatility due to increased number of shares available to meet speculative demand. The two type ofinstitutions have opposing effects on the stock’s volatility. In addition, increases in long-term de-mand would also help short-term institutions to make more trading profit by reducing the numberof shares available to meet speculative demand, whereas increases in short-term demand reducesthe amount of trading profit that short-term institutions will generate.Conditional on the realization of speculative demand, the model also gives predictions about thestock return from t = 1 to t = 2. The stock experiencing positive noise demand has lower second-period return than the stock with negative noise demand. As speculative demand volatility σuiincreases, the predictability of noise trader demand on the second period return becomes stronger.This return predictability is asymmetrical: it is stronger for overpriced stocks due to the highershort-selling cost. The next proposition formalizes this result.Proposition 10. Realized noise trader demand ui at t = 1 negatively predicts the stock’s return inthe second period. The expected second-period return, conditional on speculative demand beingnegative (i.e., underpriced stocks), increases with σui, while the expected second-period return,conditional on speculative demand being positive (i.e., overpriced stocks), decreases with σui. Therate of change in the conditional expected second-period return with respect to σui is greater inabsolute terms for overpriced stocks.The proof is in Appendix A.The asymmetrical response to speculative demand shock is a key prediction that verifies themodel’s mechanism. The model’s main cross-sectional result builds on the mechanism that sellingoverpriced stocks is more profitable than buying underpriced stocks at the time that mispricing,i.e. speculative demand shock, occurs. Due to this asymmetry, short-term arbitrageurs would liketo pay a premium for stocks that are more likely to be mispriced even before mispricing occurs.Long-term institutions cannot take advantage of this opportunity. Therefore, the optimal strategyfor long-term institutions is to avoid holding stocks that are more likely to experience mispricingin their ex ante asset allocation. Figure 2.5 plots the conditional expected return as a functionof σui. It displays a clear sign of asymmetry as the return of the overpriced stock declines at anincreasingly faster rate.2.3.4 Determinants of arbitrage capitalThroughout the model, variable λ measures the fraction of institutions that are able to engage inshort-term trading or arbitrage. This fraction can be interpreted as the economy’s arbitrage capacity18or the amount of arbitrage capital. How would λ change with parameters of the model? The nextproposition answers this question.Proposition 11. Increase in the number of stocks N (holding constant the distribution of σi acrossstocks) will increase the fraction of short-term institutions. Increase in the limit-to-arbitrage pa-rameter q will also increase the fraction of short-term institutions in equilibrium.Since short-term institutions obtain higher utility from each stock than long-term institutions,as the number of stocks increases, the difference in utility between short-term and long-term insti-tutions increases. Therefore, more institutions will also choose to be short-term investors. As thetrading environment changes due to shifts in parameter q, the fraction of short-term arbitrageurswould also change. The intuition is that when limits to arbitrage become more relaxed, there isfewer institutions to become arbitrageurs. This is because the competition among short-term arbi-trageurs becomes more intense, reducing the average trading profit of each short-term institution.These predictions can be tested in the US over time or be tested across different countries or mar-kets. The fraction of short-term versus long-term institutions has changed over time in the US, asillustrated by Stambaugh (2014). My model provides a theoretical framework to understand whatdrives that change.2.3.5 Introducing systematic riskIn this section, I introduce the presence of systematic risk, which is important for empirical testingof the model and for asset pricing in general. Suppose each asset i has an exposure to a risk factor.Denote the exposure as βi. For each stock i, every institution requires a compensation for a unitexposure to the factor. Let d denote the required rate of return for an extra unit exposure to thefactor, which means that the utility function of the long-term institutions isUL = maxxLi0E0[ΣNi=1xLio(vi2− pi0)−2dΣNi=1xLioβi−2ΣNi=1Q(xLi0)] (2.15)Similarly, the utility function of short-term arbitrageurs is nowUS = maxxSi0,xSi1(pi1)1∑t=0E[N∑i=1xSit(pit+1− pit)−dΣNi=1xSitβi−N∑i=1Q(xSit)](2.16)19Proposition 12. The expected return for stock i with exposure to the systematic factor βi andspeculative demand σui isE[v2− p0]2= dβi+q1−λ −q1−λ κi (2.17)and short-term ownership κi solvesκ=λ+(θ −1)(1−λ )2C(κ,σi) (2.18)The proof is in Appendix A.As shown by the proposition, exposure to the systematic risk does not alter the asset allocationof short-term and long-term institutional investors. The effect of introducing systematic risk is tointroduce another determinant of the stock’s expected return. In this model, two things determinethe stock’s expected return, its exposure to systematic risk β and its exposure to speculative demandσ . The two exposures have opposing effects on the stock’s expected return. Empirically, whenestimating the risk premium of the systematic factor d. Empiricists face an identification challengeif the distribution of σui in the cross section is correlated with the distribution of βi. For a givensystematic factor, if stocks with high exposure to such systematic factor also have high exposure tospeculative demand. Then, estimates of the factor’s risk premium without controlling for the effectof speculative demand would underestimate the price of risk for such a factor. The price of riskwould be overestimated if β and σ are negatively correlated. The similar issue would also affectstudies that investigate the risk taking behavior of institutional investors. If β and σ are positivelycorrelated, then short-term institutions would invest more in stocks with higher β , appearing totake on more systematic risk.2.4 Discussion of resultsThis chapter develops a model that studies a different dimension along which institutional investorsallocate their capital. Traditional theories dictate that investors make asset allocation decisionsbased on the risk-return trade-off or liquidity considerations. Specifically, investors with differentlevels of risk aversion or background risk make investment decisions along different dimensionsof risk. The commonly used investment categories, such as value and size, are often argued as twoimportant dimensions of risk (Fama and French, 1996), along which investors allocate their capi-tal. Similarly, investors with different exogenously short holding horizon would prefer more liquid20stocks than other. The model that I present provides a different theory that guides investor assetallocation decision. Rather than making risk-return trade-off or liquidity-return trade-off, investorswith different trading frequency trade-off an asset’s buy-and-hold return against its trading oppor-tunity. Assets with higher buy-and-hold returns have fewer trading opportunities, thus are moresuitable for long-term investors, while assets with lower buy-and-hold returns have more tradingopportunities, thus are more suitable for short-term investors. Based on this theory, investmentcategories should be defined along dimensions that best capture a stock’s trading opportunities.The model has many practical applications. For example, the model can be applied to thedesign of benchmark indexes that are tracked by passive mutual funds. Passively managed mutualfunds only rebalance when their benchmark indexes change composition. The model suggeststhat a passive benchmark index should take into account a stock’s exposure to speculative demandshocks. Instead of weighting each stock according to its market cap weight, the passive benchmarkshould reduce its exposure to stocks that are more likely to be mispriced.2.5 ConclusionThis chapter develops a model to analyze the asset allocation decision among institutional investorswith different holding horizons. Short-term institutions prefer to invest in stocks with greater expo-sure to speculative demand shocks, because short-term institutions can make trading profits fromthese stocks by rebalancing frequently. The excess demand from short-term institutions reducesthe buy-and-hold returns of these speculative stocks. The optimal strategy of long-term institu-tions is to reduce their holdings of speculative stocks. In equilibrium, stocks with more short-terminstitutional holdings have lower buy-and-hold returns and more trading opportunities.My model rationalizes why short-term institutions overweight low-return stocks and predictsthese institutions generate additional returns by trading these stocks actively. Furthermore, stocksprimarily held by short-term institutions should have more predictable returns, and their returnpredictability is stronger when they become overpriced. My results highlight how market fric-tions determine the equilibrium asset allocation of institutional investors according to their tradingability.21Figure 2.1: Cross-sectional effect of speculative demandThis figure plots numerical quantities of the model. The x-axis in all three panels is the volatility of noise traderdemand, σu. In Panel A, the quantity on the y-axis is the ratio between short-term demand xS0 and long-term demandxL0 at t = 0. In Panel B, the y-axis is the expected return of the stock E[v2− p0] from t = 0 to t = 2. In Panel C,the y-axis is the expected trading profit of short-term institutions from stock i. The parameters for these graphs areλ = 0.5, θ = 30, and q = 0.04.22Figure 2.2: Economies with different fractions of short-term arbitrageurThis figure plots numerical quantities of the model with different levels of λ . The solid blue lines corresponds to aneconomy with λ = 0.4. The dash orange lines corresponds to an economy with λ = 0.6. The x-axis in all three panelsis the volatility of noise trader demand, σu. In Panel A, the quantity on the y-axis is the ratio between short-termdemand xSi0 and long-term demand xLi0 at t = 0. In Panel B, the y-axis is the expected return of the stock E[vi2− pi0]from t = 0 to t = 2. In Panel C, the y-axis is the expected trading profit of short-term institutions from stock i. Otherparameters for these graphs are θ = 30 and q = 0.04.23Figure 2.3: Economies with different degrees of short selling constraintThis figure plots numerical quantities of the model with different levels of θ . The solid blue lines corresponds to aneconomy with θ = 30. The dash orange lines corresponds to an economy with θ = 100. The x-axis in all three panelsis the volatility of noise trader demand, σu. In Panel A, the quantity on the y-axis is the ratio between short-termdemand xSi0 and long-term demand xLi0 at t = 0. In Panel B, the y-axis is the expected return of the stock E[vi2− pi0]from t = 0 to t = 2. In Panel C, the y-axis is the expected trading profit of short-term institutions from stock i. Otherparameters for these graphs are λ = 0.5 and q = 0.04.24Figure 2.4: Economies with different degrees of limit to arbitrage.This figure plots numerical quantities of the model with different levels of q. The solid blue lines corresponds toan economy with q = 0.04. The dash orange lines corresponds to an economy with q = 0.06. The x-axis in all threepanels is the volatility of noise trader demand, σu. In Panel A, the quantity on the y-axis is the ratio between short-termdemand xSi0 and long-term demand xLi0 at t = 0. In Panel B, the y-axis is the expected return of the stock E[vi2− pi0]from t = 0 to t = 2. In Panel C, the y-axis is the expected trading profit of short-term institutions from stock i. Otherparameters for these graphs are λ = 0.5 and θ = 30.25Figure 2.5: Asymmetrical response to speculative demand shock.This figure plots the expected stock return after a speculative demand shock occurs. The y-axis is the expected returnof the stock i from t = 1 to t = 2 conditional on the realized speculative demand being greater or smaller than 0. Thetop (bottom) line is the conditional expected return after negative (positive) speculative demand shock. The parametersfor these graphs are λ = 0.5, θ = 30, and q = 0.04.26Chapter 3Trading Opportunities and the PortfolioChoices of Institutional Investors3.1 IntroductionInstitutional investors have grown tremendously over the past four decades with their asset undermanagement exceeding 70% of the U.S. equity market (Ben-David et al., 2019). Lewellen (2011)shows that institutional investors in aggregate hold the market portfolio, which suggests that in-stitutions on average add little value to households since their portfolio as a whole is merely areflection of the market. However, this aggregation masks the large degree of heterogeneity acrossdifferent types of institutions. In particular, institutional investors differ significantly on their hold-ing horizon or equivalently trading frequency. Pension funds and index fund families have lowturnover ratio and practice buy-and-hold strategies. The aggregate portfolio holdings of this groupof long-term investors is different from the aggregate holdings of active mutual funds and hedgefunds, which have short holding horizons and trade frequently. Understanding how an institution’sholding horizon relates to its asset allocation can shed light on how financial institutions affectasset prices and add value to the society.Chapter 2 develops a theory on how institutions with different holding horizons make assetallocation decisions. This chapter tests the main predictions of the model empirically based oninstitutional investor holdings data in the US. This chapter primarily focuses on testing the equi-librium predictions in the cross-sectional of US stocks. Specifically, stocks with more short-terminstitutional investors have lower buy-and-hold abnormal returns and offer more trading oppor-tunities that allow short-term institutions to make trading profits. First, I proxy an institutionalinvestor’s holding horizon with its turnover ratio, controlling for flow induced trades. Then, foreach stock, I compute its short-term ownership as the average turnover ratio of institutions thatown the stock, weighted by the stake of each institution. This measure of short-term ownershipis persistent, suggesting that long-term and short-term institutions have persistent differences inholdings. For example, short-term institutions invest significantly more than long-term institutionsin stocks that are younger, have higher CAPM beta and idiosyncratic volatility. At the indus-try level, healthcare and information technology industries have the highest amount of short-term27ownership, while utilities and real estate industries have the lowest.To test my model’s predictions, I sort stocks into five portfolios each year based on their averageshort-term ownership in the prior year, which I refer to as ShortOwn quintiles. Empirically, theabnormal buy-and-hold returns decline with a stock’s short-term ownership, consistent with theexisting literature. The difference in the valued-weighted monthly alphas between stocks in thetop and bottom ShortOwn quintiles are -0.56% (t-statistic: -2.36) under the capital asset pricingmodel (CAPM), -0.26% (t-statistic: -1.89) under the Fama and French (1993) three-factor model,and -0.31% (t-statistic: -2.12) with the additional control of the Carhart (1997) momentum factor.I then check if stocks with more short-term institutional investors are more susceptible to mis-pricing. To do so, I apply a trading strategy based on the mispricing score developed by Stambaughet al. (2015) to each ShortOwn quintile. This trading strategy should generate higher abnormal re-turns from the quintile with stocks more exposed to mispricing shocks. I find this to be the case.For stocks in each ShortOwn quintile, I further assign them into overpriced, fairly priced, andunderpriced terciles in the beginning of every month based on their score. Underpriced stocks inthe top ShortOwn quintile have a monthly three-factor alpha of 0.41% (t-statistic: 2.94), whileoverpriced stocks in this quintile have a monthly three-factor alpha of -0.97% (t-statistic: -6.15),resulting in a spread of 1.37% per month (t-statistic: 6.77). For stocks in the bottom ShortOwnquintile, the three-factor alphas of underpriced and overpriced stocks are 0.25% (t-statistic: 3.36)and -0.29% (t-statistic: -1.99) per month, which have a spread of only 0.53% (t-statistic: 3.17).These results indicate that stocks primarily held by short-term institutions are more likely to be-come mispriced, evidenced by the fact that their returns are more predictable by their mispricingscores. The substantial negative abnormal return of overpriced stocks in the top ShortOwn quintilealso confirms the effect of short-selling constraint. The presence of mispricing shocks or returnpredictability provide trading opportunities for investors with better trading skills.Finally, I test whether the different exposure to mispricing shocks across stocks translates intovariations in the trading profit that institutional investors generate. I compute the return of eachquintile portfolio by mimicking the trading activities of long-term and short-term institutions. Tomimic their trading activities, I group institutions according to their turnover ratio and use thetotal dollar value they invest in each stock as weights to compute a portfolio’s return. Instead ofweighting stock returns according to their market capitalization as buy-and-hold investors woulddo, holding-weighted return better captures any additional returns that institutional investors obtainfrom rebalancing their positions.The portfolio returns weighted by the holdings of short-term institutions are higher than theportfolio returns weighted by the holdings of long-term institutions in all five ShortOwn quintiles.Their difference between holding-weighted returns and buy-and-hold returns, i.e. trading profit,monotonically increases from the bottom to the top ShortOwn quintile. Collectively, short-term28institutions beat long-term institutions in the top ShortOwn quintile by 0.28% per month (t-statistic:4.28) in terms of the three-factor alpha. Their performance in the bottom ShortOwn quintile issimilar with a difference of only 0.04% per month (t-statistic: 0.86). This result is robust to avariety of other factor models and to excluding micro-cap stocks. The finding that short-terminstitutions generate more trading profit from stocks they overweight highlights the importance oftrading opportunities in their asset allocation decisions.I perform time series predictability tests to examine if the trading profit of short-term institu-tions varies over time. Pástor et al. (2017) suggest that the total number of trading opportunities inthe market changes with investor sentiment. I find that the trading profit of short-term institutionscan be predicted by proxies of market sentiment, such as Baker and Wurgler (2006) sentiment indexand the first-day returns of initial public offerings (measured according to Ibbotson et al., 1994).The time series predictability in trading profit is more significant in the top ShortOwn quintile,while it is insignificant in the bottom ShortOwn quintile. The stronger time-series predictabil-ity in the top ShortOwn quintile is another evidence that ex ante short-term ownership identifiesvariations in trading opportunities across stocks. I also rule out an alternative explanation basedon the illiquidity risk. Overall, these empirical findings support my theoretical explanation ofwhy short-term institutions overweight low-return stocks. Short-term institutions have a compara-tive advantage in trading stocks that are more exposed to mispricing shocks and overweight thesestocks in advance, despite their lower buy-and-hold returns.3.1.1 Related literatureMy findings contribute to several strands of literature. First, I contribute to the literature thatinvestigates the skill of institutional investors. There is an on-going debate on what kind of insti-tutions have better stock-picking skill. Studies that favor long-term institutions include Cremersand Pareek (2016), Borochin and Yang (2017), and Lan et al. (2015), while studies that supportshort-term institutions include Yan and Zhang (2007) and Pástor et al. (2017). The main issuelies in how to assess stock-picking skill empirically. My findings add to this debate by demon-strating that short-term institutions have the ability to trade against temporary mispricing, whichallows them to generate higher returns than buy-and-hold investors who invest in the same type ofstocks. However, short-term institutions allocate more capital toward stocks that are more likelyto become mispriced. This type of stocks has lower buy-and-hold returns. The differential trad-ing ability makes institutions hold different types of stocks. When institutions invest in differenttypes of stocks, several papers, including Ferson and Wang (2018), Busse et al. (2017), and Shenget al. (2019), indicate that the performance evaluation largely depends on the choice of benchmarkmodel, which is still an area of controversy.Finally, this paper contributes to the growing literature that investigates the heterogeneous pref-29erences among institutional investors. Basak and Pavlova (2013) present a model to illustrate thatwhen institutions care about their performance relative to a certain index, they overweight assetsthat constitute their benchmark index. Christoffersen and Simutin (2017) find that fund managerstilt more toward high-beta stocks in their benchmark after pension sponsors increase monitoring.Hanson et al. (2015) show that traditional banks prefer to hold illiquid assets with low risk becausethey qualify for deposit insurance, while shadow banks prefer to own liquid assets because they aresubject to runs. Giannetti and Kahraman (2017) find that closed-end funds are more likely to pur-chase fire-sale stocks than open-end funds because closed-end funds do not face the pressure fromfund flow. Koijen and Yogo (2018) develop a methodology to structurally estimate the preferenceparameters of different asset characteristics for various types of institutional investors. My papercontributes to this literature by demonstrating that asymmetrical arbitrage costs make short-terminstitutions prefer to own stocks that are more exposed to mispricing shocks.3.2 Hypothesis developmentThis section develops the empirical hypotheses to be tested later. Based on the idea that short-terminstitutions can trade more frequently than long-term institutions, the model built in Chapter 2predicts that stocks with more volatile speculative demand are more held by short-term institutionsthan long-term institutions. Empirically, this means that by sorting stocks according to whetherthey are more or less held by short-term institutions, I should observe variations in the expectedbuy-and-hold return and trading opportunities of stocks. Specifically, I expect to observe:• Stocks that short-term institutions overweight ex ante have lower risk adjusted returns thanstocks that long-term institutions overweight ex ante, because the additional demand fromshort-term institutions drives up the prices these stocks.• Stocks that short-term institutions overweight ex ante experience greater mispricing, eitheroverpricing or underpricing, depending on the realization of speculative demand shocks.• Short-term institutions are able to make more trading profit from stocks they ex ante over-weight than from stocks that long-term institutions ex ante overweight.Another important mechanism in the model is the presence of short-selling constraint. The pres-ence of short-selling constraint predicts that when mispricing happens, overpricing is more severethan underpricing, especially among stocks that short-term institutions ex ante overweight. Notethat these empirical predictions involve sorting stocks based the ex ante short-term ownership, i.e.the demand of short-term institutions at t = 0 in the model. The empirical measure that I develop30will try to measure the ex ante level of short-term ownership, rather than unexpected short-termownership due to trading against noise traders.Finally, the model in the previous chapter has several other economy wide predictions. Testingthose predictions are beyond the scope of this chapter because of identification challenges. Testingthose predictions is an interesting area of future research.3.3 Data, measurement, and motivating evidenceThis section presents motivating evidence on the asset allocation decision of institutional investorswith different holding horizons. Based on 13F institutional holdings data, I construct measuresof holding horizon for institutional investors and I compute short-term ownership for each stock.I use these measures to show the persistence of short-term ownership and how it correlates withother stock characteristics in this section. The next section tests my model’s main predictions.3.3.1 DataI collect data from several sources. First, I construct a dataset containing quarterly institutionalholdings. The bulk of holdings data are from Thomson Reuters S34 Database, previously knownas CDA/Spectrum, which has collected quarterly positions for institutional investors since 1980.The SEC requires institutions that conduct business in the US and manage more than $100 millionin assets to report all their holdings of publicly traded stocks within 45 days after the end ofeach calendar quarter, except for small positions that are below 10,000 shares and $200,000. Thetype of institutional investors includes investment advisors (e.g., mutual funds or hedge funds),banks, insurance companies, pension plans, and endowment funds. Because Thomson Reutersreuses the same identifier for different institutions, to track institutional investors over time, Iuse the permanent institution identifier constructed by Brian Bushee (2001). 5 Following therecommendations of Blume et al. (2014) and Wharton Research Data Services (WRDS), I correctfor errors in share splits in the S34 Database.WRDS finds that after 2013 Thomson Reuters S34 Database removed many institutional in-vestors.6 To remedy this problem, I use an alternative data source for observations after 2013:Thomson Reuters Global Ownership Database, which also contains holdings data for US institu-tions. This new database corrects for the omission problems of the S34 database.For stock return and company characteristics, I use standard datasets from the Center for Re-search in Security Prices (CRSP) and Compstat. I also download factor returns and the risk-free5Details about how Brian Bushee constructs the permanent ID can be found on his personal website athttp://acct.wharton.upenn.edu/faculty/bushee/IIclass.html6The details of the issue can be found in this documenthttps://wrds-www.wharton.upenn.edu/documents/533/Research_Note_-Thomson_S34_Data_Issues.pdf31rate from several authors’ websites. The Fama and French (1993; 2015) and Carhart (1997) factorreturns are from Ken French’s website. 7 Liquidity factor and mispricing factors are from RobertStambaugh’s website.8 I also use Baker and Wurgler (2006) sentiment index for time series analy-sis. For return predictability test, I download mispricing score created by Stambaugh et al. (2015)from Jianfeng Yu’s website.9 Appendix B provides more details on the definitions of variables.3.3.2 Measurement of stock level short-term ownershipA stock’s ownership structure is multi-dimensional. The dimension relevant to this paper is thedegree to which the stock is held by short-term institutions relative to long-term institutions. In-stitutional investors do not explicitly state their holding horizons. Therefore, I must compute theirholding horizons from the data. One simple and widely adopted approach is to proxy an insti-tution’s holding horizon with its portfolio turnover.10 In the literature, high-turnover institutionsare referred to as short-term investors, while low-turnover institutions are considered long-terminvestors. Following the literature, I proxy an institution’s holding horizon based on its portfolioturnover ratio. Specifically, I measure the average turnover ratio of institution j as of quarter t asthe sum of quarterly turnover ratios in the four most recent quartersTurn jt =t∑τ=t−3min(Purchaseτ ,Salesτ)12(Sizeτ−1+Sizeτ)(3.1)To compute aggregate purchases and sales, I assume institutions rebalance their portfolios at theend of each calendar quarter. I use the minimum of purchases and sales to reduce the influenceof fund flow induced trades. I exclude observations where an institution holds fewer than 10 UScommon stocks, and I winsorize Turn jt at the 1st and 99th percentiles. Table 3.1 Panel A reportssummary statistics for institutions in my sample. On average, I have 1309 institutions each yearfrom 1981 to 2017. The average turnover ratio among of institutions is 46% per year, whichsuggests that the average holding horizon is slightly more than two years.The turnover ratio of an institution is a persistent variable. Table 3.1 Panel B regresses Turn jton its lagged values. The coefficients for 1-year, 5-year, 10-year, and 20-year lagged Turn jt are0.9, 0.79, 0.70, and 0.53, respectively. The persistence in turnover ratio indicates that this ratiocaptures a fundamental and time-invariant dimension of institutional characteristics; it is unlikelythat institutions will frequently change the level of their turnover ratio or holding horizons. Along-term institution (e.g., Vanguard) has low turnover ratio for many years. Similarly, a short-7The link to the website is http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html8The link to the website is http://finance.wharton.upenn.edu/~stambaug/9The link to the website is https://sites.google.com/site/yujianfengaca/10For example, papers that use turnover ratio, also known as the churn rate, to classify institutions include Bushee(2001), Gaspar et al. (2005), and Yan and Zhang (2007).32term institution (e.g., Renaissance Technologies) maintains high turnover ratio for a long period oftime. Table 3.1 Panel C presents summary statistics of Turn jt for institutions with different legaldesignations. Bank trusts and public pension funds have the lowest turnover ratio, thus longestholding horizon, while investment companies, including mutual funds and hedge funds have thehighest turnover ratio or shortest holding horizon. The standard deviations of Turn jt within eachclass of institutions are large, indicating that even among institutions within the same legal defini-tion, the heterogeneity in holding horizon is still rich.There are different ways to measure a stock’s short-term ownership. One way is to classifyinstitutions into two disjointed types and aggregate a stock’s ownership by each type. However, thisapproach potentially loses a significant amount of information. Having numerically computed eachinstitution’s turnover ratio, I compute each stock’s short-term ownership as the average turnoverratio of its institutional investors weighted by the stake of each institution. For example, the short-term ownership of stock i in quarter t is measured asST Ownit =∑Nj=1 Sharesi jt×Turn jt∑Nj=1 Sharesi jt(3.2)where Sharesi jt is the number of shares of stock i that institution j holds in quarter t. If a stock’sinstitutional investors have high turnover ratio on average, this means the stock is primarily held byshort-term institutions. This measure incorporates more information by considering the turnoverratio of all institutions. The denominator of ST Ownit is the number of shares held by all insti-tutions. This scaling allows me to focus on the difference in asset allocation between short-termand long-term institutions, rather than on the difference between institutional investors and non-institutional investors. For my empirical tests, I require a stock to have more than five differentinstitutional investors in at least one quarter in the prior year. This requirement reduces the mea-surement error from stocks with very few institutional investors. Table 3.2 Panel A reports sum-mary statistics for ST Ownit and other stock characteristics. On average, I have 4025 stocks eachyear in my sample from 1981 to 2017.3.3.3 Short-term ownership and stock characteristicsThis section discusses how short-term ownership correlates with other stock characteristics. Table3.2 Panel B reports pairwise correlation between quarterly short-term ownership and various otherstock characteristics among all stocks in the sample. Short-term ownership is positively associatedwith a stock’s CAPM beta, momentum, and idiosyncratic volatility. It is negatively associatedwith a stock’s size, book-to-market ratio, and age. Table 3.2 Panel C presents the same set ofpairwise correlations by excluding micro-cap stocks, which are stocks with prior year-end marketcaps smaller than the 20th percentile of stocks traded on the New York Stock Exchange (NYSE).33The correlations become stronger in this sample due to reduced noise in short-term ownership frommicro-cap stocks.Figure 3.1 plots average short-term ownership for stocks in characteristic sorted deciles andshows that some of the relationship are not monotonic. In particular, among stocks ranked in thebottom five size deciles, short-term ownership is positively correlated with size, while for stocksin the top three deciles, short-term ownership is negatively correlated with size. This explains whysize is weakly correlated with short-term ownership in the full sample. Similarly, among stocksin the bottom five momentum deciles, short-term ownership decreases with momentum, while itincreases with momentum in the top five deciles. Stock age appears to be the best characteristicto explain short-term ownership. Stocks listed for shorter periods of time have more short-terminvestors, while stocks listed for long period of time have more long-term investors. Overall, theseplots indicate that short-term institutions prefer to invest more in younger stocks, growth stocks,and stocks with more idiosyncratic volatility. Figure 3.2 plots average short-term ownership bysector. Healthcare and information technology sectors have the highest short-term ownership,while utilities and real estate sectors have the lowest amount.Table 3.3 presents the result of a regression analysis on short-term ownership in a multivariatesetting for the full sample and all-but-micro sample. In Columns 1 and 4, the independent variableis a stock’s short-term ownership in the prior year. The coefficients are 0.61 and 0.64, respectively.The R-squared in the two columns are 40% and 48%, respectively, indicating that a stock’s short-term ownership is persistent and can be explained by its past realizations. Stocks with more short-term institutional investors on average continue to have more short-term institutional investors.Notably, the persistence in institution turnover ratio does not mechanically imply a stock’s short-term ownership is persistent. It is possible that short-term and long-term institutions only havetransitory differences in their holdings. However, long-term institutions and short-term institutionspersistently tilt towards different types of stocks as shown in this table. Columns 2 and 5 regressshort-term ownership on contemporaneous stock characteristics with sector and time fixed effects.The signs of the coefficients are consistent with pairwise correlations. Columns 3 and 6 combinelagged short-term ownership and stock characteristics. The coefficient on lagged short-term own-ership only changes slightly, while the magnitude of coefficients on other stock characteristics arereduced. Notably, the sign on the coefficient of book-to-market ratio changed from negative inColumn 5 to positive in Column 6, suggesting short-term institutions are not necessarily chasingoverpriced companies. This table indicates that short-term ownership is persistent and is corre-lated with other stock characteristics. The correlations are suggestive that short-term ownership isrelated to noise traders, since the types of stocks that short-term institutions overweight are oftenassociated with investor sentiment (Baker and Wurgler, 2006). However, correlation does not nec-essarily imply causation. It is possible that short-term ownership might influence the characteristics34of these stocks, for example, idiosyncratic volatility. Future research remains to better identify thecausal relationship between short-term institutional ownership and stock characteristics.3.4 Empirical findingsThis section presents empirical tests of my model’s cross-sectional predictions. These predictionsrelate a stock’s ex ante short-term ownership with its buy-and-hold return, return predictability,and trading profit generated by short-term institutions. Following the traditions in empirical assetpricing, I test these predictions based on portfolios sorted by ex ante short-term ownership.3.4.1 Ex ante short-term ownership sorted portfoliosAt any point in time, a stock’s short-term ownership can be affected by the realized demand of noisetraders. According to my model, ex ante short-term ownership and realized short-term ownershippredict future stock returns in different directions. Ex ante short-term ownership negatively pre-dicts a stock’s future long-term return, but realized short-term ownership positively predicts stockreturn in the short run, because short-term institutions trade against noise traders. To reduce theeffect of realized mispricing shocks, I first take the average of short-term ownership in each year.Then, in the beginning of April in year t +1, I sort stocks into five different portfolios based theiraverage short-term ownership in year t. Skipping one quarter between the measurement period andsorting period further reduces the influence of any realized shock to short-term ownership.Table 3.4 Panel A presents summary statistics on the composition of each quintile portfolio.Quintile 1 contains stocks with the lowest ex ante short-term ownership, while quintile 5 containsstocks with the highest. On average, each quintile portfolio has approximately 790 stocks. Theaggregate market weight of quintile 1 is the largest at 33% of the market. Institutions ranked in thebottom turnover decile (i.e. long-term institutions), on average, invest 41% of their total capitalin quintile 1, while institutions ranked in the top turnover decile ( i.e., short-term institutions)only invest 11% of their capital in quintile 1. The aggregate market weight for quintile 5 is 6%.Low turnover institutions underweight quintile 5, only investing 3% of their capital, while high-turnover institutions devote 21% of their capital to quintile 5, which is more than three times themarket allocation. The deviation in asset allocation indicates the sorting is effective in separatingstocks primarily held by long-term and short-term institutions.Table 3.4 Panel B depicts the transition matrix for the five quintile portfolios. This panelsconfirms the persistence of short-term ownership. Stocks in quintile 1 remain in the same quintilethe next year with a probability of 71%. Similarly, for stocks sorted into quintile 5, there is a57% probability of remaining in the same quintile the next year. The persistence indicates that thedifference in holdings between short-term and long-term institutions is not likely to be driven bydifferences in private information, since private information is often short lived. Even if any group35of institutions have long-lived private information, that information is revealed through disclosuresof quarterly holdings, which are publicly available.3.4.2 The cross-section of expected returnsTable 3.5 reports the first set of the main empirical results regarding the relationship betweenexpected return and expected short-term ownership. The portfolios are sorted based on each stock’sprior year average short-term ownership and held from the beginning of April until the end ofMarch the next year. For each portfolio, I compute its value-weighted and equal-weighted returns.The sample period is from 1982:04 to 2017:12. I control for risk using the CAPM, the Famaand French (1993) three-factor, and the Carhart (1997) four-factor models. Quintile 1 containsstocks with the lowest short-term ownership or highest long-term ownership. These stocks havethe highest risk-adjusted expected return among all five portfolios. The value-weighted CAPM,three-factor, and four-factor alphas of quintile 1 are 0.20%, 0.12%, and 0.12% per month with t-statistics at 2.79, 2.35, and 2.28, respectively. For quintile 5, the portfolio’s value-weighted CAPM,three-factor, and four-factor alphas are -0.36%, -0.14%, and -0.19% per month, respectively. Thedifference in alphas between quintile 5 and 1 are negative and statistically significant across allthree risk adjustment models. For example, in terms of the three-factor alpha, the difference invalue-weighted return between quintile 5 and 1 is -0.26% per month or -3.12% per year. Themagnitude of this difference is economically large considering the average mutual fund expenseratio is about 1% per year.The comparison in expected return is more pronounced using equal weighting, which meansthe relationship between expected return and short-term ownership is stronger among small capstocks than large cap stocks. Under equal weighting, the spread in the CAPM, three-factor, andfour-factor alphas between quintile 5 and 1 are -0.74%, -0.50%, and -0.37% per month with t-statistics at -4.64, -4.24, and -2.92, respectively. These findings are consistent with Chapter 2’sprediction that a stock’s expected return increases in its long-term ownership:E[v2− p0] = 2qxL (3.3)Based on the data of mutual fund holdings, Lan et al. (2015) also find that stocks largely held bylong-term funds have higher alphas than stocks largely held by short-term funds. The magnitudein their study is similar to what I find here.3.4.3 Return predictability and short-term ownershipThis section presents the tests for return predictability of stocks with different levels of ex anteshort-term ownership. The model predicts that stocks with higher ex ante short-term ownershiphave more predictable returns. In addition, the return predictability for overpriced stocks is stronger36than the return predictability of underpriced stocks. To test this prediction, I need a signal to proxyfor noise trader demand, which predicts stock returns. Stambaugh et al. (2015) constructed sucha proxy based on 11 asset pricing anomalies documented in the literature. These 11 anomaliesinclude financial distress, equity issuance, momentum, investment, and profitability anomalies,etc. The authors convert each stock’s anomaly characteristic into a percentile rank and average theranks across all 11 anomalies. Stocks with higher average scores are more overpriced. This mis-pricing score is effective in separating overpriced stocks from underpriced stocks in each month.In unreported analysis, when I sort all stocks in my sample each month into terciles based ontheir mispricing score, the monthly spread in the value-weighted three-factor alpha between theunderpriced tercile and overpriced tercile is 0.77% per month (t-statistics of 6.47) or 9.24% peryear.To test my model’s prediction, I perform a conditional double sort. For each year, I start withthe five portfolios sorted by ex ante short-term ownership as described in the previous section.Then, within each quintile portfolio, I further sort stocks into terciles each month based on theirmispricing scores. The three terciles represent the overpriced, fairly priced, and underpriced stockswithin each quintile portfolio. I compute the value-weighted return for all 15 sub-portfolios andreport their three-factor alphas in Table 3.6. The spread in alpha between underpriced and over-priced stocks increases with the stock’s ex ante short-term ownership. In quintile 1, the spreadin the three-factor alpha is 0.53% per month, while in quintile 5, the spread is 1.37% per month,more than double the spread in the bottom quintile. This increased spread is primarily driven bythe overpriced stocks. Overpriced stocks in quintile 1 have a monthly abnormal return of -0.29%and overpriced stocks in quintile 5 have a monthly abnormal return of -0.97%, a striking differenceof -0.68% per month. Underpriced stocks in quintile 1 have a monthly abnormal return of 0.25%and underpriced stocks in quintile 5 have a monthly abnormal return of 0.41%, a difference of only0.16% per month. Figure 3.3 plots the annualized abnormal return of each sub-portfolio. The fig-ure clearly illustrates not only that the spread in return increases with ex ante short-term ownershipbut also that such a relationship is asymmetrical: more pronounced on the downside.Both Table 3.6 and Figure 3.3 provide strong evidence that short-term institutions prefer to holdstocks with more predictable returns. The spread in abnormal return between underpriced stocksand overpriced stocks is much higher in quintile 5 than in quintile 1. This indicates that stocks inquintile 5 are much more predictable on a monthly basis than stocks in quintile 1. Any investorwho trades on this monthly predictor, the mispricing score, can make much higher abnormal returnsfrom quintile 5 than from quintile 1.Figure 3.3 also provides strong support for the model’s assumption that short-selling is morecostly. This can be seen from the fact that overpriced stocks in quintile 5 experience much greaterdecline in return in the following month than the increase in return of underpriced stocks. The profit37of an investor who trades on the mispricing score largely comes from selling overpriced stocks.This asymmetry in trading profit is due to the weaker aggregate selling pressure of overpricedstocks, which allows the degree of overpricing to be greater than underpricing. The selling pressureof overpriced stocks from arbitrageurs is weaker than their buying pressure of underpriced stocks,because selling stocks short is more costly than buying stocks.3.4.4 Trading profits of short-term and long-term institutionsMy model predicts that short-term institutions benefit more than long-term institutions from trad-ing against noise traders. More importantly, my model predicts that among stocks with more exante short-term ownership, short-term institutions generate more trading profit, because their exante ownership indicates that those stocks are more exposed to noise trader shocks. To test thisprediction, I first select institutions ranked in the top decile in terms of turnover ratio as short-terminstitutions and institutions in the bottom turnover decile as long-term institutions. Then, I aggre-gate the holdings of these two groups, which allow me to determine the number of dollars investedin each stock in each quarter by those two groups. With this information, I can compute the totalreturn generated by each group of institutions among a given portfolio of stocks. This approachallows me to measure the trading profit conditional on both the type of institutions and the type ofstocks.I start with the same quintile portfolios sorted by ex ante short-term ownership. Instead ofcomputing the buy-and-hold returns using market capitalization as weights, I compute the totalreturn of these quintile portfolios using the actual number of dollars invested in each stock asweights. Table 3.7 Panel A reports the risk-adjusted total return in each quintile by long-terminstitutions. Similar to the buy-and-hold return, long-term institutions have lower total return inquintile 5 than in quintile 1. The difference between long-term institution’s total return and marketvalue weighted return, reported in Table 3.5 , is within only a few basis points. This means thatlong-term institutions are not rebalancing much within each quintile.Table 3.7 Panel B reports the total return of short-term institutions from each quintile. Similarto long-term institutions, short-term institutions also generate higher abnormal return from quin-tile 1 than quintile 5, but the difference is smaller in both magnitude and statistical significance.Panel C shows the difference in total return between long-term and short-term institutions in eachquintile. First, short-term institutions deliver higher abnormal return in every quintile portfoliothan long-term institutions under the CAPM and the three-factor models. Second, the differencemonotonically increases with ex ante short-term ownership. In quintile 1, short-term institutionsoutperform long-term institutions by a small and statistically insignificant margin across all threemodels. However, in quintile 5, short-term institutions outperform long-term institutions by 0.25%,0.28%, and 0.17% per month under the CAPM, the three-factor, and the four-factor models. These38results are all statistically significant at the 1% level.In Panel C, this rising pattern is consistent across all three models. With the addition of the mo-mentum factor, the excess returns of short-term institutions are reduced by about one-third, whichindicates that the momentum factor explains part of the trading profit of short-term institutions.Figure 3.4 plots the market, long-term and short-term institutions’ total return from each quintile.The graph clearly indicates that long-term institutions and the market have similar returns, and theirreturns both decrease with short-term ownership, while short-term institutions generate higher re-turns than long-term institutions. This finding provides evidence that short-term institutions aremore sophisticated than long-term institutions at trading against mispricing. Short-term institu-tions anticipate which stocks are more likely to be mispriced and are willing to pay a premium forholding these stocks in order to sell them at more favorable prices in the future.Table 3.7 is based on the performance of institutions in the top and bottom turnover deciles. Ta-ble 3.8 reports the trading profit of institutions in deciles 2 to 9. Qualitatively, the results presentedTable 3.8 are similar to those in Table 3.7 . Institutions in higher turnover deciles outperform long-term institutions among stocks in quintile 5. For example, the aggregate of institutions in decile8 and 9 outperform long-term institutions among stocks in quintile 5 by 0.12% per month in termof the three-factor alpha. Institutions in deciles 4 to 7 also generate significantly more abnormalreturn in quintile 5 than institutions in the bottom turnover decile. The findings in this section con-firm my prediction that short-term institutions perform better than long-term institutions amongstocks with more ex ante short-term ownership.3.4.5 Exploring the performance of short-term institutions over timeMy model so far only predicts where short-term institutions generate more trading profit in thecross section of stocks. It is worthwhile to explore when short-term institutions deliver moretrading profit. An intuitive prediction is that during periods when investor sentiment is high, short-term institutions have better performance. This prediction can be easily seen from the modelassuming during periods with more investor sentiment, the volatility of noise trader demand σuincreases for all stocks. I test this prediction using the sentiment index constructed by Baker andWurgler (2006), which is the first principle component of six proxies of investor sentiment: the firstday return of IPOs, number of IPOs in a month, closed-end fund discount, premium on dividendpaying stocks, the ratio of equity issuance to debt issuance, and NYSE share turnover. Pástor et al.(2017) show that the BW sentiment index explains the average turnover ratio of active mutualfunds. Therefore, it is suggestive that the BW sentiment index also predicts the trading profit ofshort-term institutions, especially, in quintile 5. To test this prediction, I perform the following39time series regression:Rt = a+b∆St−1+ cMKTt +dSMBt + eHMLt + εt (3.4)where ∆St−1 is change in the BW sentiment index in month t−1 andMKTt , SMBt , HMLt are thethree Fama-French factors. Table 3.9 reports the results. In Columns 1 to 5, the dependent variableis the difference in the total return between short-term and long-term institutions in quintiles 1 to5. The coefficient b increases from 0.28 (t-statistic: 0.87) in Column 1 to 1.36 (t-statistic: 2.02)in Column 5. In Column 6, the dependent variable is the simple average of the difference in allfive quintiles. The coefficient b is 0.70 with a t-statistic of 1.87. Among the six components ofthe BW sentiment index, I find that the first day return on IPOs is the most robust predictor ofshort-term institutions’ trading profit. Table 3.10 presents the result using the IPO first day returnas the predictor.Rt = a+bRIPOt−1 + cMKTt +dSMBt + eHMLt + εt (3.5)The dependent variables are the same as in 3.9. The coefficient b increase from 0.33 (t-statistic:1.09) in Columns 1 to 1.41 (t-statistic: 2.34) in Column 5. The coefficient b in Column 6 is 1.18(t-statistic: 3.07) . This section confirms that the time series variation in investor sentiment affectsthe time-series performance of short-term institutions.3.4.6 RobustnessThis section checks the robustness of my main empirical findings. First, following the advice ofFama and French (2008) and Hou et al. (2017), I exclude micro-cap stocks from my sample tocheck whether my results rely on micro-cap stocks. Table 3.11 performs the same test as Table 3.7by removing micro-cap stocks at the portfolio sorting stage. The results are quantitatively similarto Table 3.7. Stocks primarily held by short-term institutions have negative buy-and-hold alphameasured by all three models, and short-term institutions deliver more trading profit than long-term institutions in all five quintile portfolios. The difference is monotonically increasing fromquintile 1 to quintile 5 and statistically significant in quintile 5 across all three models.I control for additional factors when I evaluate the total return of short-term institutions rela-tive to long-term institutions. The additional factors are the Pástor and Stambaugh (2003) liquidityfactor, the Fama and French (2015) five factors, and the Stambaugh and Yuan (2016) mispricingfactors. As shown in Table 3.12, the results are qualitatively consistent with previous tables. Thetrading profit in quintile 5 is the largest under across all four factor models in both all-stock sam-ple and all-but-micro sample. An interesting finding from Table 3.12 is that the model based onStambaugh and Yuan (2016) mispricing factors produces the smallest average alpha across the fivequintile portfolios. This result means that the trading profits of short-term institutions can be best40explained by mispricing factors.The previous section shows that during periods with more investor sentiment, short-term insti-tutions perform better. During the last four decades, the period with the highest level of investorsentiment is arguably the dotcom bubble era. The Nasdaq composite index reached an all-timehigh in March 2000. Several authors have documented that hedge funds generated more abnormalreturns during the dotcom bubble period (Brunnermeier and Nagel, 2004; Griffin and Xu, 2009;Griffin et al., 2011). This section shows that my result is robust when excluding the dotcom bub-ble period. Table 3.13 reproduces the results of Table 3.7 excluding the period from 1998:04 to2001:03. The results are qualitatively the same as Table 3.7. Short-term institutions outperformlong-term institutions in quintile 5 by 0.19% (t-statistics 2.57), 0.20% (t-statistics 3.30), and 0.12%(t-statistics 2.01) per month in terms of the CAPM, the three-factor, and the four-factor alphas, re-spectively.3.4.7 Alternative explanationsThis section discusses alternative explanations to why short-term institutions overweight low-return stocks relative to long-term institutions. One alternative explanation is that long-term in-stitutions have private information that short-term institutions do not have. Therefore, long-terminstitutions can select high-return stocks. This explanation suffers from two drawbacks. First,any private information not incorporated into stock prices within 45 days is revealed through thepublic disclosure of portfolio holdings. If long-term institutions have private information, rationalinvestors can mimic their strategy after observing their holdings, which eliminates the informationadvantage of long-term institutions. The private information of long-term institutions should nothave long-run return predictability beyond 45 days, which is at odds with the fact that the higherabnormal return of stocks primarily held by long-term institutions lasts beyond one year. Thesecond drawback is that this explanation does not explain why short-term institutions outperformlong-term institutions through trading. In all five quintile portfolios, short-term institutions havehigher total return than long-term institutions, which indicates that short-term institutions are moreskilled than long-term institutions in trading. Overall, the private information channel does notsystematically explain my empirical findings.The second explanation is based on liquidity risk. Long-term institutions could be more toleranttowards liquidity risk than short-term institutions (Kamara et al., 2016). Amihud and Mendelson(1986) and Beber et al. (2018) develop models that predict long-term investors take more liquidityrisk, because they are able to hold on to assets for longer period of time than short-term institutions.Therefore, stocks primarily held by long-term institutions could have higher expected return due tocompensation for illiquidity. In Table 3.14, I regress the value-weighted return of each quintile onthe three Fama-French factors, the Carhart momentum factor, and the Pastor-Stambaugh liquidity41factor. The results do not support the liquidity hypothesis. First, the additional liquidity factor doesnot explain the difference in expected return between quintile 1 and 5. In fact, the loadings on theliquidity factor have the opposite signs as the liquidity based explanation. If long-term institutionsare more willing to take illiquidity risk, the loading on the liquidity factor of quintile 1 shouldbe greater than quintile 5’s loading. The liquidity based explanation also does not explain whythe performance of short-term institutions relative to long-term institutions monotonically increasefrom quintile 1 to quintile 5 and the asymmetry in return predictability. The fact that larger andolder stocks have more long-term institutional investors further weakens the liquidity risk basedexplanation. Therefore, it is difficult to explain my findings based on heterogeneous preferencesfor liquidity among long-term and short-term institutions.3.4.8 Discussion of resultsThis paper’s findings have several implications for asset management practice and performanceevaluation. First, my results indicate that an asset’s exposure to mispricing shocks provides op-portunities for investors to make trading profits. If an institution can trade frequently, a low-returnasset might be more attractive than a high-return asset when the low-return asset provides moretrading opportunities. Moreover, if an institution is a buy-and-hold investor, such as a public pen-sion fund, it might consider hiring short-term institutions to manage assets with high exposure tonoise trader shocks or in market with tight short-selling constraints. Dyck et al. (2013) find thatactive asset management outperforms passive management in emerging markets, presumably be-cause there are more noise traders and more stringent short-selling constraints in those markets.To implement these strategies in practice, one empirical challenge is to directly measure a stock’sexposure to mispricing shocks. My findings suggest that ex ante short-term institutional ownershipis a proxy for such exposure.The performance evaluation of an asset manager depends on its asset allocation and tradingability. Since according to my model, short-term managers are expected to allocate more capi-tal to low-return stocks, their performance might be negatively affected by their asset allocationdecisions. Depending on the purpose of the evaluation, one might want to control for the nega-tive correlation between expected return and expected short-term ownership. Several authors havedeveloped methods to control for asset allocation effects. For example, Wermers (2000) decom-poses a fund’s return into stock picking and style picking components. Style picking reflects thefund manager’s asset allocation decision, while stock picking reflects the manager’s trading ability.Similarly, Kacperczyk et al. (2006a) measure the difference between the reported fund return andthe return implied from prior quarter’s holdings, which they call the return gap. This return gapalso controls for the manager’s asset allocation decision and isolates the manager’s intra-quartertrading skill. Ferson and Wang (2018) develop a panel regression methodology to measure a man-42ager’s skill. They use stock fixed effects to control for a manager’s return due to asset allocationdecisions.3.5 ConclusionThis chapter provides an empirical analysis of the asset allocation decision among institutional in-vestors with different holding horizons. Short-term institutions prefer to invest in younger, smaller,and more volatile stocks. In addition, stocks that are primarily held by short-term institutions havelower risk-adjusted returns than stocks primarily held by long-term institutions. These empiricalregularities can be explained in a model with speculative demand shocks and short-selling con-straints. In the presence of short-selling constraints, future mispricing creates a resale option forthe initial owners of a stock. Stocks with more exposure to these shocks have lower expectedreturns, because their resale options are more valuable. Since short-term institutions trade morefrequently, they benefit more from resale options than long-term institutions. In equilibrium, short-term institutions overweight stocks with more valuable resale options, while long-term institutionsoverweight stocks with higher buy-and-hold returns. The additional demand from short-term in-stitutions reduces the buy-and-hold returns of stocks that are more exposed to speculative demandshocks. In equilibrium, a stock’s exposure to speculative demand shocks explains both its ex-pected return and ownership structure. Furthermore, stocks primarily held by short-term institu-tions should have more predictable returns, and their return predictability is stronger when theybecome overpriced. Empirical findings strongly support these predictions. Short-term institutionsoutperform long-term institutions by more than 3% per year among stocks primarily held by short-term institutions, while their performance is similar among stocks primarily held by long-term in-stitutions. My results highlight how market frictions determine the equilibrium asset allocation ofinstitutional investors according to their holding horizons and short-term institutions benefit fromholding stocks more exposed to mispricing shocks in advance. Exploring my model’s implicationsin the international setting or other asset classes is of interest for future research.43Figure 3.1: Average institutional turnover ratio vs. stock characteristics.This figure presents the average turnover ratio of institutional investors for stocks in different characteristic deciles.For every stock, I measure the average turnover ratio of institutional investors that own the stock, weighted by thenumber of shares each institution owns. The characteristic decile is on the x-axis and the average turnover ratio is onthe y-axis. The characteristics are the CAPM beta, market cap, book-to-market, momentum, idiosyncratic volatility,and stock age. The sample period is from 1981 to 2017.44Figure 3.2: Average institutional turnover ratio by sector.This figure presents the average institutional turnover ratio for stocks in each sector. Sector classification is based onthe GIC sector code. For every stock, I measure the average turnover ratio of institutional investors that own the stock,weighted by the number of shares each institution owns. I then average these quantities within each sector. The sampleperiod is from 1981 to 2017.45Figure 3.3: Asymmetry in return predictability.This figure presents annualized three-factor alphas of sub-portfolios sorted by the ex ante short-term ownership andmispricing score. I first sort stocks into five quintile portfolios in the beginning of April in each year based on theirprior year’s short-term ownership averaged across four quarters (i.e. the ex ante short-term ownership). Short-termownership of a stock in each quarter is proxied by the the average turnover ratio of institutional investors that ownthe stock. Then, within each quintile and in the beginning of each month, I sort stocks into undervalued, fair-valuedand overvalued terciles based on the Stambaugh et al. (2015) mispricing score. The y-axis is the annualized abnormalreturn for each sub-portfolio. The top line represents underpriced stocks. The line in the middle represents fairly-priced stocks. And the bottom line represents the overpriced stocks. The return of each sub-portfolio is measuredwith value weights. The abnormal return is measured with respect to the Fama-French (1993) three factor model. Thesample period for returns is from 1982:04 to 2016:12.46Figure 3.4: Buy-and-hold return and rebalanced return.This figure presents the annualized Fama-French three-factor alphas for each quintile portfolio sorted by the stock’s exante short-term ownership. I first sort stocks into five quintile portfolios in the beginning of April in each year basedon their prior year’s short-term ownership averaged across four quarters (i.e. the ex ante short-term ownership). Short-term ownership of a stock in each quarter is proxied by the the average turnover ratio of institutional investors thatown the stock in the quarter. The returns of stocks in each quintile are measured with different weighting schemes: themarket-cap weighted return (market), the long-term institutions’ dollar weighted return, and the short-term institutions’dollar weighted return. Long-term (short-term) institutions are institutions ranked in the bottom (top) turnover ratiodecile. I aggregate their holdings in the beginning of each quarter to obtain the total dollars invested in each stock bythe two groups of institutions. The sample period for returns is from 1982:04 to 2017:12.47Table 3.1: Summary statistics of institutions.A. Summary statisticsN Mean Median Std. Dev. Min MaxAUM (million) 1309 4,151 386 27,854 0 1,959,319Number of holdings 1309 241 96 449 10 6074Turnover ratio 1309 0.46 0.30 0.44 0.01 2.47B. Persistence of turnover ratio(1) (2) (3) (4)VARIABLES Turnover ratio Turnover ratio Turnover ratio Turnover ratioLag 1 yr turnover ratio 0.90***(77.13)Lag 5 yr turnover ratio 0.79***(43.35)Lag 10 yr turnover ratio 0.70***(32.43)Lag 20 yr turnover ratio 0.53***(11.19)Observations 38,057 16,827 8,924 2,308Adjusted R-squared 0.838 0.659 0.516 0.266C. Turnover ratio by legal designationsInstitutional Type Average Turnover Ratio Std. Dev. in Turnover RatioBank Trusts 22% 14%Corporate Pension Sponsors 33% 30%Investment Companies 51% 45%Insurance Companies 33% 30%Public Pension Sponsors 19% 21%Universities and Endowments 30% 25%Miscellaneous and Unclassified 54% 54%This table presents the summary statistics for institutional investors in my sample. Panel A reports the summary statis-tics for their asset under management (AUM), number of stock holdings, and annualized turnover ratio. The numberof observations N is the time-series average number of institutions in my sample. Panel B reports the persistence ofturnover ratio by regressing each year’s turnover ratio on lagged turnover ratio. Panel C reports average annualizedturnover ratio for institutions with different legal designations. All t-statistics (in parentheses) are based on standarderrors clustered at both the institution and year level. Superscripts ***, **, * correspond to statistical significance atthe 1, 5, and 10 percent levels, respectively. The sample period is from 1981 to 2017.48Table 3.2: Summary statistics of stocks.A. Summary statisticsN Mean Median Std. Dev. Min MaxShort-term Ownership 4025 0.38 0.36 0.15 0.11 0.93Beta 3943 0.83 0.78 0.78 -1.14 3.22Market cap 4025 2483 226 13747 0 868,880Book-to-market 3572 0.73 0.58 0.62 0.04 3.73Momentum 3766 0.13 0.07 0.55 -0.83 2.62Idiosyncratic volatility 3943 0.03 0.02 0.02 0.01 0.12Stock age 4025 15.55 10.92 15.43 0.08 92.08B. Correlation: full sampleST Own Beta MC BM Mom IVol AgeShort-term Ownership 100%Beta 12% 100%Log(Market cap) -2% 26% 100%Book-to-market -13% -14% -30% 100%Momentum 19% 9% 17% -9% 100%Idiosyncratic volatility 12% 5% -51% 14% -18% 100%Stock age -26% 1% 38% 5% 0% -29% 100%C. Correlation: all-but-microST Own Beta MC BM Mom IVol AgeShort-term Ownership 100%Beta 17% 100%Log(Market cap) -17% 12% 100%Book-to-market -14% -13% -16% 100%Momentum 24% 6% 13% -7% 100%Idiosyncratic volatility 31% 26% -36% -12% -15% 100%Stock age -31% -8% 39% 14% -3% -32% 100%This table reports summary statistics for stocks in my sample. Panel A reports the summary statistics for stockcharacteristics. Short-term ownership for a stock in a given quarter is proxied by the the average turnover ratioof institutional investors that own the stock in the quarter, weighted by the number of shares each institution owns.Definitions of other characteristics are in Appendix B. The number of observations N is the time-series average numberof observations for each characteristic. Panel B reports the pairwise correlation of stock characteristics among allstocks in the sample. Panel C reports the pairwise correlation of stock characteristics by excluding micro-cap stocks,which are defined as stocks with a market cap less than the NYSE 20th percentile in the end of the prior year. Allstock characteristics are winsorized at the 1st and 99th percentile. The sample period is from 1981 to 2017.49Table 3.3: The cross section of short-term ownership.(1) (2) (3) (4) (5) (6)Full sample All-but-microVARIABLES ST Own. ST Own. ST Own. ST Own. ST Own. ST Own.Lag 4 qtr. ST Own. 0.61*** 0.56*** 0.64*** 0.56***(66.97) (79.78) (57.09) (75.39)Beta 1.42*** 0.44*** 1.76*** 0.52***(12.43) (6.15) (10.25) (5.26)Log(Market cap) 0.09 -0.10* -0.71*** -0.34***(0.96) (-1.95) (-8.03) (-6.79)Book-to-market -1.12*** -0.13 -0.33* 0.70***(-6.68) (-1.29) (-1.66) (6.26)Momentum 5.40*** 6.04*** 6.62*** 6.32***(32.93) (30.48) (25.94) (24.75)Volatility 33.93*** 19.58*** 124.83*** 40.97***(4.70) (4.17) (11.82) (5.70)Stock age -0.19*** -0.05*** -0.11*** -0.03***(-25.62) (-15.93) (-17.82) (-9.97)Observations 525,877 507,355 486,703 274,873 261,341 260,068Adjusted R-squared 0.400 0.224 0.503 0.476 0.357 0.610Industry FE Yes Yes Yes YesTime FE Yes Yes Yes YesThis table reports the statistical relationship between short-term ownership and other stock characteristics. Short-termownership for a stock in a given quarter is proxied by the the average turnover ratio of institutional investors that ownthe stock in the quarter, weighted by the number of shares each institution owns. Columns (1) to (3) include all stocksin the sample. Columns (4) to (6) exclude micro-cap stocks, which are stocks with prior year-end market cap smallerthan the NYSE 20th percentile. Except for lagged variables, all other independent variables in the regression aremeasured contemporaneously as the y-variable. All stock characteristics are winsorized at the 1st and 99th percentile.All t-statistics (in parentheses) are based on standard errors clustered at both the stock and quarter level. Superscripts***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.50Table 3.4: Portfolio sorts based on ex ante short-term ownership.Ex ante short-term ownership sorted portfoliosLow 2 3 4 HighPanel A: allocationNumber of stocks 789 791 790 788 785Total weight in the market portfolio 33% 32% 18% 11% 6%Total weight in long-term institutions 41% 34% 15% 7% 3%Total weight in short-term institutions 11% 22% 23% 23% 21%Panel B: transition matrixLow 2 3 4 HighLow 71 19 5 3 22 22 48 21 7 33 6 27 41 20 64 3 9 29 42 18High 2 3 9 29 57This table reports the number of stocks and their total portfolio weight in each quintile portfolio sorted by ex anteshort-term ownership. In the beginning of April in each year, I sort stocks into five different portfolios based ontheir prior year’s short-term ownership averaged across four quarters (i.e. ex ante short-term ownership). Short-termownership for a stock in a given quarter is proxied by the the average turnover ratio of institutional investors that ownthe stock in the quarter, weighted by the number of shares each institution owns. In the end of each month, I countthe number of stocks in each portfolio. I also measure the percentage of total amount of capital allocated to eachportfolio by the market, low-turnover institutions, and high turnover institutions. For the market, I take the sum themarket capitalization of stocks in each portfolio and divided by the total size of the market. For low and high turnovermanagers, I take the sum of their dollar value invested in each portfolio and then divide by the total size of their totalasset. Long-term (short-term) institutions are institutions ranked in the bottom (top) turnover ratio decile. The reportednumbers are the time series averages of each quantity. Panel B reports the transition probability matrix for stocks fromone quintile to another between two consecutive years.51Table 3.5: Cross-sectional abnormal returns of stocks.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoPanel A: value-weightedCAPM Alpha 0.20*** 0.02 0.07 -0.22** -0.36** -0.56**(2.79) (0.45) (1.25) (-2.26) (-2.03) (-2.36)FF3 Alpha 0.12** 0.01 0.07 -0.14* -0.14 -0.26*(2.35) (0.16) (1.17) (-1.87) (-1.33) (-1.89)FFC4 Alpha 0.12** 0.03 0.08 -0.12 -0.19* -0.31**(2.28) (0.60) (1.25) (-1.57) (-1.68) (-2.12)Observations 429 429 429 429 429 429Panel B: equal-weightedCAPM Alpha 0.28** 0.22* 0.12 -0.12 -0.46** -0.74***(2.10) (1.93) (1.02) (-0.81) (-2.41) (-4.64)FF3 Alpha 0.14 0.06 0.01 -0.14 -0.36*** -0.50***(1.51) (0.95) (0.21) (-1.46) (-2.82) (-4.24)FFC4 Alpha 0.27*** 0.21*** 0.18*** 0.08 -0.10 -0.37***(2.83) (3.45) (2.87) (0.82) (-0.72) (-2.92)Observations 429 429 429 429 429 429This table reports the abnormal returns of portfolios sorted by ex ante short-term ownership. In the beginning of Aprilin each year, I sort stocks into five different portfolios based on their prior year’s short-term ownership averaged acrossfour quarters (i.e. ex ante short-term ownership). Short-term ownership for a stock in a given quarter is proxied by thethe average turnover ratio of institutional investors that own the stock in the quarter, weighted by the number of shareseach institution owns. The abnormal returns are computed based on the CAPM model, the Fama-French three-factormodel (FF3), and the Fama-French-Carhart four-factor model (FFC4). Panel A computes returns using value weights.Panel B computes returns using equal weights. The sample period for returns is from 1982:04 to 2017:12. All t-statistics (in parentheses) are based on (heteroskedasticity) robust standard errors. Superscripts ***, **, * correspondto statistical significance at the 1, 5, and 10 percent levels, respectively.52Table 3.6: Asymmetry in return predictability.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoUndervalued stocks 0.25*** 0.08 0.38*** 0.32*** 0.41*** 0.16(3.36) (1.16) (4.18) (2.94) (2.94) (0.94)Fair-valued stocks 0.11 0.09 0.02 -0.04 0.11 -0.00(1.18) (1.14) (0.17) (-0.39) (0.66) (-0.01)Overvalued stocks -0.29** -0.36*** -0.36*** -0.94*** -0.97*** -0.68***(-1.99) (-3.21) (-3.14) (-6.78) (-6.15) (-3.32)Under minus overvalued 0.53*** 0.44*** 0.74*** 1.26*** 1.37*** 0.84***(3.17) (2.95) (4.80) (6.81) (6.77) (3.64)Observations 417 417 417 417 417 417This table reports the three-factor alphas of sub-portfolios sorted by the ex ante short-term ownership and mispricingscore. In the beginning of April in each year, I sort stocks into five different portfolios based on their prior year’sshort-term ownership averaged across four quarters (i.e. ex ante short-term ownership). Short-term ownership for astock in a given quarter is proxied by the the average turnover ratio of institutional investors that own the stock in thequarter, weighted by the number of shares each institution owns. Then, within each quintile and in the beginning ofeach month, I sort stocks into undervalued, fair-valued and overvalued terciles based on the Stambaugh et al. (2015)mispricing score. The return of each sub-portfolio is measured by value-weighting stocks in the sub-portfolio. Theabnormal return is measured with respect to the Fama-French three-factor model. The sample period for returns isfrom 1982:04 to 2016:12. All t-statistics (in parentheses) are based on (heteroskedasticity) robust standard errors.Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.53Table 3.7: The cross section of trading profits of institutions.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoPanel A: long-term institutionsCAPM Alpha 0.22*** 0.02 0.09 -0.23** -0.42** -0.64***(2.73) (0.47) (1.37) (-2.33) (-2.50) (-2.75)FF3 Alpha 0.14** 0.01 0.09 -0.15* -0.22** -0.36**(2.43) (0.12) (1.31) (-1.83) (-2.02) (-2.55)FFC4 Alpha 0.14** 0.03 0.09 -0.14* -0.24** -0.38***(2.35) (0.64) (1.32) (-1.69) (-2.13) (-2.59)Panel B: short-term institutionsCAPM Alpha 0.25*** 0.14** 0.21*** 0.00 -0.17 -0.42*(3.51) (2.53) (2.69) (0.01) (-0.88) (-1.76)FF3 Alpha 0.18*** 0.12** 0.21*** 0.09 0.06 -0.12(3.11) (2.23) (2.76) (0.97) (0.55) (-0.83)FFC4 Alpha 0.14** 0.07 0.15* 0.02 -0.07 -0.21(2.33) (1.31) (1.84) (0.17) (-0.61) (-1.43)Panel C: short-term minus long-termCAPM Alpha 0.03 0.11** 0.12*** 0.23*** 0.25*** 0.22***(0.64) (2.59) (2.74) (3.64) (3.78) (3.03)FF3 Alpha 0.04 0.11*** 0.12*** 0.24*** 0.28*** 0.25***(0.86) (2.81) (2.92) (4.05) (4.28) (3.26)FFC4 Alpha -0.00 0.04 0.06 0.16*** 0.17*** 0.17**(-0.09) (1.09) (1.37) (2.85) (2.73) (2.37)This table shows the abnormal returns of long-term and short-term institutions in portfolios sorted by ex ante short-term ownership. In the beginning of April in each year, I sort stocks into five different portfolios based on their prioryear’s short-term ownership averaged across four quarters (i.e. ex ante short-term ownership). Short-term ownershipfor a stock in a given quarter is proxied by the the average turnover ratio of institutional investors that own the stock inthe quarter, weighted by the number of shares each institution owns. Short-term (long-term) institutions are institutionsin the top (bottom) turnover ratio decile. The returns of each quintile in Panel A and B are computed by weightingindividual stock returns by the total dollars invested by each group of institutions. The returns in Panel C are thereturns in Panel B minus the returns in Panel A. The abnormal returns are computed based on the CAPM model,the Fama-French 3 factor model (FF3), and the Fama-French-Carhart 4 factor model (FFC4). The sample period forreturns is from 1982:04 to 2017:12. All t-statistics (in parentheses) are based on (heteroskedasticity) robust standarderrors. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.54Table 3.8: Trading profit of institutions with medium holding horizon.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoDeciles 2 and 3 -0.01 -0.02 -0.04* 0.04 0.04 0.05(-0.33) (-1.20) (-1.94) (1.13) (0.89) (0.91)Deciles 4 and 5 0.00 0.01 -0.05* 0.02 0.11** 0.11**(0.09) (0.56) (-1.86) (0.69) (2.42) (2.04)Deciles 6 and 7 0.02 -0.03* -0.05** 0.01 0.16*** 0.14**(0.71) (-1.70) (-2.28) (0.15) (3.40) (2.45)Deciles 8 and 9 0.00 0.02 0.01 0.05 0.12*** 0.12**(0.00) (1.03) (0.20) (1.48) (2.72) (2.31)Observations 429 429 429 429 429 429This table shows the difference in performance between institutions from turnover deciles 2 to 9 (i.e. medium-terminstitutions) and institutions in the bottom turnover decile (i.e. long-term institutions). In the beginning of April ineach year, I sort stocks into five different portfolios based on their prior year’s short-term ownership averaged acrossfour quarters (i.e. ex ante short-term ownership). Short-term ownership for a stock in a given quarter is proxied bythe the average turnover ratio of institutional investors that own the stock in the quarter, weighted by the number ofshares each institution owns. I then aggregate the holdings of institutions ranked in the specified deciles. I computethe dollar-weighted returns of each portfolio institutions from decile 2 to 9. I subtract their returns by the returns ofinstitutions from the bottom turnover decile. The abnormal return is measured with respect to the Fama-French threefactor model. The sample period for returns is from 1982:04 to 2017:12. All t-statistics (in parentheses) are based on(heteroskedasticity) robust standard errors. Superscripts ***, **, * correspond to statistical significance at the 1, 5,and 10 percent levels, respectively.55Table 3.9: Time varying trading profit: sentiment index.(1) (2) (3) (4) (5) (6)Low 2 3 4 High AverageLag change in sentiment 0.28 0.36 0.07 1.44** 1.36** 0.70*(0.87) (0.90) (0.16) (2.28) (2.02) (1.87)Excess Return on the Market 0.05*** 0.01 -0.01 0.01 -0.01 0.01(3.97) (0.85) (-1.11) (0.39) (-0.66) (0.99)High-Minus-Low Return -0.01 0.01 0.01 -0.04 -0.07** -0.02(-0.22) (0.46) (0.28) (-0.94) (-2.23) (-0.84)Small-Minus-Big Return 0.13*** 0.12*** 0.11*** 0.16*** 0.14*** 0.13***(7.68) (4.92) (4.64) (3.46) (3.82) (5.44)Constant 0.04 0.11*** 0.12*** 0.26*** 0.31*** 0.17***(0.85) (2.62) (2.73) (4.13) (4.40) (4.41)Observations 403 403 403 403 403 403Adjusted R-squared 0.224 0.148 0.114 0.169 0.130 0.253This table reports the results of the following regression equations. The regression equation isRt = a+b∆St−1+ cMKTt +dSMBt + eHMLt + εtwhere ∆St−1 is the change in Baker and Wurgler (2006) sentiment index and MKTt , SMBt , HMLt are the three Fama-French factors. In Columns 1 to 5, the dependent variables Rt are the differences in the rebalanced return betweenshort-term and long-term institutions in ex ante short-term ownership quintiles 1 to 5. In Column 6, the dependentvariable is the average of the first 5 columns. The quintiles are sorted in the beginning of April in each year. I sort stocksinto five different portfolios based on their ex ante short-term ownership, which is the average short-term ownership inthe prior year. Short-term ownership for a stock is measured as the average of turnover ratio of institutional investorsthat own the stock, weighted by the number of shares each institution owns. Long-term (short-term) institutions areinstitutions in the bottom (top) turnover ratio decile. I compute the rebalanced return using the aggregate holdings ofeach group of institutions. The sample period for returns is from 1982:04 to 2015:10. All t-statistics (in parentheses)are based on (heteroskedasticity) robust standard errors. Superscripts ***, **, * correspond to statistical significanceat the 1, 5, and 10 percent levels, respectively.56Table 3.10: Time varying trading profit: IPO return.(1) (2) (3) (4) (5) (6)Low 2 3 4 High AverageLag IPO return 0.33 0.80* 0.82** 2.56*** 1.41** 1.18***(1.09) (1.65) (2.53) (3.45) (2.34) (3.07)Excess Return on the Market 0.07*** 0.02 -0.01 -0.00 -0.00 0.01(5.47) (1.26) (-0.56) (-0.12) (-0.22) (1.33)High-Minus-Low Return 0.00 0.02 0.02 -0.03 -0.06* -0.01(0.10) (0.76) (0.57) (-0.61) (-1.73) (-0.39)Small-Minus-Big Return 0.13*** 0.12*** 0.11*** 0.16*** 0.15*** 0.14***(7.43) (5.12) (5.04) (3.71) (4.13) (5.75)Constant -0.05 -0.03 -0.03 -0.17 0.06 -0.04(-0.66) (-0.33) (-0.56) (-1.54) (0.56) (-0.66)Observations 393 393 393 393 393 393Adjusted R-squared 0.251 0.178 0.144 0.255 0.158 0.314This table reports the results of the following regression equations. The regression equation isRt = a+bRIPOt−1 + cMKTt +dSMBt + eHMLt + εtwhere RIPOt−1 is the average first day return of IPOs. In Columns 1 to 5, the dependent variables Rt are the differences inthe rebalanced return between short-term and long-term institutions in ex ante short-term ownership quintiles 1 to 5.In Column 6, the dependent variable is the average of the first 5 columns. The quintiles are sorted in the beginning ofApril in each year. I sort stocks into five different portfolios based on their ex ante short-term ownership, which is theaverage short-term ownership in the prior year. Short-term ownership for a stock is measured as the average of turnoverratio of institutional investors that own the stock, weighted by the number of shares each institution owns. Long-term(short-term) institutions are institutions in the bottom (top) turnover ratio decile. I compute the rebalanced return usingthe aggregate holdings of each group of institutions. The sample period for returns is from 1982:04 to 2015:12 withnon-missing IPO observations. All t-statistics (in parentheses) are based on (heteroskedasticity) robust standard errors.Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.57Table 3.11: Trading profits of institutions excluding micro-cap stocks.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoPanel A: long-term institutionsCAPM Alpha 0.15** -0.00 0.11* -0.16 -0.46*** -0.62***(2.13) (-0.05) (1.73) (-1.54) (-2.67) (-2.65)FF3 Alpha 0.08* -0.02 0.12* -0.07 -0.25** -0.34**(1.66) (-0.30) (1.75) (-0.79) (-2.21) (-2.32)FFC4 Alpha 0.09* 0.02 0.11 -0.04 -0.27** -0.36**(1.80) (0.39) (1.59) (-0.41) (-2.24) (-2.40)Panel B: short-term institutionsCAPM Alpha 0.21*** 0.14** 0.23*** 0.05 -0.22 -0.42*(3.10) (2.25) (2.87) (0.44) (-1.14) (-1.76)FF3 Alpha 0.14*** 0.12* 0.24*** 0.15* 0.02 -0.12(2.78) (1.87) (3.15) (1.73) (0.15) (-0.82)FFC4 Alpha 0.11** 0.07 0.18** 0.09 -0.11 -0.22(2.09) (1.11) (2.21) (1.08) (-0.89) (-1.45)Panel C: short-term minus long-termCAPM Alpha 0.05 0.14*** 0.11** 0.21*** 0.24*** 0.19***(1.26) (2.73) (2.36) (3.33) (3.63) (2.70)FF3 Alpha 0.06 0.13*** 0.12*** 0.22*** 0.27*** 0.21***(1.53) (2.80) (2.68) (3.62) (3.98) (2.84)FFC4 Alpha 0.02 0.05 0.07 0.13** 0.15** 0.14*(0.44) (1.13) (1.38) (2.40) (2.47) (1.92)This table shows the abnormal returns of institutions in portfolios sorted by ex ante short-term ownership. I excludestocks with market cap smaller than the NYSE 20th percentile. In the beginning of April in each year, I sort stocksinto five different portfolios based on their prior year’s short-term ownership averaged across four quarters (i.e. exante short-term ownership). Short-term ownership for a stock in a given quarter is proxied by the the average turnoverratio of institutional investors that own the stock in the quarter, weighted by the number of shares each institutionowns. Long-term (short-term) institutions are institutions in the bottom (top) turnover ratio decile. The returns of eachquintile in Panel A (B) are computed by weighting stock returns by the total dollars invested by long-term (short-term)institutions. The returns in Panel C are the difference between the two groups. The abnormal returns are computedbased on the CAPM model, the Fama-French 3 factor model (FF3), and the Fama-French-Carhart 4 factor model(FFC4). The sample period for returns is from 1982:04 to 2017:12. All t-statistics (in parentheses) are based on(heteroskedasticity) robust standard errors. Superscripts ***, **, * correspond to statistical significance at the 1, 5,and 10 percent levels, respectively.58Table 3.12: Trading profit of institutions controlling for additional factors.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoPanel A: all stocksFF3 + Liquidity Factor 0.05 0.11*** 0.13*** 0.24*** 0.29*** 0.24***(1.02) (2.67) (3.11) (4.04) (4.25) (3.11)FFC4 + Liquidity Factor 0.00 0.04 0.07 0.16*** 0.18*** 0.17**(0.08) (0.97) (1.56) (2.82) (2.78) (2.30)FF5 0.02 0.08 0.10* 0.23*** 0.26*** 0.23***(0.48) (1.51) (1.93) (3.19) (3.38) (2.80)Mispricing Factors -0.02 -0.00 0.02 0.09 0.14* 0.17*(-0.44) (-0.09) (0.35) (1.36) (1.80) (1.90)Observations 417 417 417 417 417 417Panel B: all but microFF3 + Liquidity Factor 0.06 0.12*** 0.13*** 0.23*** 0.27*** 0.21***(1.50) (2.59) (2.84) (3.71) (3.87) (2.73)FFC4 + Liquidity Factor 0.02 0.04 0.08 0.14** 0.16** 0.14*(0.43) (0.92) (1.56) (2.50) (2.42) (1.88)FF5 0.05 0.06 0.11** 0.19** 0.25*** 0.20**(1.13) (1.05) (2.11) (2.54) (3.16) (2.43)Mispricing Factors 0.00 -0.04 0.06 0.04 0.12 0.11(0.07) (-0.75) (1.03) (0.65) (1.44) (1.35)Observations 417 417 417 417 417 417This table shows the difference in the performance between high-turnover institutions and low-turnover institutions,adjusting for other factor models. The models are the Fama-French three-factor model (FF3) with Pastor and Stam-baugh (2003) liquidity, the Fama-French-Carhart four-factor model (FFC4) with Pastor and Stambaugh (2003) liquid-ity factor, the Fama-French five-factor model (FF5), and the Stambaugh and Yuan (2016) mispricing factors. Long-term (short-term) institutions are institutions in the bottom (top) turnover ratio decile. In the beginning of April ineach year, I sort stocks into five different portfolios based on their prior year’s short-term ownership averaged acrossfour quarters (i.e. ex ante short-term ownership). Short-term ownership for a stock in a given quarter is proxied bythe the average turnover ratio of institutional investors that own the stock in the quarter, weighted by the number ofshares each institution owns. I compute returns of each quintile based on the total dollars invested by each group ofinstitutions and then take the difference between the two groups. Panel A includes all stocks in the sample. PanelB excludes micro-cap stocks, which have market cap smaller than the NYSE 20th percentile. The sample period forreturns is from 1982:04 to 2016:12. All t-statistics (in parentheses) are based on (heteroskedasticity) robust standarderrors. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.59Table 3.13: Trading profit of institutions excluding the dotcom bubble.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoPanel A: long-term institutionsCAPM Alpha 0.20*** 0.00 0.05 -0.14 -0.26* -0.47**(2.80) (0.02) (0.84) (-1.57) (-1.93) (-2.45)FF3 Alpha 0.15*** -0.01 0.07 -0.09 -0.13 -0.29**(2.63) (-0.11) (1.04) (-1.16) (-1.32) (-2.12)FFC4 Alpha 0.14** 0.01 0.07 -0.09 -0.13 -0.28*(2.43) (0.13) (1.02) (-1.11) (-1.25) (-1.97)Panel B: short-term institutionsCAPM Alpha 0.21*** 0.05 0.13* -0.05 -0.08 -0.29(3.43) (1.05) (1.75) (-0.50) (-0.52) (-1.58)FF3 Alpha 0.17*** 0.05 0.15** 0.01 0.06 -0.11(3.06) (1.01) (1.99) (0.10) (0.61) (-0.84)FFC4 Alpha 0.13** 0.02 0.11 -0.03 -0.01 -0.14(2.29) (0.36) (1.46) (-0.37) (-0.13) (-1.04)Panel C: short-term minus long-termCAPM Alpha 0.01 0.05 0.08** 0.09** 0.19*** 0.18**(0.19) (1.37) (2.00) (1.98) (3.10) (2.57)FF3 Alpha 0.02 0.06* 0.08** 0.10** 0.20*** 0.18**(0.43) (1.67) (2.12) (2.33) (3.30) (2.59)FFC4 Alpha -0.01 0.01 0.04 0.05 0.12** 0.13*(-0.29) (0.40) (1.20) (1.33) (2.01) (1.91)This table shows the abnormal returns of low-turnover institutions and high-turnover institutions in portfolios sorted byex ante short-term ownership. In the beginning of April in each year, I sort stocks into five different portfolios based ontheir prior year’s short-term ownership averaged across four quarters (i.e. ex ante short-term ownership). Short-termownership for a stock in a given quarter is proxied by the the average turnover ratio of institutional investors that ownthe stock in the quarter, weighted by the number of shares each institution owns. Long-term (short-term) institutionsare institutions in the bottom (top) turnover ratio decile. The returns of each quintile in Panel A (B) are computedby weighting stock returns by the total dollars invested by long-term (short-term) institutions. The returns in PanelC are the returns in Panel B minus the returns in Panel A. The abnormal returns are computed based on the CAPMmodel, the Fama-French 3 factor model (FF3), and the Fama-French-Carhart 4 factor model (FFC4). The sampleperiod for returns is from 1982:04 to 2017:12, excluding 1998:04 to 2001:03. All t-statistics (in parentheses) are basedon (heteroskedasticity) robust standard errors. Superscripts ***, **, * correspond to statistical significance at the 1, 5,and 10 percent levels, respectively.60Table 3.14: Cross-sectional abnormal return and liquidity risk.Ex ante short-term ownership sorted portfolioLow 2 3 4 High Hi-LoMKT 0.84*** 1.01*** 1.07*** 1.16*** 1.25*** 0.41***(60.64) (81.91) (60.47) (52.91) (35.13) (8.97)HML 0.18*** 0.02 0.01 -0.20*** -0.50*** -0.69***(7.85) (0.93) (0.28) (-5.02) (-8.14) (-8.82)SMB -0.22*** -0.12*** 0.10*** 0.33*** 0.69*** 0.91***(-11.34) (-5.48) (4.11) (11.62) (15.79) (16.48)UMD 0.00 -0.03** -0.01 -0.03 0.05 0.05(0.11) (-2.30) (-0.70) (-1.35) (1.41) (1.15)LIQ -0.03* 0.04*** 0.08*** 0.08*** 0.07** 0.09**(-1.79) (2.94) (4.16) (3.91) (2.13) (2.37)Constant 0.13** 0.01 0.05 -0.15** -0.21* -0.34**(2.45) (0.31) (0.86) (-2.03) (-1.92) (-2.38)Observations 429 429 429 429 429 429Adjusted R-squared 0.920 0.964 0.950 0.940 0.918 0.748This table reports the time series regression of returns of portfolios sorted by ex ante short-term ownership on theFama-French (1983) three factors (MKT , SMB, HML), the Carhart (1997) momentum factor (UMD), and the Pastor-Stambaugh (2003) liquidity factor (LIQ).Rt = a+bMKTt + cSMBt +dHMLt + eUMDt + f LIQt + εtIn the beginning of April in each year, I sort stocks into five different portfolios based on their prior year’s short-term ownership averaged across four quarters (i.e. ex ante short-term ownership). Short-term ownership for a stockin a given quarter is proxied by the the average turnover ratio of institutional investors that own the stock in thequarter, weighted by the number of shares each institution owns. The return of each quintile is computed using valueweights. The sample period for returns is from 1982:04 to 2017:12. All t-statistics (in parentheses) are based on(heteroskedasticity) robust standard errors. Superscripts ***, **, * correspond to statistical significance at the 1, 5,and 10 percent levels, respectively.61Chapter 4Cheaper is Not Better: The SuperiorPerformance of High-Fee Mutual Funds4.1 IntroductionAt the end of 2018, domestic U.S. equity mutual funds were responsible for managing $8.65 trillionin assets. These funds continue to be the primary investment vehicle for households, with overninety million people in the U.S. holding their shares. The average fund charges over 1% in fees,and each year investors spend billions of dollars on fund expenses, which supposedly compensatemanagers for their ability to generate value.11Economic principles and theoretical arguments suggest that fees of a fund should be commen-surate with the value it creates for investors. Skilled managers should generate better before-feeperformance but capture all rents by charging higher expenses, leading to a flat relation betweenfund expenses and net-of-fees performance (Berk and Green, 2004). In stark contrast with thetheory, empirical studies do not find a positive relation between fund expense ratios and before-fee performance. The literature concludes that net of expenses, investors in high-fee funds earnsignificantly worse factor-adjusted returns than do investors in low-fee funds.12The seemingly poor factor-adjusted performance of high-fee funds has shaped asset allocationdecisions of both retail and institutional investors. For example, in his best-selling book aimedat individual investors, Malkiel (2016) writes, “The best-performing actively managed funds havemoderate expense ratios. . . I suggest that investors never buy actively managed funds with expenseratios above 50 basis points.” More sophisticated investors also avoid high-fee funds. For instance,in a study of asset flows of defined contribution pension plans, Sialm et al. (2015) show that “plansponsors and participants invest more in funds with lower expense ratios.”In addition to offering these billion-dollar practical implications, the inverse relation betweenfees and net performance raises important unanswered questions. Specifically, how should theliterature square this link with the theory, which predicts a flat relation? And, why do high-feefunds continue to exist if their managers extract more economic rents than the value they add? In11Statistics for the mutual fund industry are from Investment Company Fact Book 2018.12See, for example, Jensen (1968), Malkiel (1995), Gruber (1996), Wermers (2000), Gil-Bazo and Ruiz-Verdú(2009), Fama and French (2010).62this paper we offer an explanation, which reconciles theory with empirics, and calls for revisitingthe oft-offered practical advice to prefer low-fee funds over high-fee counterparts.In our first set of analyses, we establish that funds with different expense ratios invest in fun-damentally different stocks. In particular, relative to firms held by funds in the lowest fee decile,firms held by funds in the high-fee group grow their assets at a significantly faster rate (19% vs12% annually) and have lower gross profit ratios (28% vs 34%). Importantly, these firms are pre-cisely the types that conventional factor models misprice: firms with high asset growth and lowprofitability have significantly negative three- and four-factor alphas (Cooper et al., 2008; Novy-Marx, 2013). As a result of high-fee funds tilting their portfolios to such stocks, analyses based onconventional models lead to the premature conclusion of poor performance of these funds and thepractical guidance to avoid investing in them. We re-examine the fee-performance relation throughthe lens of a recently proposed Fama and French (2015) five-factor model, which is designed tocapture differences in average returns of stocks with different profitability and investment patternsand is hence well-suited to study factor-adjusted performance of funds with different fees.In striking contrast with the conclusions of the prior literature, we find that high-fee fundsgenerate significantly better factor-adjusted gross-of-expenses performance than do low-fee funds.Results of panel regressions of funds’ five-factor alphas on expense ratios suggest that funds thatcharge 1% higher fee deliver 1% more alpha. We show that after deducting expenses, high-feefunds do not underperform low-fee funds. In other words, the seemingly poor performance of thesefunds documented in prior literature is but an artifact of the failure to adjust performance for theexposure to priced factors. Importantly, our results strongly support the theoretical predictions ofBerk and Green (2004) that high-fee mutual funds generate higher alphas before fees, and that feesare unrelated to net-of-expenses performance because skilled managers extract rents by charginghigher fees.To better understand why high-fee funds invest more in high-investment low-profitability stocks,we consider two hypotheses. Under the naïve investor hypothesis, we conjecture that these com-panies appeal to unsophisticated investors who are also less price-sensitive, which allows high-feefunds to charge higher expenses. We find this is not the case: high-fee funds with more sophisti-cated investors exhibit similar propensities to invest in high-investment low-profitability stocks.Alternatively, under the valuation cost hypothesis, we conjecture that fees of funds that tilttheir portfolios to high-investment low-profitability companies are high because estimating intrin-sic value of these stocks is more difficult. Funds that choose to specialize in investing in hard-to-value companies must spend more resources on valuation per unit of capital, for example byhiring more talented managers, which justifies the higher fees on a percentage basis. Becausecompanies that are difficult-to-value are more likely to be the ones with fast growth rates and lowprofits, traditional factor models, being unable to correctly price such companies, lead to biased63inferences in evaluating performance of high-fee funds. To test this hypothesis, we use severalproxies for the difficulty of valuing a company. Consistent with the valuation cost hypothesis, wefind that high-fee funds invest significantly more in companies that are hard-to-value: those thathave high idiosyncratic volatility, high financial uncertainty, low asset tangibility, and low cover-age from sell-side analysts. When we decompose a fund’s expense ratio into distribution cost andasset management cost, we find that the relationship between a fund’s expense ratio and proxiesof the valuation cost of its underlying companies is entirely driven by the part of the expense ratiothat reflects the asset management cost – that is, management fees and expenses – rather than thedistribution costs such as 12b-1 fees. In other words, in line with the valuation cost hypothesis,funds investing in hard-to-value companies compensate their managers more richly by charginghigher management fees.Our results contribute to the large literature on mutual fund performance.13 An important long-standing debate in this research is whether fund managers deliver performance that justifies thefees they charge (e.g., Daniel et al., 1997; Carhart, 1997; Berk and Green, 2004; Fama and French,2010; Berk and Van Binsbergen, 2015). Our key contribution is to show that – consistent with thetheory of Berk and Green (2004) – skilled managers indeed extract rents by charging high fees. Wealso extend the growing literature that investigates how anomalies associated with investment andprofitability rates impact mutual funds. Several recent papers advance this research by addressingquestions distinct from ours. For example, Busse et al. (2017) argue that mutual fund performancemeasures should control for portfolio characteristics, such as investment and profitability. Jordanand Riley (2015) show that idiosyncratic volatility can predict mutual fund performance measuredwith three- and four-factor models, but cannot predict five-factor alpha. Jordan and Riley (2016)find that five-factor mutual fund alphas exhibit more persistence than alphas from other models,highlighting the apparent superiority of the five-factor model over its predecessors. Our paper addsto this strand of literature by documenting the implications of exposures to the investment andprofitability factors for the fee-performance relation, a central topic in the mutual fund literature.4.2 DataWe obtain mutual fund data by linking the CRSP Survivor-Bias-Free U.S. Mutual Fund Databasewith the Thomson Reuters Mutual Fund Holdings Database using the MFLINKS table (Wermers,2000). Following the literature, we apply several filters to form our sample (e.g., Kacperczyket al., 2006b). We remove passive index funds by searching through fund name and index fundindicator. We then exclude mutual funds that are not U.S. domestic equity funds based on theCRSP style code, Thomson Reuters style code, and Lipper objective name. We eliminate mixed13The literature has grown tremendously since Jensen (1968). See Ferson (2010), Musto (2011), and Wermers(2011) for recent comprehensive reviews.64funds or highly levered funds, which hold less than 70% or more than 130% of their assets inequity. For the analysis of holdings, we require a fund to have at least 10 stock holdings. Weremove extremely small funds, i.e. funds with less than $20 million in asset in real 2017 terms,which is approximately $6 million in 1980. To estimate factor-adjusted performance for each fund,we require at least five years of return history. Our final sample contains 2,828 funds and spans theperiod from 1980 to 2017.14If a fund has multiple share classes, we aggregate information of the different classes. Fund-level returns and expense ratios are the class size-weighted averages. We winsorize expense ratios,to which we refer interchangeably as fees, at the 99th percentile to remove extreme outliers. Fundsize is the aggregate of all share classes. We drop observations where any of the fund size, return, orexpense ratios is missing. We define fund age as the age of its oldest share class in our sample. Toproxy for the investor sophistication of a fund, we use the fund’s distribution channel and variablecapturing whether it is a retail or institutional fund. Following Sun (2014), we classify a shareclass as broker-sold (as opposed to directly sold), if its 12b-1 fee is higher than 25 basis points orif it charges front- or back-end load fees. We define a fund’s broker share as the fraction of assetsin broker-sold share classes. We label a share class as institutional if its name contains wordsbeginning with “inst”, if it is of class Y or I, or if its institutional flag is Y in CRSP. Similarly,we measure a fund’s institutional share as the fraction of its assets in institutional share classes.Finally, we identify funds that are in the same fund family based on their management companyname and calculate fund family size as the sum of total assets of its affiliated funds. Panel A ofTable 4.1 reports fund-level summary statistics. The average fund is 10.3 years old and charges a1.22% fee. The average broker share is 49% and the average institutional share is 29%.Our analysis of mutual fund holdings requires stock-level data, which we obtain from theCRSP, COMPUSTAT, and IBES files, restricting the sample to common stocks (share code 10and 11). For each stock, we measure characteristics such as the CAPM beta, market capitalization,book-to-market ratio, and momentum. We also compute investment- and profitability-related char-acteristics such as asset growth, equity issuance, operating profitability, and stock age. To gaugewhether a company is difficult to value, we construct proxies such as asset tangibility, idiosyncraticvolatility, readability of financial statements, and analyst coverage. The appendix provides detailson variable definitions. We winsorize firm-level variables at the top and bottom 0.5%. We take nat-ural logarithms of growth rates and market capitalization. To study portfolio-level attributes of thefunds, we take position-weighted averages of characteristics of stocks they hold at the beginningof each year. Panel B of Table 1 shows summary statistics of these stock characteristics.14In Section 6, we show that the results remain similar if we use only three-year windows to estimate risk loadings,leaving us with 3,261 unique funds.654.3 Mutual funds fees and investment stylesIn this section we uncover systematic differences in the investment strategies of high-fee and low-fee funds.Fund prospectuses provide valuable information on fund’s investment strategies (Abis, 2017).To get a first sense of whether high- and low-fee funds follow distinct investment approaches, weexamine the differences in the “Principal Investment Strategies” (PIS) section of prospectus forms497K available from EDGAR. To the extent that high- and low-fee funds differ in their investmentstyles, we expect to observe differences in the language in that section.We find that high-fee funds tend to describe their investment strategies differently from low-feefunds. A typical PIS section of high-fee funds reads:[The fund] utilizes a growth approach to choosing securities based upon fundamen-tal research which attempts to identify companies whose earnings growth rate exceedsthat of their peer group, exhibit a competitive advantage in niche markets, or do notreceive significant coverage from other institutional investors. (Emerald Mutual Fund)By contrast, a typical low-fee fund describes its investment strategy as follows:The Fund invests, under normal circumstances, primarily in U.S. common stocksthat are considered by the Fund’s subadvisers to have above-average potential forgrowth. The subadvisers emphasize stocks of well-established medium- and large-capitalization firms. (The Vantagepoint Funds)In addition, we look at fund holdings to see whether there are systematic differences between high-fee and low-fee mutual funds. We compute average characteristics of stock holdings of funds withdifferent expense ratios. In addition to the commonly considered stock characteristics such as size,book-to-market ratio, and momentum, we investigate asset growth rate, operating profitability,equity issuance rate, and stock age. For every fund at the first observation of each year, we takeposition-weighted averages across all stocks in its portfolio to calculate average characteristics ofstockholdings. We then run the following panel regression:Avgchar j,t = b0+b1Expenseratio j,t−1+ c′Controls j,t−1+FEt + ε j,t (4.1)where Avgchar j,t is one of the above-mentioned stock characteristics for fund j in year t, Expenseratio is the fund’s expense ratio in year t− 1, and Controls j,t−1 include the natural logarithm offund size, fund age (in months), and the size of other affiliated funds in the same family. Since ourfocus is on the cross-sectional comparison between high-fee and low-fee funds, we include year66fixed effects to control for time series trends in the mutual fund industry. We cluster standard errorsat the fund level and scale all variables by their standard deviations annually to better facilitate theinterpretation of the magnitudes of the coefficients.Our main focus in this test is on the coefficient on the expense ratio. For example, for assetgrowth rate, a positive coefficient indicates that high-fee funds tilt their holdings to companies withhigh asset growth rates. Table 4.2 shows that the coefficients on the expense ratio are significantfor seven out of eight characteristics we study. With respect to commonly considered characteris-tics, regressions (1)-(4) establish high-fee funds invest more in high-beta stocks, small stocks, andhigh momentum stocks. Specifications (5) and (6) show that high-fee funds also invest more instocks with high asset growth rates and high equity issuance rates. Finally, regressions (7) and (8)shows that high-fee funds invest more in young stocks and stocks with low profitability. Overall,the results of this analysis suggest that funds charging different fees have systematically differentinvestment preferences. Broadly speaking, high-fee funds prefer younger firms in a stage of rapidexpansion that have not yet achieved high profitability.In terms of the economic significance, we observe that the absolute magnitude of the coefficientin regressions (5)-(8) is often greater than that in specification (1)-(4), indicating that growth-and profitability-related characteristics are economically more important in capturing portfoliodifferences among funds charging different fees. To better gauge the economic magnitude of tiltsby high-fee funds, we plot average asset growth rates, equity issuance rates, operating profitabilityand stock age against fund fee deciles in Figure 4.1. The benefit of this plot is that it does notimpose a linear structure between fee and stock characteristics, which better demonstrates thereliability of fee as an indicator of tilt towards certain characteristics. The figure shows that stockcharacteristics change strikingly and monotonically with fees. The average asset growth rate ofcompanies invested by funds in the bottom decile is about 12% a year, while in the highest decileis about 19%. The difference of 7% represents a half of the average asset growth rate of allcompanies. The plot also reveals that companies held by bottom decile funds on average achieveoperating profitability that is 6 percentage points higher than that of companies held by top decilefunds.The landscape of the mutual fund industry and academic understanding of the determinants ofasset returns have both changed significantly since the 1990s. It is possible that the preference ofhigh-fee funds for different types of stocks has changes over time. To test this conjecture, we runregression (4.1) annually and plot the time series of the coefficients on the expense ratio in Figure4.2. The coefficients are more volatile during the early part of the sample, potentially becauseof the smaller number of observations. Importantly, the preference of funds with higher fees forlow-profitability high-growth firms is persistent over time.674.4 Mutual fund fee-performance relationThe persistent preference of high-fee funds for fast-growing, low-profitability stocks has importantimplications for the relation between expenses and performance of mutual funds. To the extent thatthese stock characteristics are associated with lower expected returns, as recent literature has shown(Fama and French, 2015; Hou et al., 2015), failure to account for these characteristics can lead toerroneous conclusions on the relation between fees and fund performance. Such failure wouldbe analogous to using CAPM to evaluate the performance of a large-cap growth fund: withoutexplicitly accounting for loadings on size and value factors, the performance of this fund wouldappear poor on average. In our context, accounting for exposures to asset growth and profitabilityfactors of funds with different fees is necessary to get a clearer picture of the relation betweenexpenses and performance of mutual funds.To control for exposures to asset growth and profitability factors, we use the five-factor modelof Fama and French (2015). To contrast our results with those of prior literature, we also usecommonly considered models such as the CAPM as well as the three- and four-factor models andevaluate robustness to other models in section 6. For each performance model and in each month t,we regress a fund’s monthly return in the previous five years on factors to obtain loadings βModeljt .We compute monthly alphas asαModelj,t = rej,t−βModel′j,t rFactort (4.2)where rejt is fund j’s excess return before fee or after fee, and rFactort is a vector of realized factorreturns in each model. We measure a fund’s gross monthly alpha using its gross return, which isnet return plus the annual expense ratio divided by 12.4.4.1 Empirical evidenceFigure 4.3 summarizes future performance of funds grouped into deciles on the basis of fees dis-closed in the most recent fiscal year end. Panel A plots before-fee alphas from different models.The results from the CAPM, three- and four-factor models confirm the findings of the prior liter-ature: gross fund performance is unrelated to fees. By contrast, alphas from the five-factor modeldisplay a very different pattern: they increase significantly with fees.Panel B shows that irrespective for the model, actively managed mutual funds with both highand low expense ratios achieve poor net-of-fees factor-adjusted performance. In addition, consis-tent with the previously established results, net-of-expenses fund performance as measured by theCAPM, three-, and four-factor models, deteriorates with fees. Strikingly, this negative relation isabsent when we use five-factor alphas. The difference in five-factor performance of funds withhigh and low expense ratios is economically small and statistically indistinguishable from zero.68Taken together, the evidence in Figure 4.3 provides one missing support of the prediction of Berkand Green (2004) that skilled managers extract rents by charging higher fees, and consequentlyactively managed funds deliver similar net-of-fees performance.The sort-based results in Figure 4.3 are informative, but to evaluate the fee-performance rela-tion more formally, we run the following panel regression:α j,t = d0+d1Expense j,t−1+h′Control j,t−1+Ft + ε j,t (4.3)where Expense j,t−1 is the fund j’s expense ratio measured at the most recent fiscal year end, andControl j,t−1 is a vector controls measured at the same time as fees, including the logarithm of fundsize, fund age (in months), and the total size of other affiliated funds in the family. To facilitatepresentation, we divide the control variables by 10. We include month fixed effects and clusterstandard errors by month.Panel A of Table 4.3 reports the results of regression (4.3) with before-fee alphas. Specifica-tions (1)-(3) show funds that charge higher fees do not provide better performance as measured byconventional factor models. However, in regression (4), which controls for fund exposure to theinvestment and profitability factors, the coefficient on the Expense ratio is significantly positive,suggesting that high-fee funds deliver better performance.Panel B of Table 4.3 repeats the analysis using after-fee alphas. Consistent with prior literature,regressions (1)-(3) show that the coefficients on the Expense ratio are large and negative, suggest-ing that performance – measures using conventional models – declines with fees. Crucially, andconsistent with the theoretical arguments that skilled managers extract rents by charging higher fees(Berk and Green, 2004), specification (4) shows that the coefficient on Expense ratio is statisticallyinsignificant from zero. In other words, expenses are not related to future after-fee performancewhen investment and profitability factors are controlled for.Why does the performance of high-fee funds improve after controlling for investment andprofitability factors? The reason is that the stocks in which high-fee funds invest most heavilyhave high asset growth rates and low profitability. Thus, high-fee funds should have low loadingson the investment and profitability risk factors, both of which carry positive factor premia. Table4.4 reports this result in a formal test. Columns (1) and (2) show the coefficients on Expenseratio are negative and significant after controlling for fund characteristics. Columns (3) and (4)shows that the coefficients are significantly negative after controlling for fund characteristics andloadings on the other risk factors, such as the market, size, and value factors. This finding suggeststhat high-fee funds tend to load less on the investment and profitability factors. The realized riskpremia of the investment factor and the profitability factor are 0.25% and 0.36% per month inthe 1985 to 2017 period. Based on the magnitude of the coefficients in columns (1) and (2), a 169percentage point increase in fee would reduce the required rate of return by 0.86 percentage point(i.e. 1.15×0.25%+1.6×0.36%=0.86) in the five-factor model. These differences in risk loadingsexplain why high-fee funds appear to have poor performance in the traditional models.4.4.2 Sub-sample analysis of the fee-performance relationshipWe next investigate whether the relation between expense ratios the performance varies acrossdifferent sub-sample of funds. To this end, we separate funds into two groups based on each of theirsize, age, family size, turnover ratio, institutional indicator, or broker sold indicator. Specifically,for each of these fund level characteristics, we define a dummy variable equal to one if the variableis greater than the sample median in each year. We then regress the five-factor alpha on the expenseratio, a characteristic dummy, and an interaction term of the dummy variable and expense ratio,controlling for other fund attributes. The coefficient of the expense ratio measures the fee-alpharelationship for the baseline group of funds with their dummy variable equal to 0. Its sum with thecoefficient on the interaction term indicates the fee-alpha relationship for the second half of funds.Table 4.5 reports the results of this test with before-fee alpha.15 Across all columns, irrespec-tive of the particular fund type used to define the dummy variable, the coefficients on Expenseratio remain statistically and economically significant. The performance of high-fee funds as mea-sured by the five-factor alpha thus appears consistent across different types of funds. Especially inColumns (1) to (3) and Column (6), the fee-alpha relationship exceeds 1 for smaller funds, youngerfunds, funds offered by smaller families and funds sold directly to investors. A coefficient greaterthan 1 means, for any additional fee that investors pay for these funds, investors are obtaining pos-itive net benefit after fee, which suggests for some types of funds, managers are not extracting allthe rents generated from their skill. The coefficients on the interaction terms in columns (1) and(2) are also significantly negative, indicating that smaller and younger funds have steeper fee-alpharelationship than larger and older funds. The higher fee-alpha relationship could be due to severalreasons. For example, smaller and younger funds are less well-known, investors might need toincur positive search cost to find these funds. Theoretically, as predicted by Gârleanu and Peder-sen (2018), investors should be compensated by higher alpha for their search effort. Alternatively,Chevalier and Ellison (1997) have shown that the response of flow to performance is more sensi-tive for younger and smaller funds. Therefore, skilled managers of these funds might be willing tocharge a lower fee to build a track record.4.5 ExplanationWe now consider two hypotheses to understand why mutual fund expense ratios relate systemati-cally to funds’ propensities to invest in firms with certain asset growth and profitability profiles.15Results obtained using after-fee alphas are similar and are omitted for brevity.704.5.1 Naive investor hypothesisThe behavioral finance literature has postulated that naïve investors overinvest in fast-growingcompanies due to cognitive biases. For example, Lakonishok et al. (1994) and Porta et al. (1997)argue that unsophisticated investors over-extrapolate high growth rate of a company into its future,causing it to be overpriced. In a related study, Frazzini and Lamont (2008) document a dumbmoney effect in retail investor flows. They find retail investors display positive sentiment towardsgrowth stocks and allocate more capital to funds that hold more such stocks.Motivated by this literature, we propose the naïve investor hypothesis, which conjectures thatfast-growing companies are more appealing to naïve investors, who are also less likely to be pricesensitive about mutual fund fees. These companies can be expected to have a high rate of assetgrowth, low profitability, and high equity issuance to finance the growth. If such companies attractunsophisticated investors, we would expect that some fund managers invest more in high-growthand low-profitability stocks to attract more unsophisticated investors. Since unsophisticated in-vestors tend to be less price sensitive, the fund manager can charge higher fees than what is justifiedby the performance.16To test the naïve investor hypothesis, we construct two measures of a fund’s investor sophistica-tion. The first proxy is the fraction of a fund’s asset that belongs to institutional share classes. It iswell recognized that institutional investors are more sophisticated than retail investors. The secondproxy is broker share, defined as the fraction of a fund’s asset that is sold through broker channelsinstead of being sold directly to investors. Funds sold through brokers charge investors highersales loads, which do not contribute to the management of the fund. Prior literature has shown thatinvestors who purchase mutual fund through brokers are less performance-sensitive than investorswho purchase mutual funds directly and, in addition, brokers’ incentives are more aligned withfund families (Guercio and Reuter, 2014; Sun, 2014). Therefore, the higher the broker share of afund, the less sophisticated the fund’s investors are. We re-run regression (1) of average portfoliocharacteristics on the expense ratio, either investor sophistication proxy, and their interaction.Table 4.6 summarizes regression results for each of the investor sophistication proxy in fourseparate panels. Under the naïve investor hypothesis, we expect to see that sophisticated high-feefunds have weaker tilt towards stock characteristics appealing to naïve investors, which impliesthat the coefficient on the interaction term of expense ratio and institutional share should be of theopposite sign to that on the expense ratio. With broker share, the coefficients on the interactionterm should have the same sign as the coefficient on the expense. We find that it is not the case.16Indeed, the literature has explored how fund managers set fees strategically to exploit investors who are lesssensitive to price. Christoffersen and Musto (2002) find that retail money funds tend to increase fees after a largeamount of outflow. They propose that outflows are an indication of performance-sensitive investors leaving the fund,which also signals a decrease in the average price sensitivity among investors remaining in the fund, causing themanagers to subsequently raise fees.71In Panel A, the coefficients on the interaction term between expense ratio and institutional shareall have the same sign as the coefficient on the expense ratio. In Panel B, the coefficients on theinteraction term between expense ratio and broker share all have the opposite sign as the coefficienton the expense ratio and are all statistically significant.In contrast to the predictions of the hypothesis, we find that high-fee institutional funds havea stronger tilt towards high-growth and low-profitability companies, while high-fee broker-soldfunds have a weaker tilt towards such companies. In other words, among funds with more sophis-ticated investors, the association between expense ratio and growth-related characteristics is thesame, if not stronger. Overall, the results summarized in Table 8 suggest that the naïve investorhypothesis does not explain the link between expense ratios and portfolio stock characteristics ofmutual funds.4.5.2 Valuation cost hypothesisWe now consider the hypothesis that funds investing in high-growth and low-profitability stockscharge high fees because their valuation is considerably more difficulty and demands more timeand effort from fund managers per unit of capital. The high valuation cost, in turn, necessitateshigher fees on a percentage basis. In other words, funds charge high fees because they invest indifficult-to-value stocks characterized by high growth and low profitability. We label this alterna-tive explanation the valuation cost hypothesis. Under this hypothesis, we would expect to observethat high-fee funds invest more in companies that are more difficult to value.To test the valuation cost hypothesis, we use four measures to identify whether a company ishard to value. Our first measure is idiosyncratic volatility (Ang et al., 2006), which has been linkedto valuation difficulty (e.g., Kumar, 2009). Our second measure is based on the textual analysisof a company’s annual reports.17 Following Loughran and McDonald (2011), we construct anuncertainty index by counting the uncertainty words such as ‘almost’ and ‘appears’, and dividingit by the total number of words in each annual report. The index is higher if the annual reportcontains more uncertain words. We deem a company as opaque if its uncertainty index is high.The third measure we consider is tangibility: valuing a firm whose intangible assets represent alarge portion of its asset base can be difficult (e.g., Baker and Wurgler, 2006). Our last measureis the number of analysts that have earning forecasts for a firm from the IBES database. Stockswith more analyst coverage likely have better information available and are thus less challenging toprice. We aggregate each company-level measure of valuation cost to the fund level using portfolioweights of a fund.Panel A of Table 4.7 shows our results from regressions of valuation cost proxies of funds’stockholdings on their expense ratios. Lending support to the valuation cost hypothesis, the results17The word list is available from Bill McDonald’s website: http://www3.nd.edu/~mcdonald/.72suggest that fund fees relate positively to each of the valuation difficulty proxies we consider. Tofurther test the hypothesis, we split a fund’s reported expense ratio into the part that representsits asset management cost and the part that represents marketing and distribution cost. A typicalfund’s expense ratio consists of three main components, including 12b-1 fee, management fee,and other operating expenses. Management fee and other operating expenses cover the cost offund managers and daily operations, while 12b-1 fee is mainly used for the fund’s marketing anddistribution, e.g., compensation to brokers who sell the fund to investors. Under the valuationcost hypothesis, funds investing in harder-to-value stocks should charge higher management feesto compensate managers for their efforts, but we do not expect marketing and distribution fees torelate to valuation difficulty of the stockholdings. We find this to be the case. In Panel B of Table4.7, the coefficient on the asset management cost is positively related with the valuation cost of theunderlying companies, while 12b-1 fee is negatively related or unrelated to the valuation cost ofstocks, lending support for the valuation cost hypothesis.To further investigate the valuation cost hypothesis, we conduct textual analysis of the PISsections. Specifically, we construct a “research index” to capture a fund’s research activities bycalculating the fraction of words that are related to research. We include the following words inlist: analysis, analyze, analyzes, analyzed, bottom-up, fundamentally-based, fundamentals-based,and research. The text data is then merged with fund variables using the links in SEC’s InvestmentCompany Series and Class information. The textual analysis covers the period is from 2010 until2016 due to data availability.To test whether high- and low-fee funds differ significantly in describing research activitiescentral to their trading strategies, we regress the research index on the expense ratio and controlvariables. Table 4.8 shows that the coefficients on the expense ratio are positive and significant inall specifications. This result provides an indication that high-fee funds focus more on research informulating their investment strategies. This finding provide further support for the valuation costhypothesis.4.6 Robustness and additional resultsTo evaluate robustness of our results, in this section we conduct several tests modifying variousaspects of our empirical methods. In Panel A of Table 4.9, we assess whether the propensity ofhigh-fee funds to hold high-growth low-profitability stocks, as established in Table 4.2, is drivenby the omission of other stock characteristics as controls. Specifically, we re-run the regressionof average portfolio characteristics on expense ratios and other variables after adding averages ofCAPM beta, market capitalization, momentum, and B/M ratio of the stockholdings as regressors.Our results remain similar to those in the base-case analysis summarized in Table 4.2.We also perform several robustness tests for the fee-alpha relationship. In Panel A of Table734.10, we perform Fama-MacBeth regressions by regressing monthly alpha measured with differentmodels on the most recent expense ratio. We find that the relationship between the expense ratioand the before-fee alpha measured with the Fama-French five factor model, the six-factor modelthat adds the momentum factor, and Hou et al. (2015) four-factor model are significantly positive.In Panel B of Table 4.10, we perform the same regression as in Table 4.3 for the sample periodof 1998 to 2017. The results are quantitatively the same as Table 4.3. In Panel C of Table 4.10,we use a shorter three-year rolling window to calculate factor loadings of the funds. The resultsare quantitatively similar to Table 4.3. Overall, we show that after controlling for exposures toprofitability and investment factors, high-fee funds significantly outperform low-fee funds beforededucting expenses, and perform equally well net of fees.We also control for any potential non-linearity effects in fee-performance regression. Table4.11 presents the results by regressing alphas on expense ratio and expense ratio squared. Theresults are quantitatively similar to Table 4.3. Before-fee alphas measured under the CAPM, theFama-French three-factor, and the Fama-French-Carhart four-factor models are not significantlyrelated with fees, but before-fee alpha under the Fama-French five-factor model is positively re-lated with fees. There is some evidence the before-fee alpha under the Fama-French five-factormodel has a non-linear relationship with fees, which remains to be explained in future research.Similarly, after-fee alphas under the CAPM, the three-factor, and the four-factor models are nega-tively associated with fees, but not under the five factor model.4.7 ConclusionPrevious literature uncovers a robust inverse relation between fees charged by actively managedmutual funds and future after-fee fund performance. Before deducting expenses, high-fee fundshave been found to perform just as well as do low-fee funds. Theoretically, this result is puzzling asit suggests that managers of high-fee funds extract more rents than the value they add. Empirically,the apparent negative relation between expenses and net-of-fees performance has helped to guideallocations of billions of dollars of retail and institutional investors, who shun high-fee funds. Therelation is also puzzling as it calls into question the continued existence of high-fee funds.This paper resolves the puzzle by showing that factor models used to establish the prior fee-performance results are inadequate to control for differences in performance of funds with differentfees. High-fee funds exhibit a strong preference for stocks with high investment rates and lowprofitability, characteristics that have been recently shown to associate with low expected returns.The commonly used three- and four-factor models produce large negative alphas for these types ofstocks, leading to a premature conclusion that high-fee funds underperform net of expenses.We evaluate the fee-performance relation using the recently proposed five-factor model thatcontrols for exposures to the investment and profitability factors. The results we obtain stand in74stark contrast with those in the prior literature. We find that high-fee funds significantly outperformlow-fee funds before deducting expenses, and do equally well net of fees. Our findings supportthe theoretical prediction that skilled managers extract rents by charging high fees, and call intoquestion the widely offered advice to avoid high-fee funds.75Figure 4.1: Characteristics of stock portfolios of funds charging different fees.This figure plots average characteristics of stocks held by mutual funds grouped into deciles on the basis of expenseratio. For each fund, we calculate its stock characteristics as the position-weighted averages across companies heldby the fund. The characteristics, defined in detail in the Appendix, are the asset growth rate, operating profitability,equity issuance rate, and stock age. The sample period is 1980-2015.76Figure 4.2: Fund fees and time series dynamics of fund portfolio characteristics.This figure presents the time series dynamics of the relation between fund fees and portfolio characteristics. For eachcharacteristic, we plot the time series of coefficients on the fee variable from annual cross-sectional regressionsAveragecharacteristics j,t = b0+b1 f ee j,t−1+b′Controls j,t−1+ ε j,twhere Averagecharacteristics j,t is one of the measures of stock characteristics (asset growth rate and operating prof-itability) for fund j in year t; f ee j,t−1 is the fund j’s expense ratio in year t− 1; Controls j,t−1 are fund level controlvariables, including the natural log of fund age (in months), fund size, and fund family size. For each fund, we calcu-late its stock characteristics as the position-weighted averages across companies held by the fund. Detailed variabledefinitions are provided in the Appendix. All variables are scaled by their standard deviation and demeaned in eachyear. The sample period if from 1980 to 2015.77Figure 4.3: Mutual fund fee-performance relationship.This figure plots expected alphas, in percent per year, of funds grouped into deciles on the basis of expense ratioreported in the most recent fiscal year. We measure alpha with four benchmark models: the CAPM, the Fama-Frenchthree-factor, the Fama-French-Carhart four-factor, and the Fama-French five-factor. A fund’s alpha in month t is thedifference between the fund’s excess return in month t and its expected return, calculated as the sum of the products offactor returns in t and factor loadings estimated from rolling regressions on five years of monthly data. Panel A plotsthe average before-fee alphas against the fee decile, and Panel B shows the corresponding plot for after-fee alphas.The sample period for alphas is from 1980-2017.78Table 4.1: Summary statistics for fund and portfolio characteristics.Mean Median SD p5 p25 p75 p95Panel A. Fund characteristicsExpense ratio 1.22% 1.18% 0.44% 0.57% 0.95% 1.47% 2.01%Fund size (million) 1,304 234 5,034 22 73 851 5,042Fund age, years 10.3 8.7 7.7 0.9 4.2 14.9 25.3Family size (million) 32,931 4,660 87,043 51 693 21,139 216,838Turnover ratio 84% 63% 80% 11% 33% 107% 229%Broker-sold share 49% 45% 45% 0% 0% 100% 100%Institutional share 29% 5% 38% 0% 0% 61% 100%12b-1 fee 0.18% 0.07% 0.23% 0.00% 0.00% 0.29% 0.67%Panel B. Portfolios characteristicsStock age 12.9 8.6 13.9 0.7 3.3 17.3 41.1CAPM beta 0.94 0.86 0.92 -0.32 0.37 1.41 2.61Market cap 1,795 115 11,179 4 26 585 5,827Book-to-market 0.80 0.61 0.73 0.11 0.33 1.01 2.16Momentum 11% 5% 59% -70% -25% 35% 118%Asset growth rate 13% 7% 38% -35% -3% 21% 85%Operating probability 8% 19% 55% -77% 4% 30% 55%Equity issuance rate 5% 0% 14% -6% 0% 3% 32%Idiosyncratic volatility 4% 3% 3% 1% 2% 5% 9%Tangibility 26% 18% 24% 1% 6% 39% 77%Financial uncertainty 1.36% 1.37% 0.35% 0.78% 1.11% 1.62% 1.92%Number of analysts 3 0 5 0 0 3 14This table reports the summary statistics for fund characteristics (Panel A) and portfolio characteristics (Panel B). Fundsize and fund family size are measured in nominal terms in millions. Broker-sold share is the estimated percentage ofa fund’s assets in share classes sold through brokers. Institutional share is the estimated percentage of a fund’s assetsin share classes sold to institutional investors. Detailed definitions are in the Appendix. The sample period is from1980 to 2017.79Table 4.2: Fund fees and characteristics of stock holdings.Panel A. FFC4 factor related characteristics(1) (2) (3) (4)CAPM Beta B/M Size MomentumExpense ratiot-1 0.20*** -0.03 -0.20*** 0.09***(14.43) (-1.52) (-11.25) (7.33)Log fund sizet-1 0.04*** 0.00 0.09*** -0.02*(2.68) (0.21) (4.79) (-1.79)Log fund aget-1 -0.03** -0.06*** 0.01 0.00(-2.47) (-3.73) (0.90) (0.13)Log fund family sizet-1 0.06*** -0.03 -0.00 0.05***(3.88) (-1.54) (-0.12) (3.57)Observations 35,134 35,131 35,134 35,132Adj. R2 0.833 0.189 0.387 0.664Year FEs Yes Yes Yes YesPanel B. Other stock characteristics(1) (2) (3) (4)Asset growth Equity Issuance Profitability Stock ageExpense ratiot-1 0.19*** 0.21*** -0.21*** -0.27***(13.68) (17.01) (-14.05) (-16.05)Log fund sizet-1 -0.01 0.01 0.01 0.01(-0.83) (1.18) (0.34) (0.69)Log fund aget-1 0.03** -0.01 0.02 -0.00(2.48) (-0.89) (1.31) (-0.18)Log fund family sizet-1 0.07*** 0.08*** -0.06*** -0.05***(4.77) (6.37) (-3.93) (-3.06)Observations 35,132 35,132 35,131 35,134Adj. R2 0.134 0.284 0.430 0.130Year FEs Yes Yes Yes YesThis table reports the results of panel regressions of the characteristics of a fund’s stockholdings (shown in the columnheading) on the fund’s attributes lagged by one year. Characteristics of stockholdings are position-weighted averagesacross all stocks in a fund’s portfolio. All variables are scaled by their cross-sectional standard deviations in each year.Regressions include year fixed effects. The sample period is from 1980 to 2015. Standard errors are clustered at thefund level. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.80Table 4.3: Mutual fund fee-performance relation: Panel regressions.Panel A. Before-fee alpha (1) (2) (3) (4)αCAPMt αFF3t αFFC4t αFF5tExpense ratiot-1 -0.15 0.11 -0.07 1.08***(-0.26) (0.31) (-0.19) (3.62)Log fund sizet-1 -0.23*** -0.08 -0.11* 0.02(-3.38) (-1.35) (-1.91) (0.29)Log fund aget-1 0.27* 0.21* 0.28** 0.13(1.81) (1.72) (2.35) (1.11)Log fund family sizet-1 0.06* 0.06** 0.05* 0.09***(1.88) (2.31) (1.70) (3.13)Observations 321,414 321,414 321,414 321,414Adj. R2 0.110 0.074 0.083 0.075Month FE Yes Yes Yes YesPanel B. After-fee alpha (1) (2) (3) (4)αCAPMt αFF3t αFFC4t αFF5tExpense ratiot-1 -1.09* -0.83** -1.01*** 0.14(-1.93) (-2.43) (-2.78) (0.46)Log fund sizet-1 -0.23*** -0.07 -0.11* 0.02(-3.33) (-1.29) (-1.85) (0.35)Log fund aget-1 0.27* 0.20* 0.27** 0.12(1.77) (1.67) (2.30) (1.06)Log fund family sizet-1 0.06* 0.06** 0.05* 0.09***(1.91) (2.35) (1.73) (3.16)Observations 321,414 321,414 321,414 321,414Adj. R2 0.110 0.074 0.083 0.074Month FEs Yes Yes Yes YesThis table presents the results of panel regressions of fund alphas on expense ratios, both in percent per month, andother fund characteristics. Alphas are computed using the CAPM, the Fama-French three-factor model (FF3), theFama-French-Carhart four-factor model (FFC4), and the Fama-French five-factor model (FF5). Alphas are calculatedusing factor loadings estimated from a five-year rolling window regression. In Panel A (B), alpha is computed usingbefore-fee (after-fee) returns. Independent variables are measured as of the most recent fiscal year of the fund. Allregressions include month fixed effects and cluster standard errors by month. The sample period is from 1980 to 2017.Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.81Table 4.4: Fund fees and loadings on the investment (CMA) and profitability (RMW) factors.(1) (2) (3) (4)CMA loading RMW loading CMA loading RMW loadingExpense ratiot-1 -1.15*** -1.60*** -0.78*** -1.32***(-7.68) (-11.61) (-5.37) (-11.15)Log fund sizet-1 -0.05 -0.03 -0.07** -0.03(-1.63) (-0.99) (-2.44) (-1.08)Log fund aget-1 -0.13 -0.08 -0.16** -0.01(-1.63) (-1.14) (-2.08) (-0.23)Log fund family sizet-1 0.00 -0.08*** 0.01 -0.06***(0.02) (-6.39) (0.47) (-4.58)FF5 market factor loadingt -0.22*** -0.02(-7.22) (-0.60)FF5 HML factor loadingt -0.03* 0.31***(-1.74) (19.65)FF5 SMB factor loadingt -0.14*** -0.02**(-13.19) (-2.06)Observations 25,636 25,636 25,636 25,636Adj. R2 0.091 0.050 0.135 0.183Year FEs Yes Yes Yes YesThis table reports the results of panel regressions of funds’ investment or profitability factors loadings in the beginningof each year on annual expense ratios and other fund characteristics. To obtain the loadings, we regress a fund’smonthly before-fee return in the previous five years on Fama-French five-factor portfolios and use the coefficients asrisk loadings. Control variables include the log of fund size, fund age (in months), and fund family size, measuredfrom the most recent fiscal year, as well as contemporaneous loadings on market, size, and value factors. Regressionsinclude year fixed effects. Standard errors are clustered at the fund level. The sample period is from 1980 to 2017.Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.82Table 4.5: Fee-performance relation and different fund characteristics.(1) (2) (3) (4) (5) (6)αFF5tExpense ratiot-1 1.39*** 1.23*** 1.24*** 0.82*** 0.94*** 1.24**(4.58) (4.07) (3.36) (3.28) (2.84) (2.55)Size dummy 0.07**(2.57)Expense ratiot-1 × Size dummy -0.76***(-2.83)Age dummy 0.03(1.13)Expense ratiot-1 × Age dummy -0.41*(-1.68)Family size dummy 0.03(1.28)Expense ratiot-1 × Family dummy -0.33(-1.16)Turnover dummy -0.02(-0.73)Expense ratiot-1× Turnover dummy 0.42(1.14)Institutional share dummy -0.03(-1.03)Feet-1× Inst. dummy 0.03(0.10)Broker share dummy -0.00(-0.09)Feet-1× Broker share dummy -0.13(-0.36)Observations 321,414 321,414 321,414 315,411 284,212 306,522Adj. R2 0.075 0.075 0.075 0.075 0.071 0.074Fund level controls Yes Yes Yes Yes Yes YesMonth FEs Yes Yes Yes Yes Yes YesThis table presents results of regressions of the monthly before-fee gross Fama-French Five-Factor alpha on the fund’smonthly expense ratio, i.e. fee, and its interactions with fund characteristic dummies. For each of characteristics,i.e. fund size, age, family size, turnover ratio, institutional share, and broker share, we create a dummy variable tobe 1 or 0 if the characteristic value is above or below the cross-sectional median. We also include other fund levelcontrol variables, which are the log of fund size, fund age (in months), and fund family size. All independent variablesare measured as of the most recent fiscal year end of the fund. Regressions include month fixed effects and clusterstandard errors by month. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percentlevels, respectively.83Table 4.6: Fund fees and characteristics of stock holdings: Investor sophistication.Panel A. Institution share (1) (2) (3) (4)Asset growth Equity issuance Profitability Stock ageExpense ratiot-1 0.23*** 0.24*** -0.25*** -0.35***(13.76) (16.39) (-13.57) (-17.28)Institution sharet-1 0.08*** 0.07*** -0.06*** -0.15***(4.56) (4.72) (-3.43) (-7.24)Expense ratiot-1× Institution sharet-1 0.03 0.02 -0.01 -0.09***(1.57) (1.53) (-0.34) (-4.68)Log fund sizet-1 -0.01 0.02 -0.02 -0.01(-0.91) (1.12) (-1.15) (-0.49)Log fund aget-1 0.05*** -0.00 0.01 -0.00(3.30) (-0.02) (0.87) (-0.07)Log fund family sizet-1 0.07*** 0.08*** -0.06*** -0.05***(4.42) (5.44) (-3.62) (-2.71)Observations 26,730 26,731 26,729 26,732Adj. R2 0.140 0.294 0.358 0.134Year FEs Yes Yes Yes YesPanel B. Broker share (1) (2) (3) (4)Asset growth Equity issuance Profitability Stock ageExpense ratiot-1 0.24*** 0.24*** -0.26*** -0.35***(14.91) (16.86) (-14.07) (-18.99)Broker sharet-1 -0.06*** -0.03** 0.05*** 0.11***(-3.88) (-2.43) (3.21) (6.35)Expense ratiot-1× Broker sharet-1 -0.03** -0.04*** 0.06*** 0.09***(-2.36) (-3.71) (3.95) (5.53)Log fund sizet-1 -0.01 0.02* -0.00 -0.01(-0.39) (1.67) (-0.14) (-0.27)Log fund aget-1 0.04*** -0.01 0.01 -0.01(2.64) (-0.81) (0.93) (-0.40)Log fund family sizet-1 0.07*** 0.08*** -0.07*** -0.07***(5.13) (6.31) (-4.48) (-3.72)Observations 32,410 32,410 32,409 32,412Adj. R2 0.138 0.294 0.408 0.151Year FEs Yes Yes Yes YesThis table reports the results of panel regressions of the characteristics of a fund’s stockholdings (shown in columnheading) on the fund’s expense ratio, a proxy of investor sophistication, and the interaction of the two, controlling forother fund level characteristics. All independent variables are measured at the most recent fiscal year. Characteristicsof stockholdings are position-weighted averages across all stocks in a fund’s portfolio. In Panel A, the proxy forinvestor sophistication is institutional share, which measures the fraction of a fund’s asset from institutional shareclasses. In Panel B, the proxy for investor sophistication is broker share, which measures the fraction of a fund’s assetfrom share classes that are sold through brokers. All independent variables are scaled by the cross-sectional standarddeviation and de-meaned in each year. Regressions include year fixed effects and cluster standard errors at the fundlevel. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.84Table 4.7: Fund fees and the valuation cost of stock holdings.Panel A. Expense ratio and valuation cost(1) (2) (3) (4)IdiosyncraticvolatilityFinancialuncertaintyAssettangibilityNumber ofanalystsExpense ratiot-1 0.28*** 0.22*** -0.11*** -0.16***(16.99) (13.66) (-6.23) (-8.82)Log fund sizet-1 -0.02 0.00 -0.02 0.04**(-1.49) (0.28) (-1.08) (2.22)Log fund aget-1 -0.02 -0.00 0.00 0.04**(-1.32) (-0.06) (0.18) (2.39)Log family sizet-1 0.05*** 0.07*** 0.02 0.03(3.13) (4.52) (0.94) (1.64)Observations 35,134 29,794 35,131 33,239Adj. R2 0.293 0.952 0.078 0.097Year FEs Yes Yes Yes YesPanel B. Asset management fee and valuation cost(1) (2) (3) (4)IdiosyncraticvolatilityFinancialuncertaintyAssettangibilityNumber ofanalystsManagementfeet-10.45*** 0.32*** -0.17*** -0.30***(25.06) (18.30) (-9.09) (-15.30)12b-1 feet-1 -0.06*** -0.02 0.02 0.09***(-3.66) (-1.43) (0.77) (5.31)Log fund sizet-1 0.06*** 0.05*** -0.05*** -0.02(3.45) (3.07) (-2.76) (-1.35)Log fund aget-1 -0.03** -0.00 0.01 0.05***(-2.02) (-0.13) (0.61) (2.98)Log family sizet-1 0.11*** 0.12*** -0.01 -0.02(6.97) (7.48) (-0.24) (-1.46)Observations 32,412 29,794 32,409 32,412Adj. R2 0.317 0.953 0.039 0.133Year FEs Yes Yes Yes YesThis table reports the results of panel regressions of the characteristics of a fund’s stockholdings (shown in the columnheading) on the fund’s attributes measured at the most recent fiscal year. Characteristics of stockholdings are position-weighted averages across all stocks in a fund’s portfolio. Panel A regresses on expense ratio. Panel B regresses onmanagement fee and 12b-1 fee, which add up to expense ratio. All variables are scaled by their cross-sectional standarddeviations and de-meaned in each year. Regressions include year fixed effects. Standard errors are clustered at thefund level. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.85Table 4.8: Textual analysis of mutual fund prospectus.(1) (2) (3)Research Index Research Index Research IndexExpense ratio 0.16*** 0.13*** 0.15***(4.91) (3.41) (3.87)Constant 0.01*** -0.01*** -0.01***(23.90) (-5.30) (-6.14)Observations 6,036 6,036 6,036Adj. R2 0.004 0.030 0.036Controls No Yes YesYear FEs No No YesThis table reports a textual analysis of fund prospectus. We extract the text of “Principal Strategies” from 497K filingsfrom EDGAR database and construct a “research index” by calculating the fraction of words that are research-related.The control variables used in Column (3) include fund size, fund age, and family size. Standard errors are clusteredat the fund level. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels,respectively.86Table 4.9: Robustness check about fund fees and characteristics of stock holdings.(1) (2) (3) (4)Asset growth Equity issuance Profitability Stock ageExpense ratiot-1 0.07*** 0.08*** -0.08*** -0.06***(10.01) (8.86) (-7.65) (-7.49)Avg. CAPM betat 0.07*** 0.08*** -0.08*** -0.06***(10.01) (8.86) (-7.65) (-7.49)Avg. B/M ratiot (15.84) (17.24) (-20.81) (-30.12)-0.52*** -0.03** -0.21*** 0.29***Avg. market capt (-41.90) (-2.10) (-13.21) (24.13)-0.28*** -0.24*** 0.39*** 0.74***Avg. momentumt (-29.37) (-18.04) (31.62) (84.29)0.18*** 0.20*** 0.02 -0.05***Observations 35,129 35,129 35,129 35,129Adj. R2 0.552 0.483 0.643 0.754Fund level controls Yes Yes Yes YesYear FEs Yes Yes Yes YesThis table reports the results of panel regressions of the characteristics of a fund’s stockholdings (shown in columnheading) on the fund’s attributes lagged fund expense ratio. Additional control variables include log of fund size, fundage (in months), and fund family size, all measured at the same time as the expense ratio. All variables are scaledby their cross-sectional standard deviations in each year. Control variables also include contemporaneous portfoliocharacteristics. Regressions include year fixed effects. Standard errors are clustered at the fund level. Superscripts***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.87Table 4.10: Robustness of the mutual fund fee-performance relation: additional models(1) (2) (3) (4) (5) (6)Gross alpha Net alphaFF5 FFC6 HXZ4 FF5 FFC6 HXZ4Panel A: Fama-MacBeth regressionExpense ratio 0.79** 0.56* 0.92** -0.12 -0.35 0.01(2.43) (1.85) (2.15) (-0.38) (-1.17) (0.02)Panel B: sample period 1998 to 2017Expense ratio 1.06*** 0.87*** 0.72 0.10 -0.09 -0.24(3.18) (2.74) (1.41) (0.31) (-0.29) (-0.46)Adjusted R2 0.075 0.086 0.060 0.075 0.086 0.060Month FE and controls Yes Yes Yes Yes Yes YesPanel C: three-year rolling windowExpense ratio 1.32*** 0.84** 1.30** 0.38 -0.09 0.37(3.44) (2.59) (2.31) (0.99) (-0.28) (0.65)Adj. R2 0.073 0.082 0.056 0.073 0.082 0.056Month FEs and controls Yes Yes Yes Yes Yes YesThis table presents the results of regressions of fund alphas on lagged expense ratios, both in percent per month.Alphas are computed using the CAPM, the Fama-French three-factor model (FF3), the Fama-French-Carhart four-factor model (FFC4), the Fama-French five-factor model (FF5), Fama-French five-factor augmented with Carhartmomentum factor model (FFC6), and Hou, Xue, and Zhang four-factor model (HXZ4). In Panel A, regressions areFama-MacBeth regressions with expense ratio as the only independent variable and standard errors are adjusted for 4lags of auto-correlation. In Panel B, the results are based on the 1998-2017 sample with fund level control variablesand month fixed effects. Factor loadings for each fund in each month in both Panel A and B are based on five-yearrolling regression windows. In Panel C, we measure factor loadings using three-year rolling window. Standard errorsin Panel B and C are clustered at the month level. Superscripts ***, **, * correspond to statistical significance at the1, 5, and 10 percent levels, respectively.88Table 4.11: Robustness of the mutual fund fee-performance relation: non-linearity testPanel A. Before-fee alpha (1) (2) (3) (4)αCAPMt αFF3t αFFC4t αFF5tExpense ratiot-1 -0.04 0.08 -0.12 0.97***(-0.07) (0.24) (-0.32) (3.09)Expense ratio2t-1 -7.22 1.69 3.07 7.07**(-1.63) (0.49) (0.90) (2.15)Log fund sizet-1 -0.23*** -0.08 -0.12* 0.01(-3.34) (-1.36) (-1.93) (0.22)Log fund aget-1 0.25 0.21* 0.29** 0.15(1.64) (1.78) (2.43) (1.30)Log fund family sizet-1 0.06* 0.06** 0.05* 0.09***(1.92) (2.30) (1.68) (3.07)Observations 321,414 321,414 321,414 321,414Adj. R2 0.110 0.074 0.083 0.075Month FE Yes Yes Yes YesPanel B. After-fee alpha (1) (2) (3) (4)αCAPMt αFF3t αFFC4t αFF5tExpense ratiot-1 -0.98* -0.86** -1.06*** 0.02(-1.71) (-2.54) (-2.91) (0.08)Expense ratio2t-1 -6.81 2.09 3.47 7.49**(-1.54) (0.61) (1.02) (2.28)Log fund sizet-1 -0.23*** -0.07 -0.11* 0.02(-3.30) (-1.31) (-1.87) (0.27)Log fund aget-1 0.24 0.21* 0.28** 0.15(1.61) (1.74) (2.40) (1.27)Log fund family sizet-1 0.06* 0.06** 0.05* 0.09***(1.95) (2.33) (1.71) (3.10)Observations 321,414 321,414 321,414 321,414Adj. R2 0.110 0.074 0.083 0.074Month FEs Yes Yes Yes YesThis table presents the results of panel regressions of fund alphas on expense ratios, both in percent per month, andother fund characteristics. Alphas are computed using the CAPM, the Fama-French three-factor model (FF3), theFama-French-Carhart four-factor model (FFC4), and the Fama-French five-factor model (FF5). Alphas are calculatedusing factor loadings estimated from a five-year rolling window regression. In Panel A (B), alpha is computed usingbefore-fee (after-fee) returns. Independent variables are measured as of the most recent fiscal year of the fund. BothExpense Ratio and Expense Ratio2 (i.e. expense ratio squared) are cross-sectionally de-meaned at the monthly level.All regressions include month fixed effects and cluster standard errors by month. The sample period is from 1980 to2017. Superscripts ***, **, * correspond to statistical significance at the 1, 5, and 10 percent levels, respectively.89Chapter 5ConclusionThis thesis addresses several questions about institutional investors. In the first essay, Chapter 2, Itheoretically investigate how the holding horizon of an institution determines its portfolio choiceand the related asset pricing implications. Institutional investors different significantly in theirholding horizon or their trading frequency. Empirically, institutions with different holding hori-zons also prefer to invest in different types of stocks. To analyze this phenomenon, I develop amodel in which short-term institutions can make more frequent portfolio rebalancing than long-term institutions, and stocks in the cross section experience different degrees of speculative demandshocks. In equilibrium, short-term institutions prefer to invest in stocks with greater exposure tospeculative demand shocks. The additional demand from short-term institutions reduces the buy-and-hold returns of these speculative stocks, making them less desirable for long-term institutionsto hold. My model rationalizes why short-term institutions overweight low-return stocks and pre-dicts these institutions generate additional returns by trading these stocks actively. Furthermore,stocks primarily held by short-term institutions should have more predictable returns, and theirreturn predictability is stronger when they become overpriced.In the second essay, Chapter 3, I construct empirical measures to test the main predictions ofmy theoretical model. Empirically, short-term institutions prefer to invest in younger, smaller, andmore volatile stocks. Furthermore, stocks primarily held by short-term institutions should havemore predictable returns, and their return predictability is stronger when they become overpriced.Empirical findings strongly support these predictions. Short-term institutions outperform long-term institutions by more than 3% per year among stocks primarily held by short-term institutions,while their performance is similar among stocks primarily held by long-term institutions. BothChapter 2 and 3 enhance our understanding of the behaviors of institutional investors with differentholding horizons.In Chapter 4, a joint work with Jinfei Sheng and Mike Simutin, we re-examine the fee perfor-mance relationship of active mutual funds. Previous literature uncovers a robust inverse relationbetween fees charged by actively managed mutual funds and future after-fee fund performance.Before deducting expenses, high-fee funds have been found to perform just as well as do low-feefunds. This paper resolves the puzzle by showing that factor models used to establish the priorfee-performance results are inadequate to control for differences in performance of funds with dif-ferent fees. High-fee funds exhibit a strong preference for stocks with high investment rates and90low profitability, characteristics that have been recently shown to associate with low expected re-turns. The commonly used three- and four-factor models produce large negative alphas for thesetypes of stocks, leading to a premature conclusion that high-fee funds underperform net of ex-penses. We evaluate the fee-performance relation using the recently proposed five-factor modelthat controls for exposures to the investment and profitability factors. The results we obtain standin stark contrast with those in the prior literature. We find that high-fee funds significantly out-perform low-fee funds before deducting expenses and do equally well net of fees. Our findingssupport the theoretical prediction that skilled managers extract rents by charging high fees, andcall into question the widely offered advice to avoid high-fee funds.5.1 Future workThe three essays in this thesis could be extended along several dimensions. First of all, the the-ory that I develop in Chapter 2 offers more predictions that are not tested in Chapter 3. Empiricallyverifying these additional predictions could further the understanding of institutional investors andthe mechanism that allows them to set asset prices. Second, the empirical asset pricing literaturehas identified many variables that predict the stock returns in the cross section. Chapter 2 of-fers a new non-risk based interpretation of why a variable can predict stock return. 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To simplify presentation, I drop the stock index i. Denote theexpected final pay-off of a stock E[v2] as v¯. The optimal demand of short-term institutions at t = 1isxS1(p1) =v¯−p1q v¯≥ p1v¯−p1θq v¯ < p1(A.1)Based on the market clearing conditionλxS1+u = κ (A.2)The price at t = 1 isp1 =v¯+qλ (u−κ) u≤ κv¯+ θqλ (u−κ) u > κ= v¯+qλ(u−κ)+ (θ −1)qλmax(u−κ,0) (A.3)Taking expectationE[p1] = v¯− qλ κ+(θ −1)qλC(κ,σ) (A.4)where, by direct integration,18C(κ,σ) = E[max(u−κ,0)] = σ2√2piσ2e−κ22σ2 −κ(1−Φ(κσ))(A.5)Consider equilibrium at t = 0, the demand of short-term institutions isxS0(p0) =E[p1]−p0q E[p1]≥ p0E[p1]−p0θq E[p1]< p0(A.6)18Note that function Φ is the cumulative distribution function of a standard normal random variable.99The demand of long-term institutions isxL0(p0) =v¯−p02q v¯≥ p00 v¯ < p0(A.7)There are four cases to consider: 1) E[p1]≥ p0 and v¯≥ p0, 2) E[p1]≥ p0 and v¯< p0, 3) E[p1]< p0and v¯ ≥ p0, and 4) E[p1] < p0 and v¯ < p0. In the first case, both short-term institutional demandand long-term institutional demand are positive,λxS0+(1−λ )xL0 = 1 (A.8)Solve for κ , p0, and E[p1] based on equations (A.4), (A.6), and (A.7) we haveκ = λ +(θ −1)(1−λ )2C(κ,σ) (A.9)In the second case, we have xL0 = 0, then κ = 1. This case happens when the solution to (A.9) isgreater than 1. The third case is not possible, which can be shown by contradiction. Suppose itwere true, then κ < 0 andE[p1]− p0 = v¯− p0− qλ κ+(θ −1)qλC(κ,σ)> 0 (A.10)contradicting the condition E[p1]− p0 < 0. The last case is not possible either, since if xS0 < 0and xL = 0, the market does not clear at t = 0. Therefore, in equilibrium, the ex ante short-termownership isκ = min(1,λ +(θ −1)(1−λ )2C(κ,σ))(A.11)The right-hand-side of (A.9) is monotonically decreasing in κ , since∂C∂κ=−(1−Φ(κσ))< 0 (A.12)By the intermediate value theorem, a unique root to equation (A.9) exists. Q.E.DA.0.2 Proof of Lemma 2The utility of each institution is the sum of its utility derived from each stock. This lemma can beproved by showing that the utility derived from each stock for long-term institutions is increasingin the fraction of short-term institutions λ and for short-term institutions is decreasing in λ . To100simplify presentation, I drop the stock index i. The utility for long-term institutions from stock i isUL = maxE[xL(v2− p0)−2Q(xL)] (A.13)Also, by the first order condition and the definition of ex ante short-term ownership κ , I have1−κ1−λ = xL =v¯− p02q(A.14)Assuming that long-term demand is not zero, I can rewrite a long-term institution’s utility asUL = qx2L = q(1−κ1−λ)2(A.15)Differentiate UL with respect to λ ,∂UL∂λ=2q(1−κ)(1−λ )2(1−κ1−λ −∂κ∂λ)(A.16)Based on (A.9),1−κ1−λ = 1−θ −12C > 0 (A.17)Differentiate κ with respect to λ based on Equation (A.9),∂κ∂λ= 1− θ −12C+(1−λ )(θ −1)2∂C∂κ∂κ∂λ(A.18)=1− θ−12 C1− (θ−1)(1−λ )2 ∂C∂κ(A.19)> 0 (A.20)Given that ∂C∂κ < 0 as shown in Proposition (1), we have1−κ1−λ −∂κ∂λ=−(1−λ )(θ −1)2∂C∂κ∂κ∂λ> 0 (A.21)Hence,∂UL∂λ> 0 (A.22)The utility of a long-term institution is the sum of its utility derived from each stock. Therefore,the utility of long-term institution increases with λ .101The utility of a short-term institution from stock i isUS = maxE[xS0(p1− p0)+ xS1(v2− p1)−Q(xS0)−Q(xS1)] (A.23)Based on the first order condition and the definition of κ , I can writexS0 =κλ=E[p1]− p0q(A.24)xS1 =v¯−p1q v¯≥ p1v¯−p1θq v¯ < p1(A.25)Substituting into the above equation,US =qκ22λ 2+12q∫ κ−∞(v¯− p1)2 f (u)du+ 12qθ∫ ∞κ(v¯− p1)2 f (u)du (A.26)=qκ22λ 2+q2λ 2E[(κ−u)2]+ q(θ −1)2λ 2∫ ∞κ(κ−u)2 f (u)du (A.27)=q(2κ2+σ2)2λ 2+q(θ −1)2λ 2∫ ∞κ(κ−u)2 f (u)du (A.28)where f (u) is the probability density function of the speculative demand shock u.By direct integration∫ ∞κ(κ−u)2 f (u)du = (κ2+σ2u )(1−Φ(κσu))− σ2uκ√2piσ2ue− κ22σ2u (A.29)= σ2u(1−Φ(κσu))−κC(κ,σ) (A.30)> 0 (A.31)Hence,US =q(2κ2+σ2)2λ 2+q(θ −1)2λ 2[σ2u(1−Φ(κσu))−κC(κ,σ)](A.32)I can denote this equation asUS = A+BH (A.33)whereA =q(2κ2+σ2)2λ 2> 0 (A.34)B =q(θ −1)2λ 2> 0 (A.35)102H = σ2u(1−Φ(κσu))−κC(κ,σ)> 0 (A.36)To show that US decreases with λ , it is suffice to show that A, B, and H decrease with λ , given thatA, B, and H are all positive. I can show that∂∂λq(2κ2+σ2)2λ 2=2qκλ(λ ∂κ∂λ −κ)λ 4− qσ2λ 3(A.37)<2qκλ (λ −κ)λ 4− qσ2λ 3(A.38)< 0 (A.39)The first inequality is based on∂κ∂λ= 1− θ −12C+(1−λ )(θ −1)2∂C∂κ∂κ∂λ< 1 (A.40)The second inequality is based on the fact that κ ≥ λ .In addition,∂∂λq(θ −1)2λ 2=−q(θ −1)λ 3< 0 (A.41)Finally,∂∂λ[σ2u(1−Φ(κσu))−κC]=− σ2√2piσ2e−κ22σ2∂κ∂λ−C∂κ∂λ−κ ∂C∂κ∂κ∂λ(A.42)=−[σ2√2piσ2e−κ22σ2 +C+κ∂C∂κ]∂κ∂λ(A.43)=−[σ2√2piσ2e−κ22σ2 +C−κ(1−Φ(κσ))] ∂κ∂λ(A.44)=−2C(κ,σ)∂κ∂λ(A.45)< 0 (A.46)Hence, US is decreasing in λ . The utility of a short-term institution is the sum of its utility derivedfrom each stock. Therefore, the utility of short-term institution decreases with λ . Q.E.D.A.0.3 Proof of Proposition 3Lemma (2) has established that the utility of short-term institutions decrease with λ and theutility of long-term institutions increase with λ . Hence, the difference in their utility decreaseswith λ . Now, I show that as λ approaches 0. The utility of short-term institutions approaches103infinity, while the utility of long-term institutions remain finite. Based (A.32)US >qσ22λ 2(A.47)Hence,limλ→0US ≥ limλ→0qσ22λ 2= ∞ (A.48)The utility of long-term institutions is maximized when λ = 1. When λ = 1, the utility of long-term institutions is finite. Therefore, as λ approaches 0, the utility of long-term institutions is finite.Hence, the differential of their utilities approaches infinity. By the intermediate value theorem, forany large cost c, there exists a positive λ such that the after cost utility of short-term institutionsequals to the utility of long-term institutions when λ < 1. For small c, the utility of short-terminstitutions will be greater than the utility of long-term institutions even if λ = 1. Hence, all insti-tutions will be short-term institutions Proposition (1) has established the existence and uniquenessof stock level equilibrium for any given λ . Therefore, the equilibrium of this model exists and isunique. Q.E.D.A.0.4 Proof of Proposition 4A stock’s ex ante short-term ownership κ is the solution to the equation (2.10). From (A.5), wehave∂C∂σ=σ2√2piσ2e−κ22σ2 −κ(1−Φ(κσ))=1√2pie−κ22σ2 > 0 (A.49)∂C∂κ=−(1−Φ(κσ))< 0 (A.50)Hence, based on (A.9),∂κ∂σu=(θ−1)(1−λ )2∂C∂σ1− (θ−1)(1−λ )2 ∂C∂κ≥ 0 (A.51)Therefore, stocks with higher σ have higher ex ante short-term ownership. From the first ordercondition of long-term institutions, the buy-and-hold return of a stock isE[v2− p0] = 2qxL0 = 2q1−κ1−λ (A.52)It is immediate that the buy-and-hold return decreases with σ (i.e., decreases with κ). Q.E.D.A.0.5 Proof of Proposition 5By definition, the trading profit of long-term institutions is always 0 for each stock. The trading104profit of short-term institutions for stock i isRTS ≡ x0(p1− p0)+ x1(v2− p1)− x0(v2− p0) = (x1− x0)(v2− p1) (A.53)Taking expectationE[(x1− x0)(v2− p1)] = E[x1(v2− p1)]−E[x0(v2− p1)] (A.54)Evaluate each component separatelyE[x1(v2− p1)] = qλ 2 E[(κ−u)2]+q(θ −1)λ 2∫ ∞κ(κ−u)2 f (u)du (A.55)=qλ 2(κ2+σ2)+q(θ −1)λ 2[σ2u(1−Φ(κσu))− 2κ(κ−λ )(θ −1)(1−λ )](A.56)=qλ 2[κ2− 2κ(κ−λ )1−λ]+qλ 2σ2[1+(θ −1)(1−Φ(κσu))](A.57)The second equality is based on (A.30).E[x0(v2− p1)] = κλ(qλκ− (θ −1)qλC)(A.58)=qλ 2(κ2− 2κ(κ−λ )1−λ)(A.59)Combining the two terms, I haveE[(x1− x0)(v2− p1)] = qλ 2σ2u[1+(θ −1)(1−Φ(κσu))](A.60)It is clear that qλ 2σ2u increases with σu. It is suffice to show that[1+(θ −1)(1−Φ(κσu))]alsoincreases with σu. Differentiate it with respect to σu∂∂σu[1+(θ −1)(1−Φ(κσu))]=−(θ −1)σ2uφ(κσu)(σu∂κ∂σu−κ)(A.61)105where φ is the probability density function of standard normal distribution. I can show thatσu∂κ∂σu= σu(θ−1)(1−λ )2∂C∂σu1− (θ−1)(1−λ )2 ∂C∂κ(A.62)=(θ−1)(1−λ )2σ2u√2piσ2ue− κ22σ2u1+ (θ−1)(1−λ )2(1−Φ(κσu)) (A.63)<(θ−1)(1−λ )2 C1+ (θ−1)(1−λ )2(1−Φ(κσu)) (A.64)< κ (A.65)where the first inequality is based on equation for the value of the resale option, Equation (A.5),and the second inequality is based on the equation for κ , Equation (A.9). Hence,∂∂σu[1+(θ −1)(1−Φ(κσu))]> 0 (A.66)By the product rule,∂∂σuE[(x1− x0)(v2− p1)]> 0 (A.67)Q.E.D.A.0.6 Proof of Proposition 6It is clear from Lemma (2) that the difference in utility between long-term and short-terminstitutions is monotonic in the fraction of short-term institutions. As the cost of becoming a short-term institutions increases, the break-even utility differential also increases, which means that thefraction of short-term institutions declines.Now let me compare two economies with two different fractions of short-term institutions.In economy 1, the fraction of short-term institutions is λ1 and in economy 2, the fraction is λ2.Suppose λ1 > λ2, I show that the dispersion of ex ante short-term ownership, i.e. Var(κ1i), ineconomy 1 is smaller than the dispersion in economy 2. Start with the equilibrium conditionκ = λ +(θ −1)(1−λ )2C(κ,σ) (A.68)First, I show that∂ 2∂σ∂λκ < 0 (A.69)106From equation (A.51), we know∂κ∂σu=∂C∂σ2(θ−1)(1−λ ) − ∂C∂κ(A.70)Differentiate with respect to λ∂ 2∂σ∂λκ =−∂C∂σ(2(θ −1)(1−λ ) −∂C∂κ)−2 2(θ −1)(1−λ )2 < 0 (A.71)We also have∂κ∂λ=11− θ−12 ∂C∂κ> 0 (A.72)Hence, κ1i is greater than κ2i for every stock i, but the difference, κ1i−κ2i, is decreasing in σui.Denote the difference between the two as δi. We haveκ2i = κ1i−δi (A.73)Given that κ1i is increasing in σui, κ1i and δi must have negative co-variance. Hence,Var(κ2i) =Var(κ1i−δi) (A.74)=Var(κ1i)+Var(δi)−2Cov(κ1i,δi) (A.75)>Var(κ1i) (A.76)The expected return of each stock is a linear function of ex ante short-term ownership κ . Hence,the variance in the cross section of expected return is also greater in economy 2 than in economy1. The trading profit isE[(x1− x0)(v2− p1)] = qλ 2σ2[1+(θ −1)(1−Φ(κσu))](A.77)Given that κ is increasing in λ ,∂∂λ[1+(θ −1)(1−Φ(κσu))]< 0 (A.78)∂∂λ[ qλ 2σ2]< 0 (A.79)Based on the chain rule,∂∂λE[(x1− x0)(v2− p1)]< 0 (A.80)107The trading profit of short-term institutions in economy 2 is greater than that in economy 1. Q.E.D.A.0.7 Proof of Proposition 7Consider two economies, 1 and 2. Economy 1 has more stringent short-selling constraint θ1,while economy 2 has less stringent short-selling constraint θ2, i.e. θ1 > θ2. Similar to Proposition6,∂ 2∂σ∂θκ =∂C∂σ(2(θ −1)(1−λ ) −∂C∂κ)−2 2(1−λ )(θ −1)2 > 0 (A.81)We also have∂κ∂θ=1−λ2 C(κ,σ)1− (θ−1)(1−λ )2 ∂C∂κ> 0 (A.82)Denote the difference between κ2i and κ1i as δi (δi > 0)κ1i = κ2i+δi (A.83)We have that δi is increasing in σi. Hence, the co-variance between κ2i and δi is positive,Var(κ1i) =Var(κ2i+δi) (A.84)=Var(κ2i)+Var(δi)+2Cov(κ2i,δi) (A.85)>Var(κ2i) (A.86)Similarly, the expected return of each stock is a linear function of ex ante short-term ownershipκ . Hence, the variance in the cross section of expected return is also greater in economy 1 than ineconomy 2. Q.E.D.A.0.8 Proof of Proposition 8It is clear from Equation (A.9) that ex ante short-term ownership is not affected by changes inq. Given that long-term return isE[v2]− p0 = 2q1−κ1−λ (A.87)An increase in q increases the cross-sectional variation in expected return. The trading profit ofshort-term institutions also increases with q, since∂∂qE[(x1− x0)(v2− p1)] = ∂∂qqλ 2σ2[1+(θ −1)(1−Φ(κσu))](A.88)=σ2λ 2[1+(θ −1)(1−Φ(κσu))](A.89)> 0 (A.90)108Q.E.D.A.0.9 Proof of Proposition 9Based on the market clearing condition at t = 0, an exogenous increase in either short-termdemand or long-term demand will increase the price of the stock at t = 0, reducing its buy-and-hold return. Now consider return volatility, given that the price at t = 1 isp1 = v¯+qλ(u−κ)+ (θ −1)qλmax(u−κ,0) (A.91)clearly, we can see that holding constant σu, an increase (decrease) in κ will reduce (increase)Var(p1) by reducing (increasing) the variance of max(u−κ,0). Given that trading profit isE[(x1− x0)(v2− p1)] = qλ 2σ2[1+(θ −1)(1−Φ(κσu))](A.92)holding constant σu, an increase (decrease) in κ will reduce (increase) the trading profit of short-term institutions. Q.E.D.A.0.10 Proof of Proposition 10To compute the expected second-period return for overpriced and under-priced stocks, I takethe conditional expectation of the second period return based on (A.3),R+ ≡ E[v2− p1|u < 0] = qλ κ−qλE[u|u < 0] = qλκ+q√2λ√piσ (A.93)R− ≡ E[v2− p1|u > 0] = qλ κ−qλE[u|u > 0]− q(θ −1)λE[u−κ|u > 0] (A.94)=qλκ− q√2λ√piσ − 2q(θ −1)λC (A.95)Differentiate R+ with respect to σu and since ∂κ∂σ ≥ 0∂R+∂σ=qλ∂κ∂σ+q√2λ√pi> 0 (A.96)To find the derivative of R−with respect to σu, first substitute C using equation (A.9)R− =− (3+λ )q(1−λ )λ κ−q√2λ√piσ +4q1−λ (A.97)109Hence,∂R−∂σ=− (3+λ )q(1−λ )λ∂κ∂σ− q√2λ√pi< 0 (A.98)The difference in the absolute value of these two derivatives is∣∣∣∣∂R−∂σ∣∣∣∣− ∣∣∣∣∂R+∂σ∣∣∣∣= 2(1+λ )q(1−λ )λ ∂κ∂σ ≥ 0 (A.99)Hence, the return predictability is stronger for overpriced stocks than under-priced stocks as σincreases. Q.E.D.A.0.11 Proof of Proposition 11Since the additional utility that short-term institutions obtain from each stock is positive, in-crease in the number of stocks increases the total extra utility that short-term institutions obtain,increasing the incentive for institutions to switch to be short-term investors. Hence, the fraction ofshort-term institutions λ increases with the number of stocks N. From Lemma 2, I have thatUS =q(2κ2+σ2)2λ 2+q(θ −1)2λ 2∫ ∞κ(κ−u)2 f (u)du (A.100)=q(2κ2+σ2)2λ 2+q(θ −1)2λ 2[σ2u(1−Φ(κσu))−κC(κ,σ)](A.101)It is easy to see that∂US∂q=(2κ2+σ2)2λ 2+(θ −1)2λ 2∫ ∞κ(κ−u)2 f (u)du > 0 (A.102)Therefore, an increase in q increases the utility of short-term institutions, resulting in higher λ .Q.E.D.A.0.12 Proof of Proposition 12At t = 1, short-term investorsxS1(p1) =v¯−dβ−p1q v¯≥ p1v¯−dβ−p1θq v¯ < p1(A.103)Price at t = 1p1 =v¯−dβ +qλ (u−κ) u≤ κv¯−dβ + θqλ (u−κ) u > κ= v¯−dβ + qλ(u−κ)+ (θ −1)qλmax(u−κ,0) (A.104)110E[p1] = v¯−dβ − qλ κ+(θ −1)qλC (A.105)At t = 0, long-term demandxL0 =v¯−2dβ − p02q=1−κ1−λ (A.106)xS0 =E[p1]−dβ − p0q=κλ(A.107)Solve for κ and p0, we have the expected stock return and short-term ownership asv¯− p02= dβ +q1−λ (1−κ) (A.108)κ = λ +(θ −1)(1−λ )2C(κ,σ) (A.109)Q.E.D.111Appendix BAppendix to Chapter 3: Variable DefinitionTurnover ratio of institutional investors: quarterly turnover ratio is defined as the minimum ofpurchases and sales in a quarter divided by the average asset. The turnover ratio of an institutionas of quarter t is the sum of its turnover ratios in four most recent consecutive quarters. Purchasesand sales are computed as changes in the number of shares between two quarter ends multipliedby the last quarter-end price.Turn jt =t∑τ=t−3min(Purchaseτ ,Salesτ)12(Sizeτ−1+Sizeτ)(B.1)Short-term ownership: short-term ownership of stock i in quarter t is defined as the weightedaverage of turnover ratios of institutions that invest in the stock, weighted by the number of shareseach institution ownsST Ownit =∑Nj=1 Sharesi jt×Turn jt∑Nj=1 Sharesi jt(B.2)Ex ante short-term ownership: defined as the average short-term ownership of a stock over fourquarters in the prior year.Beta: measured as the regression coefficient of a stock’s daily excess return on the daily marketexcess return in each quarter.Idiosyncratic volatility: measured as the residual volatility of regressing a stock’s daily excessreturn on daily Fama-French three-factor returns in each quarter.B/M ratio: the ratio of a stock’s book equity at the end of its fiscal year to its December marketcapitalization. Book equity is measured as common equity plus deferred taxes (if available). Ifcommon equity is not available, I replace it with total asset minus liability minus preferred equity(if available).Momentum: the cumulative return of a stock from month t−12 to month t−2.Mispricing score: constructed by Stambaugh et al. (2015), it is the average percentile rankingof eleven anomaly characteristics, which include financial distress, O-Score, net stock issuance,momentum, etc. Jianfeng Yu provides detailed documentation about this mispricing score on hispersonal website.1919https://sites.google.com/site/yujianfengaca/112Appendix CAppendix to Chapter 4: Variable DefinitionCAPM beta: Following Lewellen and Nagel (2006), we measure a stock’s daily CAPM beta asthe sum of the slope coefficients from a regression of the stock excess return in day t on the marketexcess returns in t, t-1, and average market excess return during t-4 through t-2. We estimate thebetas annually using one calendar year of data.Market capitalization: The natural logarithm of stock i’s market capitalization, measured in theend of December of each year.B/M ratio: The ratio of stock i’s book equity at the end of its fiscal year to its December endmarket capitalization. We adjust market capitalization for any share issuance between the fiscaland calendar year end. Following Fama and French (2008), book equity is common equity plusdeferred taxes (if available). If common equity is not available, we replace it with total asset minusliability minus preferred equity (if available). The formula for B/M ratio isB/Mi,t =Book EquityitMarket Equityit(C.1)Momentum: The cumulative return of a stock from January to November of each year.Asset growth: The asset growth rate of company i in year t is defined as the natural logarithmof the ratio of its total asset in year t to total asset in year t-1. Total asset is measured as of thefiscal year endAGi,t = lnAssetitAssetit−1(C.2)Equity issuance: Equity issuance: equity issuance for company i in year t is defined as thenatural logarithm of the ratio of number of shares outstanding in year t to the number of sharesoutstanding in year t-1. Number of shares outstanding is measured as of December of each year.We adjust for stock splits between two year ends. The formula isEIit = lnAd justed sharesoutstandingitAd justed sharesoutstandingit−1(C.3)Operating profitability: For company i year t, we measure its operating profitability followingFama and French (2015). Specifically, profitability is measured as of the end of fiscal year asrevenue minus cost of goods sold, minus selling, general, and administrative expenses, minus113interest expense, all divided by the book equity. The formula isOPit =(REV −COGS−SG&A− INT EXP)itBook Equityit(C.4)Stock age: Number of years a stock is publicly listedSales growth: The sales growth rate of company i in year t is defined as the natural logarithmof the ratio of its total sales in year t to total sales in year t-1.Uncertain words: Loughran and MacDonald (2011) firm level uncertainty index.Tangibility: For company i in year t, its tangibility is measured as the ratio of the amount ofproperty, plant and equipment to its total asset.Number of analysts: Number of analysts that provides earnings forecasts for a stock.Idiosyncratic volatility: For company i in year t, IVOL is measured as the standard deviationof the residual of daily Fama-French three-factor regression as in Ang et al. (2006).114

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