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An investigation of certain accounting-related stock market anomalies 2012

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     An Investigation of Certain Accounting-Related Stock Market Anomalies  by  Soh Yung Kim  M.S., State University of New York at Buffalo, 2004 B.B.A., Seoul National University, 2001  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF   DOCTOR OF PHILOSOPHY   in  The Faculty of Graduate Studies (Business Administration)        THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2012 © Soh Yung Kim, 2012   ii Abstract In financial markets, anomalies refer to empirical regularities in which security returns deviate from what would be expected in an informationally efficient market. This dissertation investi- gates explanations for stock market anomalies related to accounting information as documented by Dichev (1998) and Piotroski (2000). Using Ohlson’s (1980) measure of bankruptcy risk (O-Score), Dichev (1998) documents a bankruptcy risk anomaly in which firms with high bankruptcy risk earn lower than average returns. My study first demonstrates that the negative association between bankruptcy risk and returns does not generalize to alternative measures of bankruptcy risk. Then, by examining the nine individual components of O-Score, I find that funds from operations (FFO) is the only com- ponent that is associated with returns. Furthermore, I show that the return-predictive power of FFO is due to cash flows from operations. Taken as a whole, this study provides evidence that Dichev’s bankruptcy risk anomaly is a manifestation of investors’ under (over)-pricing of cash flows (accrual) component of earnings, i.e., the accrual anomaly documented by Sloan (1996). The second study investigates the effects of two potentially problematic research design choices which are often made in accounting-based studies of anomalies. I explore these issues by re-examining the results in Piotroski (2000), who finds that a simple, financial statement-based heuristic, when applied to a subset of firms with high book-to-market ratios, can discriminate between the firms that will eventually provide high returns and those that will be poor perform-  iii ers. I find that the relationship between Piotroski’s fundamental signals and subsequent returns is partly driven by the choice of return accumulation periods and the use of equally weighted re- turns. When the research design controls for both problems, the relationship disappears. Because the methods used in Piotroski are typical of those often employed in the accounting literature, this study suggests that evidence of profitable trading strategies and market inefficiency in the literature is likely to be overstated.     iv Preface A version of Chapter 2 in this dissertation has been accepted for publication at Review of Ac- counting Studies [Kim, S. 2012. What is behind the magic of O-Score? An alternative interpreta- tion of Dichev’s (1998) bankruptcy risk anomaly, Review of Accounting Studies, Forthcoming].  v Table of contents Abstract.............................................................................................................................. ii Preface............................................................................................................................... iv Table of contents ................................................................................................................v List of tables..................................................................................................................... vii List of figures .................................................................................................................. viii Acknowledgements........................................................................................................... ix Dedication ...........................................................................................................................x Chapter 1: Introduction ....................................................................................................1 Chapter 2: What is behind the magic of O-Score? An alternative interpretation of Dichev’s (1998) bankruptcy risk anomaly ...................................................................9 2.1 Introduction......................................................................................................................... 9 2.2 Empirical analysis I: How robust is the bankruptcy risk anomaly when using an alternative measure of bankruptcy risk?.......................................................................... 14 2.2.1 Sample formation and variable measurement.............................................................. 14 2.2.2 Results.......................................................................................................................... 20 2.3 Empirical analysis II: What is inside the magic of O-Score? ....................................... 26 2.3.1 Results.......................................................................................................................... 26 2.4 Empirical analysis III: What is the source of the predictive power of FFO/TL?....... 29 2.4.1 Funds from operations, cash flows from operations, and accrual anomaly................. 29 2.4.2 Sample formation and variable measurement.............................................................. 31 2.4.3 Results.......................................................................................................................... 32 2.4.4 Sensitivity tests ............................................................................................................ 36 2.5 Conclusion ......................................................................................................................... 39 Chapter 3: Implementability of trading strategies based on accounting information: Piotroski (2000) revisited.............................................................................................65  vi 3.1 Introduction....................................................................................................................... 65 3.2 Background and motivation ............................................................................................ 70 3.2.1 Equal- versus value-weighting..................................................................................... 70 3.2.2 The problem of unknown portfolio weights ................................................................ 71 3.2.3 Survey of prior accounting studies related to accounting anomalies........................... 74 3.3 Description of the empirical tests .................................................................................... 77 3.3.1 F-Score......................................................................................................................... 77 3.3.2 Details on Analysis 1 and Analysis 2 .......................................................................... 80 3.4 Sample................................................................................................................................ 84 3.5 Empirical results ............................................................................................................... 87 3.5.1 The problem of unknown portfolio weights ................................................................ 87 3.5.2 Equal- versus value-weighting..................................................................................... 91 3.5.3 Real-world implementation of F-Score-based trading strategy ................................... 92 3.5.4 Replication of Xie (2001) ............................................................................................ 94 3.6 Conclusions........................................................................................................................ 97 Chapter 4: Conclusions .................................................................................................120 References .......................................................................................................................123 Appendices ......................................................................................................................130 Appendix A Estimation of Hillegeist et al.’s (2004) BSM-Prob ........................................ 130 Appendix B An association of a variable with a score: An econometric interpretation..... 133   vii List of tables Table 2.1: Characteristics of O-Score [BSM-Prob] decile portfolios........................................... 42 Table 2.2: Association of returns with O-Score [BSM-Prob]....................................................... 43 Table 2.3: Association of returns with the components of O-Score ............................................. 45 Table 2.4: Returns to zero-investment trading strategies using FFO/TL...................................... 47 Table 2.5: Association of returns with O-Score after controlling for FFO/TL............................. 49 Table 2.6: Characteristics of FFO/TL decile portfolios................................................................ 50 Table 2.7: Association of returns with CFO/ATA........................................................................ 51 Table 2.8: Returns to zero-investment trading strategies using CFO/ATA.................................. 52 Table 2.9: Associations of returns with FFO/TL before/after controlling for CFO/ATA............ 54 Table 2.10: Associations of returns with O-Score before/after controlling for CFO/ATA.......... 56 Table 2.11: Returns across FFO/TL and O-Score quintile portfolios after controlling for CFO/ATA ................................................................................................................................. 58 Table 2.12: Sensitivity tests using post-SFAS No. 95 observations............................................. 60 Table 2.13: Sensitivity tests using Sloan’s (1996) original accrual measure ............................... 62 Table 3.1: Implementability of trading strategies in prior accounting studies ............................. 99 Table 3.2: The sample composition across Analysis 1 and Analysis 2 by F-Score.................... 100 Table 3.3: The sample composition across Analysis 1 and Analysis 2 by year ......................... 102 Table 3.4: One-year market-adjusted returns by F-Score........................................................... 104 Table 3.5: One-year market-adjusted returns to F-Score-based equal-weighted portfolios ....... 105 Table 3.6: The impact of the unknown portfolio weights problem on the profitability of hedge portfolios ................................................................................................................................. 108 Table 3.7: One-year market-adjusted returns to F-Score-based value-weighted portfolios ....... 110 Table 3.8: The impact of the unknown portfolio weights problem and change in portfolio weighting on the profitability of hedge portfolios .................................................................. 112 Table 3.9: Profitability of implementing F-Score-based hedge portfolios multiple times a year114 Table 3.10: The impact of the unknown portfolio weights problem and change in portfolio weighting on the profitability of hedge portfolios in the context of Xie (2001)..................... 117   viii List of figures Figure 2.1: Returns to zero-investment trading strategy using FFO/TL and CFO/ATA.............. 64 Figure 3.1: Illustration of the unknown portfolio weights problem............................................ 119   ix Acknowledgements I offer my enduring gratitude to the faculty, staff, and my fellow students at the UBC, who have inspired me to continue my journey of learning. I owe particular thanks to Professors Sandra Chamberlain and Kin Lo, whose penetrating questions taught me to question more deeply. I thank Professor Gerald (Jerry) Feltham for providing theoretical training and for being an excel- lent example as a researcher, a teacher, and a father. I also thank Professors Joy Begley, Kai Li, and Dan Simunic for their advice on my research and support toward completion of PhD degree. Special thanks are owed to my parents and parents-in-law, who have supported me throughout my lengthy years of education, both morally and financially.   x Dedication To my wife Sue, for being a patient endurer, for being a candle flame in dark times, and for being there with me.  To my children Christine, Elizabeth, and Kenneth, for being proud of me for who I am.  I love you!   1 Chapter 1: Introduction In financial markets, anomalies refer to empirical regularities in which security returns deviate from what would be expected in an informationally efficient market. This dissertation investi- gates explanations for stock market anomalies related to accounting information as documented in two separate studies by Dichev (1998) and Piotroski (2000). This chapter briefly reviews the existing literature and highlights where my studies fit in with the existing literature. Fama (1970) defines an efficient market as one in which “security prices fully reflect all available information (p. 383).” Whether securities markets are informationally efficient is of great interest to investors, standard setters, researchers, and other market participants because securities prices determine the allocation of wealth among individuals and the allocation of scarce resources among firms (Kothari, 2001). Not surprisingly, there is a large amount of litera- ture in finance and accounting that investigates whether information appears to be efficiently impounded into prices. Early capital market studies that examined security prices around economic events such as earnings announcements (Ball and Brown, 1968; Beaver, 1968) or stock splits (Fama, Fisher, Jensen, and Roll, 1969) largely support market efficiency. However, later studies with more refined data challenge market efficiency. For example, studies on stock price reactions to earn- ings announcements find that returns drift follows the initial price reaction. Foster, Olsen, and Shevlin (1984) and Bernard and Thomas (1990) document that abnormal returns following earn-  2 ings announcement last up to a year and that the magnitude of the effect is both statistically and economically significant for the extreme good and bad earnings news portfolios, suggesting that the market underreacts to information in earnings announcements. More recently, Sloan (1996) challenges market efficiency with what has been termed as the ‘accrual anomaly.’ His evidence suggests that the market assigns a higher persistence to the accrual component of earnings and over (under)-prices firms with earnings containing high (low) accrual components. As a result, an investment strategy that exploits this mispricing earns abnormal returns of around 10 percent in the year following the release of financial statements. Sloan suggests that the market fails to correctly incorporate the information in accruals into stock prices. Although long-horizon tests of market efficiency report economically large abnormal re- turns, not all researchers accept these returns as evidence of market inefficiency. For example, Kothari (2001) emphasizes that long-horizon tests suffer from several data problems such as risk adjustments, sample selection biases, and inference problems arising from cross-sectional de- pendence. A number of studies (e.g., Fama, 1998; Guay, 2000) argue that studies purporting to identify market inefficiencies typically do not provide a plausible and rejectable alternative hy- pothesis to market efficiency. With the exception of a few studies (e.g., Bernard and Thomas, 1990; Sloan, 1996), most studies that show evidence of inefficiency fail to provide a theory that  3 specifies conditions under which market under- and over-reaction is forecasted.1 Guay remarks, “Rather than providing evidence in support of a pricing theory, they are marketed as descriptive evidence of a ‘puzzle’, to be resolved by future research (p. 50).” This statement precisely de- scribes the current status of the bankruptcy risk anomaly literature and for that reason, Chapter 2 of this dissertation investigates this anomaly. The bankruptcy risk anomaly, documented by Dichev (1998), refers to the empirical reg- ularity in which a composite measure of bankruptcy risk predicts future returns. Using Ohlson’s (1980) measure of bankruptcy risk (O-Score), Dichev finds that firms with high bankruptcy risk earn lower than average returns during his sample period of 1981 to 1995. As noted in Dichev, his original expectation was to find the opposite relationship based on the conjecture that higher risk, more insolvent firms should have higher average subsequent returns compared with less insolvent firms. As a result of his findings, Dichev suggests that market prices do not fully im- pound the implications of available bankruptcy information. Dichev (1998) is a seminal work in this literature; it is the first study that investigates the relationship between bankruptcy risk and returns. Prior to Dichev, the focus of bankruptcy stud- ies had been on the development of models to better predict future bankruptcy (e.g., Beaver,   1  There is a growing body of research that comes under the heading of “limited attention” that appears to offer such a theory (e.g., Hirshleifer and Teoh, 2003; Hirshleifer et al., 2008; Hirshleifer, Lim, and Teoh, 2009; Hirshleifer, Lim, and Teoh, 2011).  4 1966; Altman, 1968; Ohlson, 1980; Zmijewski, 1984). Dichev’s counterintuitive results led to numerous follow-up studies. However, use of allegedly better measures of bankruptcy risk and different samples in these studies make comparisons problematic. An example of these comparability issues can be seen in Vassalou and Xing (2004) and Campbell, Hilscher, and Szilagyi (2008), two often cited follow-up studies. Interestingly, both studies were published in The Journal of Finance, but they reach different conclusions. The former, using a market-based measure of bankruptcy risk, Default Likelihood Indicator (DLI), derived from Merton’s (1974) framework, finds evidence that firms with high bankruptcy risk earn higher returns. By contrast, the latter, using its own measure of bankruptcy risk based on accounting information as well as market information, finds that stocks with high bankruptcy risk have delivered low returns since 1981. Subsequent studies show either a positive or a nega- tive relationship between their measures of bankruptcy risk and returns (e.g., Chava and Pur- nanadam, 2010; George and Hwang, 2010). Thus, the literature seems far from settled with respect to the relationship between bankruptcy risk and returns. To help understand these mixed results and the bankruptcy risk anomaly, I analyze a sin- gle sample with two different proxies for bankruptcy risk: Ohlson’s (1980) O-Score, the indica- tor of risk used by Dichev (1998), and BSM-Prob, a DLI measure used in Hillegeist et al. (2004). Using O-Score, I successfully replicate the results of Dichev but, using BSM-Prob, I am unable to replicate his results. Next, I investigate the source of O-Score’s predictive ability by examin-  5 ing the individual components of O-Score. I find that funds from operations (FFO) is the only component that is associated with returns. Furthermore, I show that the return-predictive power of FFO is due to cash flows from operations. Taken as a whole, Chapter 2 provides evidence that Dichev’s bankruptcy risk anomaly is a manifestation of investors’ under (over)-pricing of cash flows (accrual) component of earnings, i.e., Sloan’s (1996) accrual anomaly. The bankruptcy risk anomaly and the accrual anomaly are only two examples of anoma- lies documented in the literature. As noted in Keim (2008), the number of documented anomalies is large and growing. While anomaly studies report economically significant anomalous returns, many other studies (e.g., Malkiel, 1995; Carhart, 1997) document that, on average, managers of mutual funds and other actively managed funds do not outperform the market. If a primary ob- jective of fund managers is to invest their capital in assets that generate the highest possible risk- adjusted returns, then why are returns earned by fund managers not as great as returns docu- mented by academic researchers? Moreover, how does documented mispricing persist without being arbitraged away by fund managers?2 These questions motivate Chapter 3 of this disserta- tion, where I investigate the implementability of trading strategies based on accounting informa- tion. The chapter investigates the effects of two potentially problematic research design choic-   2  Some work has been done to address this question. For example, Mashruwala, Rajgopal, and Shevlin (2006) explain Sloan’s (1996) accrual anomaly using idiosyncratic risk and transaction costs.  6 es that are often made in accounting-based studies of anomalies. Both of these research design choices are relevant to the class of studies that employ zero-investment hedge portfolios. The two issues are: 1) the use of equal- versus value-weights in forming the portfolios and 2) the selection of return accumulation periods based on firm specific fiscal year-ends, rather than es- tablishing a common investment date for all firms in the two hedge portfolios. Fama and French (2008) argue that equal weighting of stocks within the hedge portfolios can be called into question because of real-world implementation issues. For example, research- ers that use equal-weighted portfolios assume that sufficient quantities of small-cap stocks can be acquired or shorted, contrary to real-world conditions. Despite this, many accounting studies of anomalies use equal-weighted portfolios and do not provide evidence that their results are robust to an alternative portfolio weighting scheme. Secondly, accounting researchers sometimes em- ploy a return-aggregation approach that cannot be implemented by money managers. If a money manager were to sort firms on the variable of interest such as book-to-market, she cannot deter- mine the total number of firms in each side of the hedge portfolio until the accounting informa- tion of the entire portfolio becomes available. However, in forming portfolios shortly after the fiscal year-end, accounting researchers assume knowledge about the identity and weighting of firms that could not be known to money managers. I refer to this issue as the problem of un- known portfolio weights. I explore these two methodological issues by re-examining the results in Piotroski (2000).  7 Piotroski finds that a simple, financial statement-based heuristic, when applied to a subset of firms with high book-to-market ratios, can discriminate between the firms that will eventually provide high returns and those that will perform poorly. In documenting this evidence, Piotro- ski’s research design is subject to both of the aforementioned methodological issues. His study is worth revisiting for two reasons. First, his research question leads him to employ a subset of firms that are likely to be particularly vulnerable to the implementation issues that surround equally weighting firms in hedge portfolios. Second, the research in finance that originally doc- uments excess returns to investing in firms with high book-to-market ratios aggregates returns using a common calendar date (e.g., July 1st) rather than relying on fiscal year-ends to define the return aggregation period as in Piotroski. Thus, the question arises, would Piotroski have ob- tained similar results even if he had followed the approach used in the finance studies upon which he relied? I find that the relationship between Piotroski’s (2000) fundamental signals and subse- quent returns is partly driven by the choice of return accumulation periods and the use of equally weighted returns. When the research design controls for both problems, the relationship disap- pears. Because the methods used in Piotroski are typical of those often employed in the account- ing literature, this study suggests that evidence of profitable trading strategies and market inefficiency in the literature is likely to be overstated. The remainder of the dissertation is structured as follows. In Chapter 2, I re-examine the  8 bankruptcy risk anomaly and provide an alternative interpretation of Dichev’s (1998) findings. In Chapter 3, I investigate the impact of the difference in return accumulation periods and different weighting schemes on the evidence of market efficiency by replicating and extending the analy- sis in Piotroski (2000). In the final chapter, I summarize the findings from prior chapters and outline major contributions made by this dissertation.  9 Chapter 2: What is behind the magic of O-Score? An alternative interpretation of Dichev’s (1998) bankruptcy risk anomaly3 2.1 Introduction The bankruptcy risk anomaly documented by Dichev (1998) refers to the empirical regularity in which a composite measure of bankruptcy risk predicts future returns. Using Ohlson’s (1980) measure of bankruptcy risk (O-Score), Dichev finds that firms with high bankruptcy risk earn lower than average returns during his sample period of 1981−1995. As noted in Dichev, his orig- inal expectation was to find the opposite relationship based on the conjecture that “if the risk of bankruptcy is at least partly systematic, then more insolvent firms should have higher average subsequent returns as compared to less insolvent firms (p. 1134).” As a result of his findings, Dichev suggests that market prices do not fully impound the implications of available bank- ruptcy information. Subsequent studies using different measures of bankruptcy risk and samples provide mixed evidence. A group of researchers that use Ohlson’s (1980) O-Score as a proxy of bank- ruptcy risk supports Dichev’s (1998) findings. For example, Griffin and Lemmon (2002) find that the negative relationship between O-Score and returns is strong among firms with low book- to-market ratios (i.e., growth firms), suggesting that the bankruptcy risk anomaly is likely to   3  A version of this chapter has been accepted for publication at Review of Accounting Studies.  10 occur as a result of a high degree of information asymmetry among growth firms, and George and Hwang (2010) assert that the negative relationship between returns and leverage is responsi- ble for the negative association between bankruptcy risk and returns. By contrast, another group of researchers, relying on the other measures of bankruptcy risk, challenges Dichev’s conclusion by showing a positive relationship between bankruptcy risk and returns (e.g., Vassalou and Xing, 2004; Chava and Purnanandam, 2010) or no reliable relationship between the two (e.g., Anginer and Yildizhan, 2010).4 Although the latter group of studies refute Dichev’s conclusion, the caus- es of Dichev’s findings have not been answered. This study attempts to fill this gap. To help understand these mixed results and the bankruptcy risk anomaly, I analyze a sin- gle sample with two different proxies of bankruptcy risk: O-Score and BSM-Prob (Hillegeist et al., 2004). I choose to use BSM-Prob because Hillegeist et al. empirically show that their meas- ure is superior to O-Score in terms of bankruptcy prediction. Using two distinct proxies increases the ability to identify the source of the anomaly and employing two proxies within the identical research setting ensures that my results are not affected by differences in sample periods or com- position. With a dataset spanning 1978 to 2007, I find a reliable negative association between O- Score and returns, but fail to find any association between BSM-Prob and returns. These results   4  One exception is Campbell, Hilscher, and Szilagyi (2008), where they find that stocks with high bank- ruptcy risk have delivered low returns since 1981. Their (own) measure of bankruptcy risk utilizes ac- counting information as well as market information and lies outside the scope of this study.  11 suggest that the bankruptcy risk anomaly is construct-dependent: some measures of bankruptcy risk predict future returns while others do not. The question arises: what is the source of O- Score’s predictive ability? I tackle this question by examining the individual components of O- Score. In regressions of returns on the individual components of O-Score, I find that out of the nine accounting variables, funds from operations divided by total liabilities (FFO/TL) is the only component that predicts returns. In a complementary analysis, I show that the zero-investment trading strategy long on firms with the highest decile rank of FFO/TL and short on firms with the lowest decile rank produces economically and statistically positive net returns over the period of 1978−2007. Further investigation reveals that the association between O-Score and subsequent returns disappears once FFO/TL is controlled for. This implies that the return-predictive power of O-Score is driven by the association of returns with FFO/TL, the component that is intended to capture the degree to which the internally generated working capital of a firm is available to satisfy its debt obligations. Given this result, the question becomes: why does FFO/TL predict returns? Prompted by a close relationship between funds from operations and cash flows from op- erations, I conjecture that FFO/TL mimics cash flows from operations deflated by average total assets (CFO/ATA). Since Sloan (1996) and Houge and Loughran (2000) find CFO/ATA to be associated with subsequent returns, I conjecture that the ability of FFO/TL to predict returns is  12 not distinct from the ability of CFO/ATA to predict returns. The zero-investment trading strategy long on firms with the highest decile rank of CFO/ATA and short on firms with the lowest decile rank generates returns of a similar or higher magnitude, in comparison to that using FFO/TL. A close comparison of annual net returns from the two trading strategies reveals that (1) signs of net returns from the two strategies agree in most of my sample years, and that (2) when the strat- egy using CFO/ATA fails to provide positive net returns, the strategy using FFO/TL also fails to produce positive net returns, with few exceptions. Furthermore, the regression analysis demon- strates that once CFO/ATA is controlled for, the association of returns with FFO/TL diminishes, suggesting that the return-predictive power of FFO/TL is related to the association of returns with CFO/ATA. Lastly, this finding is confirmed in the analysis using a two-way sort using quintiles that are independently formed according to the rankings of FFO/TL and CFO/ATA. Closing the investigation, I predict and find that O-Score is no longer associated with subsequent returns once CFO/ATA is controlled for. The most striking evidence is unveiled in the analysis using quintiles that are independently formed using O-Score and CFO/ATA. Not all firms with high O-Score earn lower than average returns; among firms in the highest quintile of O-Score, only the firms that belong to the lowest quintile of CFO/ATA deliver low returns. Taken as a whole, my results suggest that the negative association between Ohlson’s (1980) measure of bankruptcy risk and subsequent returns is a manifestation of Sloan’s (1996)  13 accrual anomaly.5 Thus, it appears that Dichev’s (1998) anomaly is due to investors not fully impounding the implication in the accruals and cash flows components of earnings, rather than their failure to incorporate available bankruptcy information. FFO/TL happens to serve as a bridge between the two seemingly unrelated stock market anomalies. This study contributes to the existing research in several ways. First, it provides an alter- native explanation for Dichev’s (1998) findings. In this sense, this study is complementary to the explanations provided by Griffin and Lemmon (2002), which suggest that the bankruptcy anom- aly documented by Dichev is likely to occur as a result of a high degrees of information asym- metry among firms with low book-to-market ratios, and George and Hwang (2010), which suggests that the negative relationship between returns and leverage is responsible for the Di- chev’s results. Second, this study highlights that the choice of bankruptcy risk measure can lead to different conclusions. Third, by relating the bankruptcy risk anomaly to the accrual anomaly, this study contributes to a stream of research that investigates the relationship between anomalies (e.g., Collins and Hribar, 2000; Desai, Rajgopal, and Venkatachalam, 2004).   5  The results in Houge and Loughran (2000) and Pincus, Rajgopal, and Venkatachalam (2007) suggest that there may be an accrual anomaly and a cash flow anomaly and that they do not always occur together, i.e., there is no mechanical relationship going on such that if one is present, the other must also be present. Section 2.4.4 investigates whether the negative association between O-Score and returns would disappear if Sloan’s original accrual measure is employed.  14 2.2 Empirical analysis I: How robust is the bankruptcy risk anomaly when using an alter- native measure of bankruptcy risk? This section investigates the robustness of the bankruptcy risk anomaly using O-Score and BSM- Prob, where the former exclusively uses information from financial statements and the latter extracts the bankruptcy-related information from market prices as well as financial statement data. Employing the two measures in an identical setting ensures that my results are not affected by differences in sample periods or composition. I use BSM-Prob as an alternative proxy be- cause using two distinct proxies increases the ability to identify the source of the anomaly. In addition, Hillegeist et al. (2004) empirically show that their measure is superior to those from Altman’s (1968) and Ohlson’s (1980) models in terms of bankruptcy prediction. Specifically, Hillegeist et al. employ relative information content tests on out-of-sample predictions and dem- onstrate that BSM-Prob contains significantly more information about the probability of bank- ruptcy than any of accounting-based measures: the original Z-Score and O-Score and “updated” Z-Score and O-Score (scores computed using updated coefficient estimates). If there is a bank- ruptcy risk anomaly, then a better measure of bankruptcy risk should be able to better predict returns. The description of the sample and the definition of the variables are provided in Section 2.2.1, followed by empirical results in Section 2.2.2. 2.2.1 Sample formation and variable measurement The empirical tests in Section 2.2 are conducted using NYSE/AMEX/NASDAQ firms with all  15 available data in the intersection of the 2008 versions of the Center for Research in Security Prices (CRSP) monthly stock file and the merged COMPUSTAT/CRSP annual fundamental file (the successor to the industrial file). I exclude Canadian firms to avoid having to adjust account- ing numbers into a common currency.6 I further restrict the sample to industrial firms because Ohlson’s (1980) models are intended for industrials. Thus, this study only includes firms with CRSP Standard Industrial Classification (SIC) codes 1 to 3999 and 5000 to 5999. I also limit the sample to firms with ordinary shares (CRSP share codes of 10 and 11); i.e., I exclude ADRs, REITs, and units of beneficial interest from my analysis. I restrict the sample to post-1976 years because Ohlson derives his models using accounting data from 1970 to 1976. Furthermore, my research design requires accounting data for year t−1 and as a result, the sample period begins in 1978. The sample period ends in 2007 because I require returns data for year t+1. After restricting firm-years to those with sufficient data to compute the variables de- scribed below, my final sample is 74,737 firm-years representing 8,616 firms. The analyses in this study use firms with any fiscal year-end month in order to maximize sample size. However, some researchers prefer to restrict their sample to firms with a December 31 year-end to facilitate implementation of the trading strategies (e.g., Lakonishok, Shleifer, and Vishny, 1994; Abar- banell and Bushee, 1998). Thus, I also analyze a sample of firms with a December 31 year-end.   6  Unlike the COMPUSTAT Industrial File, in which all data were displayed in U.S. dollars, the Funda- mental File displays data for Canadian companies (dual listed or not) using Canadian dollars.  16 Griffin and Lemmon (2002) find that the bankruptcy risk anomaly can be traced to firms with a small market capitalization and low book-to-market ratios.7 To address these alternatives, I ex- amine four subsamples. The small (large) subsamples include those firms with market capitaliza- tion smaller (larger) than the first quintile cutoff of NYSE size distribution at the end of June of each year t.8 The growth (value) subsamples include firms whose book-to-market is smaller (larger) than the median of NYSE book-to-market distribution computed at the end of June of each year t. I obtain NYSE size break-points and book-to-market break-points from Professor Kenneth French’s data library.9 Consistent with Dichev (1998), Griffin and Lemmon (2002), and George and Hwang   7  More precisely, Griffin and Lemmon find that the negative association between Ohlson’s (1980) meas- ure of bankruptcy risk and subsequent returns is primarily from growth firms, suggesting that the bank- ruptcy risk anomaly is likely to occur as a result of a high degree of information asymmetry among growth firms. However, I repeat my analysis using small and large firms as well as growth and value firms because growth firms tend to be small and Kothari (2001) documents that evidence of market inef- ficiency tends to be more pronounced among small firms. 8  Firms listed in AMEX or NASDAQ tend to be smaller than those in NYSE. Hence, using the median of NYSE size distribution leads me to classify less than 20 percent of firm-years to the subsample of large firms. Thus, I employ the first quintile of NYSE size distribution. In any case, the tenor of results remains unchanged when I use the median as a size cutoff. 9  The data library is available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.  17 (2010), the variable O-Score is calculated using the original coefficients from Model 1 in Ohlson (1980) as follows: O-Score =  –1.32 – 0.407*log(total assets/GNP price-level index) + 6.03*(total liabili- ties/total assets) – 1.43*(working capital/total assets) + 0.076*(current li- abilities/current assets) – 1.72*(1 if total liabilities > total assets, else 0) – 2.37*(net income/total assets) – 1.83*(funds from operations/total liabili- ties) + 0.285*(1 if net loss for the last two years, else 0) – 0.521*(net in- comet – net incomet-1)/ (|net incomet| + |net incomet-1|). The inputs to the calculation of O-Scoret are from the financial statements of fiscal years ending in calendar year t−1, which ensures that O-Score is estimated on an ex ante basis. All the inputs to the calculation of O-Score are readily available from COMPUSTAT, except funds from opera- tions, which are only available up to year 1987. In post-1987 years, I derive funds from opera- tions by subtracting non-cash working capital adjustments from cash flows from operations. Using Ohlson’s (1980) original coefficients implicitly assumes that the association be- tween the accounting variables and the probability of bankruptcy has not changed since Ohlson’s original sample period of 1970−1976. However, as noted in Hillegeist et al. (2004, p. 15), the assumption does not necessarily hold. First, the Bankruptcy Reform Act of 1978 made a substan- tial change in the legal environment, which was followed by an increase in the number of strate- gic bankruptcy filings. Second, significant intervening changes in accounting rules have also changed the original associations through differences in how the accounting variables are meas-  18 ured. Nevertheless, the (in)validity of this assumption does not pose any problem for the pur- poses of this study, as my focus is the association of returns with Ohlson’s original measure of bankruptcy risk as documented in Dichev (1998), not on how well Ohlson’s measure predicts future bankruptcies.10 The market-based measure of bankruptcy risk used in this study, BSM-Prob, is from Hil- legeist et al. (2004), which use the insights from Black and Scholes (1973) and Merton (1974) (BSM). The BSM approach views the firm’s equity as a call option on the value of the firm’s assets. The measure captures the idea that when the value of a firm’s assets is greater than the strike price (i.e., the face value of the liabilities), equity holders find it profitable to continue owning the firm. When the value of the firm’s assets is smaller than the strike price at time T, the call option is assumed to be unexercised and the equity holders turn over bankrupt firm to  the debtholders. The probability of each outcome is an important determinant of the value of the call option, and these probabilities are embedded in the BSM option-pricing model. Estimation of BSM-Prob requires five key inputs, namely common dividends, preferred dividends, total liabilities, market value of equity at the fiscal year-end, and annualized standard deviation of the daily returns. I calculate the annualized standard deviation of a firm’s returns by multiplying the daily standard deviation by the square root of 252, the average number of trading   10  Studies that examine the bankruptcy-predictive power of Ohlson’s O-Score include Begley, Ming, and Watts (1996) and Hillegeist et al. (2004).  19 days in a year. Note that as in the estimation of O-Scoret, all applicable accounting data for the estimation of BSM-Probt is derived from the financial statements of fiscal year ending in calen- dar year t−1. Details on the estimation of BSM-Prob are outlined in Appendix A. For each firm-year, I compute subsequent realized returns (Ret1yrt), which are defined as the buy-and-hold returns from July of year t to June of year t+1. This study requires a minimum six-month gap to ensure that the accounting data is available to calculate bankruptcy measures before it is used to explain the returns. Although Ohlson (1980, Table 2, p. 116) shows that the financial reports of firms that go bankrupt are often delayed, sometimes significantly, I choose a six-month lead time as in Dichev (1998), who supports this choice by noting the evidence in Alford, Jones, and Zmijewski (1994) that 98 percent of the 10-K reports are filed by the end of the fifth month after fiscal year-end. Consistent with prior research, when a firm delists, I use the delisting return in the delisting month. If a firm’s delisting is due to liquidation or a forced delist- ing by either the exchange delisting code or the Securities and Exchange Commission (SEC) (CRSP delisting codes 400 to 699) and the delisting return is missing, the delisting return is set to negative 100 percent. I also compute measures of asset pricing risk that are shown to be associated with subse- quent returns (i.e., firm beta, size, and book-to-market). Controlling for these risk measures is important to the extent that returns and bankruptcy risk are both correlated with these measures. Following Fama and French (1992), Betat is estimated with the Capital Asset Pricing Model  20 (CAPM) using monthly returns for at least 24 of 60 months preceding July of year t. Size (MEt) is defined as the log of a firm’s market equity in millions at the end of June of year t. Book-to- market (BE/MEt) is defined as book value of common equity for the fiscal year ending in calen- dar year t−1, divided by market value of equity at the end of December of year t−1. Instead of BE/ME, Fama and French and other studies commonly use log(BE/ME) and exclude firms with negative book value of equity because log(BE/ME) is not defined. However, as in Dichev (1998), I do not remove these firms from the sample because having a negative book value of equity is not a random event; rather, these firms are likely to have a high bankruptcy risk. Note that the positive/negative book value dichotomy is an explicit prediction variable in Ohlson’s (1980) model and thus, eliminating firms with negative book value is inappropriate. In any case, the results remain qualitatively unchanged in a sensitivity check eliminating firms with negative book values (1,910 out of 74,737 firm-years) and using log(BE/ME). 2.2.2 Results To better understand the relationship between Ohlson’s (1980) measure of bankruptcy risk and the other variables, I form portfolios according to the rankings of O-Scoret at the end of June of each year t and report the average values of each variable in Panel A of Table 2.1. In Panel A, I also provide the return distribution association with O-Prob. O-Prob is a monotonic transforma- tion of O-Score derived using the logistic cumulative distribution (i.e., O-Prob = eO-Score/(1 + eO- Score  * 100%), for ease of comparison with BSM-Prob in Panel B. Patterns of O-Prob and BSM-  21 Prob display extreme right skewness, which is expected given the low frequency of actual bank- ruptcy in the COMPUSTAT population.11 Note that the choice between O-Score and O-Prob does not have any impact on the results of the subsequent analyses because I use relative rank- ings of the variables in each year t in the analyses. In Panel A, firms in the extreme high or low O-Score deciles have higher Beta. Firms with higher O-Score have smaller market capitalization; this is not surprising given that smaller firms are more likely to go bankrupt. Indeed, Shumway (2001) finds that firm size is highly re- lated to bankruptcy. The pattern of BE/ME demonstrates that firms with higher O-Score tend to have higher book-to-market, with exception of firms in the highest O-Score decile, which have the smallest book-to-market, consistent with the pattern shown in Dichev (1998, Table 4, p. 1140).12 As suggested by Dichev, the reason for this pattern is that, unlike market value which is always positive, the book value of firms with the highest bankruptcy risk can be very small or negative if losses are high enough. The pattern of Ret1yr suggests that market prices do not fully   11  The average annual bankruptcy rate during 1980−2000 period was 0.97 percent among the industrial firms in the intersection of the CRSP and COMPUSTAT databases (Hillegeist et al., 2004, Table 1, p. 12). 12  A decline of book-to-market from the second highest O-Score decile portfolio to the highest decile portfolio is much milder in Dichev because he winsorizes all the variables at the 1st and 99th percentile, whereas I use the variables without any adjustment. I intentionally do not follow Dichev in this respect due to the concern raised by Kothari, Sabino, and Zach (2005), where they demonstrate that data deletion induces a spurious association between subsequent returns and ex ante information variables.  22 impound the implications of available bankruptcy information as proxied by O-Score. Although firms with higher bankruptcy risk do not necessarily have lower subsequent returns, firms in the highest O-Score decile do have the lowest subsequent returns, followed by the second highest O- Score decile having the second lowest subsequent returns. Dichev (Table 6, p. 1145) also reports a similar non-monotonic relationship between O-Score and subsequent returns. With respect to BSM-Prob, Panel B shows that firms with higher BSM-Prob have higher Beta; this is expected because BSM-Prob is an increasing function of stock price volatility, which includes both systematic and idiosyncratic components. Consistent with Panel A, firms with higher bankruptcy risk tend to have smaller market capitalization. The pattern of BE/ME is similar to that in Panel A, except that the decline of book-to-market from the second highest decile portfolio to the highest decile portfolio is much milder in Panel B. The pattern of Ret1yr in Panel B displays a striking difference in comparison to that in Panel A. Firms in the highest BSM-Prob decile do not have the lowest subsequent returns. Rather, the lowest two BSM-Prob deciles have the two lowest average subsequent returns. Moreover, firms in the second highest BSM-Prob decile have the highest subsequent returns. Combined, the results in Table 2.1 con- firm Dichev’s (1998) findings that O-Score is positively related to future returns. However, the results using BSM-Prob challenge his conclusion that market prices do not fully impound the implications of available bankruptcy information. An interesting finding in Panel A of Table 2.1 is that the pattern of Ret1yr goes against  23 the size effect, i.e., prior studies find that firms with a smaller market capitalization tend to have higher returns. Hence, I expect that the relationship between O-Score and Ret1yr will be more evident once firm size is controlled for. Another interesting finding is that the pattern of Ret1yr closely resembles that of BE/ME, which casts doubt on the existence of (any) relationship be- tween O-Score and Ret1yr. In other words, it is not clear whether the pattern of subsequent re- turns reported in Panel A is evidence of the negative association of returns with Ohlson’s (1980) bankruptcy risk measure or a manifestation of the book-to-market effect. Thus, controlling for the book-to-market effect as well as the size effect seems indispensable for the investigation of an association between Ohlson’s bankruptcy risk measure and subsequent returns. Table 2.2 presents the results of Fama-MacBeth regressions of subsequent returns on each measure of bankruptcy risk along with Beta, ME, and BE/ME. For each year from 1978 to 2007, I rank the independent variables into deciles and then convert them to scaled decile ranks from −0.5 to 0.5 by the following transformation: subtract 1, divide by 9 and subtract 0.5. After the conversion, the dependent variable is regressed on the scaled decile ranks of the independent variables. The mean of the coefficient estimates over the 30 sample years is reported along with the t-statistic, which is the mean of the coefficient estimates divided by the time-series standard error of the coefficient estimates. The use of decile ranks controls for outliers and non-linearity and facilitates interpretation of the economic magnitudes of the independent variables in relation to the dependent variable. An additional advantage of using decile ranks is that the coefficient on  24 the independent variable represents the net return from a zero investment strategy of going long on the highest decile of the independent variable under consideration and short on the lowest decile while controlling for other variables. The scheme of scaled decile ranks has been com- monly used in other studies that examine market inefficiency, especially studies that examine post-earnings-announcement drift (e.g., Mendenhall, 2004; Narayanamoorthy, 2006). In Panel A of Table 2.2, the mean coefficient on the decile ranks of O-Score for the full sample is −6.06, with a t-statistic of −3.36. This suggests that one can obtain on average a 6.06 percent return (before transaction costs) by buying firms in the lowest decile of O-Score and shorting firms in the highest decile over the period from 1978 to 2007, after controlling for Beta, ME, and BE/ME. Using only firms with a December 31 year-end, I find that the mean coefficient on the decile ranks of O-Score is similar to that for the full sample and the return-predictive power of O-Score is not subsumed by the size and the book-to-market effects. The regression analyses using subsamples confirm Griffin and Lemmon’s (2002) findings that the negative relationship between Ohlson’s (1980) bankruptcy risk measure and subsequent returns is primarily from firms with a small market capitalization and low book-to-market ratios (growth firms). The mean coefficients on the decile ranks of O-Score for the subsamples of small and growth firms are negative and significantly different from zero, whereas those for the sub- samples of large and value firms are not reliably different from zero. In both Panels A and B of Table 2.2 (as well as throughout this study), the positive and  25 significant intercepts represent the average annual raw returns from investing in firms with me- dian values of each variable over the sample period. The mean coefficients on Beta are insignifi- cant, which is expected given that the CAPM has failed to describe average realized stock returns since the early 1960s (Campbell and Vuolteenaho, 2004). Interestingly, the mean coefficients on ME are also insignificant, but this is consistent with other studies that also document that the size effect is weak to nonexistent in the 1980s and 1990s (e.g., Fama and French, 1992). The mean coefficients on BE/ME are economically and statistically different from zero, except the one for the subsample of value firms, which is likely due to the relatively small cross-sectional variations in BE/ME in the subsample of value firms. In Panel B of Table 2.2, none of the mean coefficients on the decile ranks of BSM-Prob are significantly different from zero. Recall that BSM-Prob has been shown to provide a better prediction of bankruptcy than O-Score. If market prices do not fully incorporate the implications of bankruptcy information, why is it the case that BSM-Prob is unrelated to subsequent returns?13 Moreover, Griffin and Lemmon’s (2002) explanation of Dichev’s (1998) findings does not seem to apply when BSM-Prob is the proxy of bankruptcy risk: the mean coefficients on the decile ranks of BSM-Prob for the subsamples of small and growth firms are not reliably different from   13  Note that BSM-Prob is a measure based on market prices. If the market is not adequately anticipating bankruptcy probabilities, then it is possible for BSM-Prob not to show the bankruptcy anomaly even if the anomaly exists. I can not confirm or refute this possibility.  26 zero. Taken as a whole, Table 2.2 suggests that Dichev’s conclusion is potentially idiosyncratic to Ohlson’s (1980) measure of bankruptcy risk. This raises the question: why is O-Score nega- tively associated with subsequent returns? This is the question I explore in the next section. 2.3 Empirical analysis II: What is inside the magic of O-Score? The measure of bankruptcy risk proposed by Ohlson (1980) is a score − a linear combination of accounting variables. As demonstrated in Appendix B, when there is an association between a variable and a score, it must be true that one or more components of the score have nontrivial associations with the variable, holding all other components constant. Thus, the association be- tween returns and Ohlson’s measure of bankruptcy risk ensures that one or more components of O-Score are associated with subsequent returns. 2.3.1 Results To examine which components of O-Score are responsible for the association of returns with the score, I run Fama-MacBeth regressions of subsequent returns on the components of O-Score and report the results in Table 2.3. This table is similar to Panel A of Table 2.2, except that I use the components of O-Score rather than O-Score itself. The regression results in Table 2.3 reveal that FFO/TL is the only component that is con- sistently associated with subsequent returns. Other components are also associated with subse- quent returns but the associations are only observed for a single subset of firms. By contrast, the  27 association of returns with FFO/TL is economically and statistically different from zero in each and every case. For example, the mean coefficient on the decile ranks of FFO/TL for the full sample is 6.87, with a t-statistic of 3.21. This suggests that one can obtain on average a 6.87 percent return (before transaction costs) by buying firms in the highest decile of FFO/TL and shorting firms in the lowest decile over the period from 1978 to 2007, after controlling for the other components of O-Score, Beta, ME, and BE/ME. Note that the mean coefficients on the decile ranks of O-Score for the subsamples of large and value firms are not reliably different from zero in Panel A of Table 2.2, whereas the corresponding mean coefficients on the decile ranks of FFO/TL in Table 2.3 are significantly different from zero. While an association of a variable with a score implies an association of the variable with at least one component of the score, the reverse does not follow. To corroborate the results in Table 2.3, I assess the profitability of a trading strategy us- ing FFO/TL. At the end of June of each year from 1978 to 2007, I construct a zero-investment trading strategy based on buying an equal-weighted (value-weighted) portfolio of firms with the highest decile ranks of FFO/TL and shorting an equal-weighted (value-weighted) portfolio of firms with the lowest decile ranks and report the annual returns in Panel A (Panel B) of Table  28 2.4.14 Consistent with Table 2.3, firms with high FFO/TL earn higher returns than firms with low FFO/TL.15 The equal-weighted as well as value-weighted trading strategy generates economi- cally sizable profits over my sample period. The mean and median annual return on the equal- weighted (value-weighted) trading strategy is 7.53 and 12.47 percent (13.03 and 15.25 percent), respectively. In addition, the profitability of the strategy is consistent; firms with high FFO/TL outperform firms with low FFO/TL in 21 (22) out of 30 years in Panel A (Panel B). The results presented so far suggest that the FFO/TL component of O-Score is associated with returns. Next, I examine whether the return-predictive power of O-Score disappears once FFO/TL is controlled for. Table 2.5 presents the results of Fama-MacBeth regressions of Ret1yr on both O-Score and FFO/TL (along with Beta, ME, and BE/ME). The mean coefficients on the decile ranks of O-Score are no longer negative. Thus, the results in Table 2.5, in conjunction with those in Panel A of Table 2.2, suggest that the association of returns with O-Score is driven by the association of returns with its component, FFO/TL. Note that the mean coefficients on the decile ranks of FFO/TL in Table 2.5 are larger than those in Table 2.3 but they are statistically   14  I include value-weighted portfolio analysis because Fama (1998) finds that when value-weighted re- turns are examined, evidence of stock market inefficiency shrinks substantially and typically becomes statistically unreliable. 15  The trading strategy in Table 2.4 (as well as in Table 2.8) earned large negative net returns in 1999. This period is believed to be a time in which mispricing was prevalent (see Ritter and Welch, 2002; La- mont and Thaler, 2003).  29 less significant, which is expected given the variance inflation resulting from the high correlation between O-Score and FFO/TL.16 2.4 Empirical analysis III: What is the source of the predictive power of FFO/TL? Results presented to this point show that the return-predictive power of O-Score found in Dichev (1998) is due to the association of returns with its component, FFO/TL. Prompted by a close relationship between funds from operations (FFO) and cash flows from operations (CFO), I con- jecture that the rankings of funds from operations mimic those of cash flows from operations. The relation between funds from operations and cash flows from operations, along with the ac- crual anomaly, is discussed in Section 2.4.1. The description of the sample and the definition of the variables are provided in Section 2.4.2, followed by empirical results in Section 2.4.3 and the results of sensitivity tests are reported in Section 2.4.4. 2.4.1 Funds from operations, cash flows from operations, and accrual anomaly FFO was one of the disclosure requirements in the statement of changes in financial position (SCFP) before the statement of cash flows became mandatory.17 Most firms prepared SCFP on a   16  The Pearson (Spearman) correlation coefficient is −0.74 (−0.85). 17  In 1963, the Accounting Principle Board (APB) issued APB Opinion No. 3, The Statement of Source and Application of Funds (AICPA, 1963). This standard encouraged firms to present a funds statement, a predecessor of SCFP, as an integral part of a company’s financial statements.  30 working capital basis, meaning that FFO represented working capital generated from operations. In this case FFO is essentially CFO before the adjustments of non-cash working capital in the indirect method of presenting the statement of cash flows. Some firms reported SCFP on a cash basis. In this case FFO is the same as CFO. Ohlson’s (1980) models of bankruptcy prediction use FFO divided by total liabilities. The idea is to capture the degree to which the internally generated working capital of a firm is available to satisfy its debt obligations. As firms with large liabilities tend to have large recorded assets, the cross-sectional rankings of FFO/TL are likely to follow those of CFO/ATA, which has been found to be associated with subsequent returns in Sloan (1996) and Houge and Loughran (2000). Sloan (1996) finds that firms with higher accruals tend to have lower subsequent returns, i.e., accruals have a negative association with subsequent returns. Sloan conjectures that inves- tors fixate on current earnings and fail to fully price the different information contained in the accruals and cash flows components of earnings. In regard to testing his hypotheses, Sloan does not use the magnitude of accruals for his tests. Rather, he uses relative accruals, i.e., accruals deflated by average total assets to control for size. While the trading strategy in Sloan is based on accruals, he also documents in his footnote 15 (p. 306) that the negative association between accruals and cash flows ensures that the trading strategy using CFO/ATA produces positive returns of a similar magnitude; this is expected as earnings are the sum of accruals and cash  31 flows. Indeed, a subsequent study by Houge and Loughran (2000) shows that CFO/ATA has a positive association with subsequent returns with a dataset spanning 1963 to 1993, confirming Sloan’s findings that investors overestimate the persistence of accruals relative to that of cash flows. 2.4.2 Sample formation and variable measurement I follow Sloan (1996) and Houge and Loughran (2000) with regard to variable definitions. I define the variable CFO/ATA as cash flows from operations divided by average total assets. Cash flows from operations are operating income after depreciation minus accruals.18 Accruals are defined as the change in non-cash current assets minus the change in current liabilities, excluding the current portion of long-term debt and taxes payable, minus depreciation expense, i.e., (∆CA − ∆Cash) − (∆CL − ∆STD − ∆TP) − Depreciation. I use the financial statements of fiscal years ending in calendar year t−1 to calculate CFO/ATAt so that the variable is estimated on an ex ante basis. The empirical analysis in this section begins with the sample used in the previous sections. After restricting firm-years to those with sufficient data to compute the variables described above, my final sample is 74,364 firm-years representing 8,594 firms.   18  Note that cash flows from operations could be derived from reported funds from operations for obser- vations on pre-SFAS No. 95 regime, but it is standard practice to adopt Sloan’s definitions of accruals (and cash flows from operations, if applicable) among studies that examine the accrual anomaly.  32 2.4.3 Results To demonstrate the relationship between FFO/TL and CFO/ATA, I form portfolios according to the rankings of FFO/TL at the end of June of each year from 1978 to 2007. The average values of the two variables along with other variables are reported in Table 2.6. As can be seen, the pattern of Ret1yr confirms that FFO/TL has return-predictive power. Although the pattern is not monotonic, firms in the two lowest FFO/TL deciles have the lowest subsequent returns. The close relationship between FFO/TL and CFO/ATA is demonstrated in the pattern of CFO/ATA. The monotonically increasing pattern of CFO/ATA demonstrates that the rankings of FFO/TL indeed mimic those of CFO/ATA. BE/ME does not display any meaningful pattern, which in turn suggests that the association of returns with FFO/TL is not driven by the book-to-market effect. Table 2.7 presents the results of Fama-MacBeth regressions of Ret1yr on CFO/ATA (along with Beta, ME, and BE/ME). The mean coefficient on the decile ranks of CFO/ATA for the full sample is 11.04, with a t-statistic of 4.27. This suggests that one can obtain on average an 11.04 percent return (before transaction costs) by buying firms in the highest decile of CFO/ATA and shorting firms in the lowest decile over the period from 1978 to 2007, after controlling for Beta, ME, and BE/ME. Just as FFO/TL is found to be positively associated with returns within each subset of firms in Table 2.3, there is a positive association between CFO/ATA and returns in Table 2.7, with the mean coefficient on the decile ranks of CFO/ATA ranging from 7.10 to 11.39. In summary, Table 2.7 demonstrates the positive association of returns with CFO/ATA.  33 To corroborate the results in Table 2.7, I assess the profitability of a trading strategy us- ing CFO/ATA. At the end of June of each year from 1978 to 2007, I construct a zero-investment trading strategy based on buying an equal-weighted (value-weighted) portfolio of firms with the highest decile ranks of CFO/ATA and shorting an equal-weighted (value-weighted) portfolio of firms with the lowest decile ranks and report annual return in Panel A (Panel B) of Table 2.8. The returns to trading strategies reported in Table 8 is comparable to those based on FFO/TL in Table 2.4. The mean and median annual return on the equal-weighted (value-weighted) trading strategy is 10.99 and 14.97 percent (12.17 and 21.16 percent), respectively. As in Table 4, the profitability of the strategy is consistent; firms with high CFO/ATA outperform firms with low CFO/ATA in 24 (20) out of 30 years in Panel A (Panel B) of Table 2.8. To enhance the comparability between Tables 2.4 and 2.8, annual net returns from the ze- ro-investment trading strategy using FFO/TL and CFO/ATA are plotted side by side in Figure 2.1. The figure reveals strong similarities between the results from the two different strategies. The signs of net returns from the two strategies agree in 27 (26) out of 30 years in Panel A using equal-weighted portfolios (Panel B using value-weighted portfolios). Moreover, when the strat- egy using CFO/ATA fails to produce positive net returns, the strategy using FFO/TL also fails to produce positive net returns, with few exceptions. The results presented so far suggest that the association of returns with FFO/TL is related to the association of returns with CFO/ATA. Next, I examine whether the return-predictive power of FFO/TL disappears once CFO/ATA is controlled  34 for. Table 2.9 presents the results of Fama-MacBeth regressions of Ret1yr on FFO/TL before and after controlling for CFO/ATA in Panels A and B, respectively. Panel A shows that FFO/TL predicts subsequent returns, but Panel B demonstrates that the association of returns with FFO/TL diminishes once CFO/ATA is controlled for. While the mean coefficients on the decile ranks of FFO/TL are still statistically different from zero in Panel B, their economic significance is reduced by roughly half when compared to Panel A. For example, the mean coefficient on the decile ranks of FFO/TL for the full sample is 8.07 with a t-statistic of 4.38 in Panel A, whereas the corresponding mean coefficient in Panel B is 3.51 with a t-statistic of 2.25. Note that the variable CFO is derived from the accounting information in the balance sheet and the income statement, whereas the variable FFO is derived from the statement of changes in financial posi- tion (the statement of cash flows) before (after) SFAS No. 95 becomes effective. When I limit my analysis to post-SFAS No. 95 observations and derive both variables from the statement of cash flows, the decile ranks of FFO/TL are no longer associated with returns (see Section 2.4.4). In Section 2.3, I showed that the association of returns with O-Score is due to the associa- tion of returns with FFO/TL. Hence, if the association of returns with FFO/TL is driven by the association of returns with CFO/ATA, I expect the return-predictive power of O-Score to dimin- ish or disappear once CFO/ATA is controlled for. Table 2.10 shows that once CFO/ATA is con- trolled for, the mean coefficients on the decile ranks of O-Score are no longer statistically and  35 economically different from zero, except for the subsample of small firms. Throughout Tables 2.9 and 2.10, the mean coefficients on the decile ranks of CFO/ATA are economically and statis- tically different from zero, suggesting that the return-predictive power of CFO/ATA is not sub- sumed by either FFO/TL or O-Score. Thus, the results presented so far support my prediction that the association of returns with FFO/TL (and with O-Score) is largely due to the association of returns with CFO/ATA. To corroborate the regression analysis, I conduct a two-way sort according to an observa- tion’s quintile ranking of FFO/TL (O-Score) and CFO/ATA at the end of June of each year from 1978 to 2007. Each Panel in Table 2.11 reports average annual returns for each of 25 portfolios. It also reports the average number of firms over the sample years for each portfolio in bracket and the average of the difference in Ret1yr between the extreme quintiles, followed by a time- series t-statistic in parenthesis. Note that with regard to O-Score, I report Ret1yr of the lowest quintile minus that of the highest quintile because firms with lower O-Score are found to have higher subsequent returns. The concentration of firms in the main diagonal cells in Panel A is expected given the positive correlation between FFO/TL and CFO/ATA. As shown in the bottom two rows of Panel A, within each CFO/ATA quintile column, firms with higher FFO/TL do not necessarily have higher subsequent returns. However, as shown in the last column, for four out of five FFO/TL quintile rows, firms with higher CFO/ATA earn higher subsequent returns. These results in Panel  36 A support the findings in Table 2.9 that the association of returns with FFO/TL is due to the association of returns with CFO/ATA. In Panel B, the concentration of firms in the minor diagonal cells demonstrates a negative correlation between O-Score and CFO/ATA. The pattern in each column, with the exception of the first, suggests that firms with higher O-Score do not earn lower subsequent returns, once CFO/ATA is controlled for. Recall that the negative association of returns with O-Score is pri- marily driven by the poor performance of firms with high O-Score (see Panel A of Table 2.1). An examination of firms in the highest O-Score quintile row unveils striking evidence that only the quintile of firms with low CFO/ATA earns lower than average returns (4.63 percent). Taken as a whole, the evidence reported in Panel B confirms the findings that the negative association of returns with Ohlson’s (1980) measure of bankruptcy risk is a manifestation of Sloan’s (1996) accrual anomaly. 2.4.4 Sensitivity tests The measure of cash flows utilized to this point is the difference between operating income after depreciation minus accruals derived from the balance sheet and income statement. This method of estimating the cash flow involves measurement error relative to measuring accruals directly from the statement of cash flows, as noted in Hribar and Collins (2002). Thus, as a sensitivity test, I limit the analysis to firm-years in the post-SFAS No. 95 regime and then repeat the analy- sis using a cash flow measure from the statement of cash flows.  37 Specifically, I use cash flows from continuing operations, which are cash flows from op- erations minus the cash portion of discontinued operations and extraordinary items, as suggested by Hribar and Collins (2002). Note that in the main analysis, the variable CFO is derived from the accounting information in the balance sheet and the income statement, whereas the variable FFO is derived from the statement of changes in financial position (the statement of cash flows) before (after) SFAS No. 95 became effective. Thus, the analysis in this section effectively elimi- nates any possible inconsistency in the calculation of FFO and CFO as both variables are de- rived from the statement of cash flows. Furthermore, using observations in the post-SFAS No. 95 regime ensures cross-sectional comparability in the calculation of FFO because I no longer re- sort to reported funds from operations. However, these benefits come at the cost of reduction in power in a statistical test because the sample includes only observations in the post-SFAS No. 95 regime. Table 2.12 presents the replication of Tables 2.7, 2.9, and 2.10 using only the post-SFAS No. 95 observations. The sample consists of 47,948 firm-years (6,309 firms), spanning 19 years from 1989 to 2007. For brevity, I only report the results of the variables of interest. Throughout Table 2.12, the mean coefficients on the decile ranks of CFO/ATA are more or less of a similar magnitude to the corresponding mean coefficients in the matching tables. However, they become less significant because the analysis only employs 19 time-series. Consistent with Table 2.7, Panel A demonstrates a positive association between subsequent returns and CFO/ATA. In Table  38 2.9, the coefficients on FFO/TL become smaller but still statistically significantly different from zero when CFO/ATA is controlled for. By contrast, Panel B of Table 2.12 shows that FFO/TL is no longer associated with subsequent returns once CFO/ATA is controlled. This is so because the analysis in Panel B effectively eliminates inconsistency in the calculation of FFO and CFO (i.e., both variables are derived from the statement of cash flows). Panel C confirms that a negative association of returns with O-Score disappears once CFO/ATA is controlled for. The results provided so far support that Dichev’s (1998) bankruptcy risk anomaly is es- sentially Sloan’s (1996) accrual anomaly in disguise and yet rely on cash flows to proxy the accrual anomaly in lieu of the conventional accrual measure. As noted in Sloan, the two compo- nents of earnings are highly correlated, but their correlation is unlikely to be perfect. Thus, the natural question that follows is whether the negative association between O-Score and returns would disappear when I employ Sloan’s original accrual measure.19 Panel A of Table 2.13 presents the results of Fama-MacBeth regressions of Ret1yr on O- Score and ACC/ATA along with Beta, ME, and BE/ME, where ACC/ATA represents Sloan’s (1996) original accrual measure. To be consistent with the main analysis, I convert independent variables into scaled decile ranks. As in Table 2.12, Table 2.13 only reports the results of the variables of interest. The most striking observation from Panel A is that, contrary to the results in   19  I want to express my gratitude to an anonymous referee for raising this question.  39 the main analysis, the negative association of O-Score with returns does not disappear. Thus, the evidence provided in Panel A seems to contradict the evidence provided in the main analysis. However, that is not necessarily the case. When two highly correlated independent variables are regressed, their explanatory power and the significance of their coefficients are divided up be- tween the two. Since the ability of O-Score to predict returns is not distinct from the ability of CFO/ATA to predict returns, O-Score will “dominate” ACC/ATA to the extent that CFO/ATA better explains the variation in returns than ACC/ATA. Moreover, this scenario provides good explanation for the marginal association between ACC/ATA and returns. To investigate which proxy of Sloan’s (1996) accrual anomaly better predicts returns, I run Fama-MacBeth regressions of Ret1yr on both ACC/ATA and CFO/ATA along with Beta, ME, and BE/ME and present the results in Panel B of Table 2.13. Once cash flows are controlled for, Sloan’s original accrual measure is no longer associated with returns, which, in turn, explains the results in Panel A. Panel C reports the association of O-Score after controlling for ACC/ATA and CFO/ATA. As expected, CFO/ATA is the only variable that is associated with future returns. 2.5 Conclusion Using Ohlson’s (1980) measure of bankruptcy risk, Dichev (1998) documents that firms with high bankruptcy risk earn lower than average returns in subsequent years. This anomaly suggests that market prices do not fully impound the implications of available bankruptcy information. This study challenges that conclusion.  40 The first empirical analysis in this study investigates the robustness of the bankruptcy risk anomaly using O-Score and BSM-Prob within identical research settings. With a dataset spanning 1978 to 2007, I find a reliable negative association between O-Score and returns, but fail to find any association between BSM-Prob and returns, suggesting that the negative associa- tion between bankruptcy risk and returns is construct-dependent. I then examine the individual components of O-Score and find that the funds from operations component (FFO/TL) is the only one that is associated with future returns. I show that the association of returns with this compo- nent is responsible for the association of O-Score and returns. In light of these results, the final empirical analysis investigates the source of the return-predictive power of FFO/TL. FFO/TL and CFO/ATA are closely related and thus, I conjecture and find that the cross-sectional rank- ings of FFO/TL follow those of CFO/ATA, an alternative implementation vehicle of Sloan’s (1996) accrual anomaly. Taken as a whole, the results of this study suggest that the negative association between Ohlson’s (1980) measure of bankruptcy risk and subsequent returns is a manifestation of investors’ under (over)-pricing of cash flows (accruals) component of earnings, i.e., Sloan’s accrual anomaly. This study is the first attempt to relate the bankruptcy risk anomaly to the accrual anom- aly. It clearly demonstrates that the two seemingly unrelated stock market anomalies share the same underlying cause. Given the substantial number of anomalies in the literature, it is possible, and even likely, that there are more such commonalities among other anomalies. Therefore, re-  41 searchers should carefully consider alternative explanations, including existing anomalies, before claiming the discovery of a new anomaly.   42 Table 2.1: Characteristics of O-Score [BSM-Prob] decile portfolios Panel A: Characteristics of O-Score decile portfolios   Portfolio O-Score ranking  lowest 2 3 4 5 6 7 8 9 highest  O-Score −8.63  −6.56  −5.76  −5.16  −4.63  −4.09  −3.52  −2.78  −1.66  2.67  O-Prob 0.04  0.15  0.33  0.60  1.02  1.75  3.14  6.55  18.46  67.11  Beta 1.24  1.14  1.11  1.11  1.09  1.08  1.10  1.13  1.17  1.34  ME 5.43  5.56  5.55  5.33  5.01  4.63  4.21  3.72  3.14  2.82  BE/ME 0.57  0.70  0.75  0.81  0.87  0.93  0.99  1.02  0.92  0.04  Ret1yr 14.49  16.23  16.58  16.97  16.62  16.32  17.31  17.81  12.02  6.16  Panel B: Characteristics of BSM-Prob decile portfolios   Portfolio BSM-Prob ranking  lowest 2 3 4 5 6 7 8 9 highest  BSM-Prob 0.00  0.00  0.00  0.00  0.02  0.13  0.52  1.87  6.27  28.31  Beta 0.90  1.05  1.10  1.15  1.16  1.21  1.22  1.23  1.26  1.26  ME 6.05  5.83  5.50  5.19  4.81  4.50  4.12  3.70  3.17  2.46  BE/ME 0.41  0.55  0.62  0.66  0.72  0.79  0.89  0.98  1.08  0.90  Ret1yr 13.11  13.00  14.64  14.53  14.83  15.44  16.06  16.99  18.32  13.44  Note to Table 2.1: Panel A (Panel B) of this table presents mean values of characteristics for ten portfolios formed annually at the end of June of year t from 1978 to 2007 by assigning firms to deciles based on the magnitude of O- Scoret (BSM-Probt). The sample consists of 74,737 firm-years representing 8,616 firms. O-Score is a measure of bankruptcy risk from Model 1 in Ohlson (1980) and higher values of O-Score signify higher probability of bankruptcy. O-Prob is a probability form of O-Score derived using the logistic cumulative distribution function. BSM-Prob is a probability of bankruptcy that is from Hillegeist et al. (2004). Betat is estimated using the Capital Asset Pricing Model (CAPM) for each firm using monthly returns for at least 24 of the 60 months preceding July of year t. MEt is log of a firm’s market equity in millions at the end of June of year t. BE/MEt is book common equity for the fiscal year ending in calendar year t−1, divided by market equity at the end of December t−1. Ret1yrt is the buy-and-hold returns (in percent) over one-year period beginning July of year t.  43 Table 2.2: Association of returns with O-Score [BSM-Prob] Dependent variable = Ret1yr  All Firms (N= 74,737) December Firms (N= 38,859) Small Firms (N=49,915) Large Firms (N=24,822) Growth Firms (N=43,866) Value Firms (N=30,871)  Panel A: Association of returns with O-Score  Intercept 15.05***  14.94***  15.54***  14.36***  12.01***  19.33***  (3.55) (3.74) (3.19) (4.33) (2.86) (4.30)  O-ScoreD −6.06***  −5.79**  −7.86***  −2.20  −5.76***  −3.01  (−3.36) (−2.53) (−3.83) (−0.96) (−2.79) (−1.30)  BetaD −1.64  −1.40  0.01  −4.51  −2.86  0.28  (−0.34) (−0.30) (0.00) (−0.94) (−0.58) (0.06)  MED −2.43  −1.83  −3.64  1.53  0.40  −6.40  (−0.53) (−0.40) (−1.04) (0.66) (0.09) (−1.42)  BE/MED 13.12***  13.73***  14.45***  5.91**  11.56***  1.71  (3.94) (3.92) (4.12) (2.05) (4.67) (0.63)  Avg. Adj. R2 (%) 4.04 4.52 3.28 6.30 4.73 2.13  Panel B: Association of returns with BSM-Prob  Intercept 15.06***  14.94***  15.54***  14.36***  12.00***  19.33***  (3.55) (3.74) (3.19) (4.34) (2.86) (4.30)  BSM-ProbD 0.78  1.90  0.18  0.41  −0.27  2.86  (0.34) (0.69) (0.07) (0.22) (−0.13) (0.95)  BetaD −2.04  −2.23  −0.60  −4.25  −2.68  −0.44  (−0.46) (−0.51) (−0.13) (−0.91) (−0.55) (−0.11)  MED 1.31  2.52  −0.32  1.92  3.31  −3.73  (0.31) (0.57) (−0.09) (0.83) (0.75) (−0.85)  BE/MED 14.25***  14.40***  16.41***  6.09*  13.08***  1.02  (4.29) (3.94) (4.60) (2.01) (5.34) (0.36)  Avg. Adj. R2 (%) 4.07 4.57 3.21 6.15 4.71 2.27  Note to Table 2.2 This table presents the results of Fama-MacBeth regressions using 74,737 firm-years (8,616 firms), span- ning 30 years from 1978 to 2007. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables each year. The regression coefficient reported here is the mean of the coefficient estimates over 30 sample years and t-statistic reported in parenthesis is the mean of the coefficient estimates divided by time-series standard error of the coefficient estimates. Variable definitions are in Table 2.1. Superscript D (D) denotes decile ranks. December Firms are firms with a  44 December 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (lar- ger) than the first quintile of NYSE size distribution. Growth (Value) Firms include firms whose book-to- market is smaller (larger) than the median of NYSE book-to-market distribution. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  45 Table 2.3: Association of returns with the components of O-Score Dependent variable = Ret1yr  All Firms (N=74,737) December Firms (N=38,859) Small Firms (N=49,915) Large Firms (N=24,822) Growth Firms (N=43,866) Value Firms (N=30,871)  Intercept 15.15***  15.06***  15.61***  14.26***  12.27***  19.37***  (3.67) (3.88) (3.27) (4.33) (2.94) (4.46)  Components of O-Score  SizeD −1.89  −5.01  −4.02  −5.87  −1.07  −23.29***  (−0.37) (−0.86) (−1.03) (−0.98) (−0.17) (−3.09)  TL/TAD 1.75  2.63  1.44  5.45*  3.64  3.85  (0.47) (0.72) (0.33) (1.86) (0.88) (0.92)  WC/TAD 5.78  7.86  7.01  2.84  12.54**  1.34  (1.26) (1.44) (1.44) (0.90) (2.23) (0.27)  CL/CAD 3.19  4.46  2.62  2.48  8.81**  −0.22  (1.10) (1.28) (0.81) (0.99) (2.30) (−0.07)  OENEG −3.63  0.54  −4.11  −0.70  −1.90  (−1.22) (0.15) (−1.12) (−0.13) (−0.63) N/A  NI/TAD 1.23  −0.99  0.12  −0.09  −0.17  −6.57  (0.41) (−0.30) (0.03) (−0.03) (−0.04) (−1.69)  FFO/TLD 6.87***  8.30***  8.91***  7.50***  8.82***  7.65***  (3.21) (3.18) (3.14) (3.09) (3.23) (2.83)  INTWONEG −1.06  −1.79  −0.89  −0.12  −1.81  −1.18  (−0.73) (−1.07) (−0.56) (−0.05) (−1.25) (−0.66)  CHIND 1.01  1.62  0.82  2.02  0.12  4.45  (0.76) (1.22) (0.47) (1.57) (0.10) (1.52)  BetaD −0.96  −0.57  0.82  −2.84  −1.80  1.36  (−0.27) (−0.17) (0.22) (−0.81) (−0.53) (0.34)  MED 0.17  4.24  −0.51  6.40  2.27  16.80**  (0.03) (0.69) (−0.11) (1.28) (0.35) (2.53)  BE/MED 14.23***  15.58***  16.35***  10.15***  11.87***  5.64**  (5.14) (5.26) (5.36) (3.45) (4.63) (2.19)  Avg. Adj. R2 (%) 5.81 6.81 4.85 9.39 6.81 4.10  Note to Table 2.3: This table presents the results of Fama-MacBeth regressions using 74,737 firm-years (8,616 firms), span- ning 30 years from 1978 to 2007. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables, with the exception of the indicator variables, OENEG and INTWONEG, each year. The regression coefficient reported here is the mean of the coefficient estimates over 30 sample years and t-statistic reported in parenthesis is the mean of the coefficient estimates divided  46 by time-series standard error of the coefficient estimates. Definitions of the components of O-Score are as follows: Size is the log(total assets/GDP price level index); TL/TA is total liabilities divided by total as- sets; CL/CA is current liabilities divided by current assets; NI/TA is net income divided by total assets; FFO/TL is funds from operations divided by total liabilities; INTWONEG is an indicator variable equal to one if cumulative net income over the previous two years is negative, and zero otherwise; OENEG is an indicator variable equal to one if owner’s equity is negative, and zero otherwise; CHIN = (NIt − NIt−1)/(|NIt| + |NIt−1|) is the scaled change in net income. Refer to Table 2.1 for the definitions of Ret1yr, Beta, ME, and BE/ME. Superscript D (D) denotes decile ranks. December Firms are firms with a Decem- ber 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (larger) than the first quintile of NYSE size distribution. Growth (Value) Firms include firms whose book-to-market is smaller (larger) than the median of NYSE book-to-market distribution. *, **, *** denote two-tail signifi- cance at the 10%, 5%, and 1% level, respectively.  47 Table 2.4: Returns to zero-investment trading strategies using FFO/TL  Panel A: Equal-weighted portfolio  Panel B: Value-weighted portfolio Year FFO/TL Highest Decile Ret FFO/TL Lowest Decile Ret Net Ret  FFO/TL Highest Decile Ret FFO/TL Lowest Decile Ret Net Ret  1978 17.60  11.00  6.61   13.02  11.63  1.39 1979 22.95  7.45  15.50   −0.64  13.20  −13.84 1980 41.60  41.74  −0.13   21.29  26.32  −5.03 1981 −18.00  −26.38  8.38   −4.65  −29.63  24.98 1982 80.58  111.66  −31.08   73.83  106.70  −32.87 1983 −16.14  −30.85  14.71   −12.89  −32.05  19.17 1984 9.85  −20.04  29.89   20.65  −19.58  40.23 1985 25.70  9.81  15.89   31.35  15.61  15.74 1986 7.19  −3.04  10.23   15.84  −7.59  23.43 1987 −11.28  −29.60  18.32   −17.30  −32.36  15.06 1988 7.47  −8.75  16.22   1.61  −12.37  13.98 1989 16.01  −8.34  24.35   15.27  4.86  10.41 1990 6.22  10.23  −4.01   9.23  10.45  −1.22 1991 14.36  28.65  −14.29   10.79  5.65  5.14 1992 19.56  23.26  −3.70   15.77  −18.51  34.28 1993 1.47  −17.26  18.73   −7.07  −35.51  28.44 1994 39.74  23.18  16.56   58.45  15.75  42.70 1995 19.64  48.77  −29.14   18.21  35.21  −17.00 1996 7.05  −32.70  39.75   33.77  −25.87  59.64 1997 11.03  −15.24  26.27   27.88  −15.42  43.30 1998 4.34  0.57  3.77   49.35  4.48  44.87 1999 57.88  138.39  −80.51   98.89  124.52  −25.63 2000 5.81  −25.81  31.62   −51.20  −27.31  −23.89 2001 −4.79  −40.17  35.38   −33.00  −56.54  23.54 2002 9.49  20.88  −11.39   13.35  9.14  4.21 2003 36.26  41.21  −4.94   34.75  32.77  1.98 2004 14.09  −19.41  33.50   −1.57  −24.88  23.31 2005 14.80  5.87  8.93   1.17  2.40  −1.24 2006 14.03  3.88  10.15   20.00  −0.31  20.30 2007 −10.20  −30.46  20.26   −6.23  −21.67  15.45  Mean  7.53*    13.03*** (t) (1.71)    (3.17)  Median  12.47**    15.25*** (signed rank)      (119.5)        (134.5)  No. of positive  21/30**    22/30** (Z) (2.19)    (2.56)  Note to Table 2.4: This table presents returns to zero-investment trading strategies using funds from operations divided by total liabilities (FFO/TL) from 74,737 firm-years (8,616 firms), spanning 30 years from 1978 to 2007. At the end of June of each year t, firms are assigned into deciles according to their rankings of FFO/TLt. Ret  48 is the return on each portfolio (in percent) over one-year period beginning July of year t. Mean at the bottom of the Net Ret column is the average of the Net Ret figures. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  49 Table 2.5: Association of returns with O-Score after controlling for FFO/TL Dependent variable = Ret1yr  All Firms (N=74,737) December Firms (N=38,859) Small Firms (N=49,915) Large Firms (N=24,822) Growth Firms (N=43,866) Value Firms (N=30,871)  Intercept 15.05***  14.94***  15.54***  14.35***  12.01***  19.33***  (3.54) (3.74) (3.19) (4.33) (2.86) (4.30)  O-ScoreD 3.64  5.46  0.68  6.50*  9.18  2.98  (0.74) (0.96) (0.13) (1.76) (1.56) (0.75)  FFO/TLD 10.91**  12.73**  10.25  10.53***  15.61***  7.64*  (2.26) (2.39) (1.65) (3.51) (2.89) (1.72)  BetaD −0.77  −0.12  0.99  −3.48  −1.60  0.89  (−0.18) (−0.03) (0.23) (−0.75) (−0.36) (0.20)  MED −0.66  −0.03  −2.88  3.13  2.97  −5.07  (−0.14) (−0.01) (−0.78) (1.29) (0.65) (−1.06)  BE/MED 14.98***  15.52***  15.94***  8.40**  13.17***  2.85  (4.16) (4.11) (4.12) (2.66) (5.09) (0.97)  Avg. Adj. R2 (%) 4.48 5.08 3.73 6.88 5.25 2.63  Note to Table 2.5: This table presents the results of Fama-MacBeth regressions using 74,737 firm-years (8,616 firms), span- ning 30 years from 1978 to 2007. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables each year. The regression coefficient reported here is the mean of the coefficient estimates over 30 sample years and t-statistic reported in parenthesis is the mean of the coefficient estimates divided by time-series standard error of the coefficient estimates. Variable definitions are in Table 2.1. Superscript D (D) denotes decile ranks. December Firms are firms with a December 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (lar- ger) than the first quintile of NYSE size distribution. Growth (Value) Firms include firms whose book-to- market is smaller (larger) than the median of NYSE book-to-market distribution. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  50 Table 2.6: Characteristics of FFO/TL decile portfolios  Portfolio FFO/TL ranking  lowest 2 3 4 5 6 7 8 9 highest  FFO/TL −1.83  −0.14  0.04  0.11  0.15  0.20  0.26  0.35  0.51  1.23  CFO/ATA −0.31  −0.03  0.05  0.08  0.10  0.12  0.14  0.16  0.17  0.20  Beta 1.46  1.28  1.13  1.07  1.05  1.05  1.05  1.10  1.11  1.20  ME 3.11  3.29  3.92  4.53  4.93  5.18  5.37  5.19  5.05  4.82  BE/ME 0.66  0.90  0.77  0.96  0.88  0.80  0.72  0.69  0.65  0.56  Ret1yr 7.20  12.27  13.90  16.50  17.24  16.66  17.33  18.30  16.40  14.78  Note to Table 2.6: This table presents mean values of characteristics for ten portfolios formed annually at the end of June of year t from 1978 to 2007 by assigning firms to deciles based on the magnitude of FFO/TLt. The sample consists of 74,364 firm-years representing 8,594 firms. FFO/TL is funds from operations divided by total liabilities and CFO/ATA is cash flows from operations divided by average total assets. Cash flows from operations are operating income after depreciation minus accruals. Accruals are defined as the change in non-cash current assets minus the change in current liabilities excluding the current portion of short-term debt and taxes payable minus depreciation expense. Betat is estimated using the Capital Asset Pricing Model (CAPM) for each firm using monthly returns for at least 24 of the 60 months preceding July of year t. MEt is log of a firm’s market equity in millions at the end of June of year t. BE/MEt is book com- mon equity for the fiscal year ending in calendar year t−1, divided by market equity at the end of Decem- ber t−1. Ret1yrt is the buy-and-hold returns (in percent) over one-year period beginning July of year t.  51 Table 2.7: Association of returns with CFO/ATA Dependent variable = Ret1yr  All Firms (N=74,364) December Firms (N=38,691) Small Firms (N=49,648) Large Firms (N=24,716) Growth Firms (N=43,662) Value Firms (N=30,702)  Intercept 15.06***  14.96***  15.54***  14.37***  12.01***  19.35***  (3.55) (3.75) (3.19) (4.35) (2.86) (4.30)  CFO/ATAD 11.04***  11.31***  11.39***  7.33***  10.77***  7.10**  (4.27) (3.62) (3.43) (4.06) (3.48) (2.75)  BetaD −0.04  0.28  1.36  −2.86  −0.96  0.98  (−0.01) (0.07) (0.31) (−0.61) (−0.22) (0.21)  MED −3.29  −3.26  −2.96  0.75  −0.80  −6.72  (−0.78) (−0.79) (−0.82) (0.34) (−0.20) (−1.48)  BE/MED 14.39***  14.77***  15.43***  8.21**  12.57***  2.19  (4.60) (4.51) (4.85) (2.70) (5.70) (0.76)  Avg. Adj. R2 (%) 4.50 5.04 3.74 6.57 5.31 2.34  Note to Table 2.7: This table presents the results of Fama-MacBeth regressions using 74,364 firm-years (8,594 firms), span- ning 30 years from 1978 to 2007. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables each year. The regression coefficient reported here is the mean of the coefficient estimates over 30 sample years and t-statistic reported in parenthesis is the mean of the coefficient estimates divided by time-series standard error of the coefficient estimates. Variable definitions are in Table 2.6. Superscript D (D) denotes decile ranks. December Firms are firms with a December 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (lar- ger) than the first quintile of NYSE size distribution. Growth (Value) Firms include firms whose book-to- market is smaller (larger) than the median of NYSE book-to-market distribution. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  52 Table 2.8: Returns to zero-investment trading strategies using CFO/ATA  Panel A: Equal-weighted portfolio  Panel B: Value-weighted portfolio Year CFO/ATA Highest Decile Ret CFO/ATA Lowest Decile Ret Net Ret  CFO/ATA Highest Decile Ret CFO/ATA Lowest Decile Ret Net Ret  1978 19.77  15.54  4.24   17.68  17.81  −0.13 1979 21.17  11.99  9.18   9.32  17.66  −8.34 1980 41.45  47.58  −6.13   11.49  24.64  −13.15 1981 −16.90  −30.63  13.73   −10.11  −29.45  19.35 1982 86.50  98.15  −11.65   73.60  122.62  −49.02 1983 −11.85  −37.65  25.81   −8.70  −33.54  24.84 1984 20.91  −13.13  34.04   26.89  −11.83  38.72 1985 37.79  17.60  20.19   45.08  15.26  29.82 1986 16.34  −5.47  21.80   21.00  −15.49  36.49 1987 −7.33  −29.74  22.40   −10.70  −31.81  21.11 1988 13.40  −9.62  23.02   11.53  −7.36  18.89 1989 10.86  −5.36  16.21   20.44  −1.16  21.60 1990 9.48  6.85  2.63   22.20  −1.38  23.59 1991 14.05  37.96  −23.91   12.51  2.24  10.27 1992 22.68  21.93  0.75   1.38  −4.52  5.90 1993 1.47  −15.63  17.10   0.02  −21.30  21.32 1994 31.52  20.54  10.98   44.03  13.09  30.94 1995 29.96  47.50  −17.53   27.97  34.55  −6.58 1996 15.82  −32.74  48.56   38.90  −25.69  64.59 1997 15.63  −12.13  27.76   28.40  −18.18  46.58 1998 4.24  −5.38  9.62   25.78  2.32  23.47 1999 28.75  119.26  −90.51   42.24  104.21  −61.97 2000 12.45  −23.97  36.42   −36.85  −30.97  −5.88 2001 11.54  −40.15  51.70   −10.20  −48.65  38.45 2002 7.45  13.28  −5.83   6.49  22.72  −16.22 2003 36.81  30.03  6.78   12.51  26.66  −14.15 2004 14.40  −20.58  34.98   0.65  −20.57  21.22 2005 11.96  5.41  6.55   2.65  13.96  −11.31 2006 18.18  0.26  17.92   25.57  −3.74  29.31 2007 −5.88  −28.82  22.94   4.73  −20.74  25.46  Mean  10.99**    12.17** (t) (2.31)    (2.47)  Median  14.97***    21.16*** (signed rank)      (145.5)        (129.5)  No. of positive  24/30***    20/30* (Z) (3.29)    (1.83)  Note to Table 2.8: This table presents returns to zero-investment trading strategies using cash flows from operations divided by average total assets (CFO/ATA) from 74,363 firm-years (8,594 firms), spanning 30 years from 1978 to 2007. At the end of June of each year t, firms are assigned into deciles according to their rankings of  53 CFO/ATAt. Ret is the return on each portfolio (in percent) over one-year period beginning July of year t. Mean at the bottom of the Net Ret column is the average of the Net Ret figures. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  54 Table 2.9: Associations of returns with FFO/TL before/after controlling for CFO/ATA Dependent variable = Ret1yr  All Firms (N=74,364) December Firms (N=38,691) Small Firms (N=49,648) Large Firms (N=24,716) Growth Firms (N=43,662) Value Firms (N=30,702)  Panel A: Association of returns with FFO/TL before controlling for CFO/ATA  Intercept 15.06***  14.96***  15.54***  14.37***  12.01***  19.35***  (3.55) (3.75) (3.19) (4.35) (2.86) (4.30)  FFO/TLD 8.07***  8.36***  9.64***  5.02**  8.30***  5.60**  (4.38) (3.84) (3.36) (2.62) (4.32) (2.16)  BetaD −1.01  −0.60  0.86  −4.06  −2.08  0.85  (−0.22) (−0.14) (0.19) (−0.83) (−0.43) (0.18)  MED −1.86  −1.60  −2.91  1.63  0.60  −6.06  (−0.42) (−0.36) (−0.83) (0.71) (0.14) (−1.31)  BE/MED 14.28***  14.68***  15.86***  7.09**  12.04***  2.63  (4.59) (4.45) (4.87) (2.46) (5.36) (0.92)  Avg. Adj. R2 (%) 4.23 4.71 3.57 6.27 4.88 2.32  Panel B: Association of returns with FFO/TL after controlling for CFO/ATA  Intercept 15.06***  14.96***  15.54***  14.37***  12.01***  19.35***  (3.55) (3.75) (3.19) (4.35) (2.86) (4.30)  FFO/TLD 3.51**  3.72**  5.13**  1.66  3.61**  3.50  (2.25) (2.27) (2.42) (0.69) (2.06) (1.45)  CFO/ATAD 9.14***  9.28***  8.69***  6.40**  8.51**  5.65**  (3.44) (2.93) (2.94) (2.75) (2.42) (2.35)  BetaD 0.03  0.48  1.61  −3.04  −1.06  1.22  (0.01) (0.12) (0.38) (−0.66) (−0.24) (0.27)  MED −3.72  −3.69  −3.64  0.79  −1.00  −6.87  (−0.90) (−0.92) (−1.07) (0.35) (−0.25) (−1.55)  BE/MED 14.33***  14.80***  15.34***  7.99**  12.21***  2.74  (4.62) (4.51) (4.97) (2.58) (5.38) (0.96)  Avg. Adj. R2 (%) 4.62 5.17 3.92 6.83 5.37 2.62  Note to Table 2.9: This table presents the results of Fama-MacBeth regressions using 74,364 firm-years (8,594 firms), span- ning 30 years from 1978 to 2007. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables, each year. The regression coefficient reported here is the mean of the coefficient estimates over 30 sample years and t-statistic reported in parenthesis is the mean of the coefficient estimates divided by time-series standard error of the coefficient estimates. Variable  55 definitions are in Table 2.6. Superscript D (D) denotes decile ranks. December Firms are firms with a December 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (lar- ger) than the first quintile of NYSE size distribution. Growth (Value) Firms include firms whose book-to- market is smaller (larger) than the median of NYSE book-to-market distribution. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  56 Table 2.10: Associations of returns with O-Score before/after controlling for CFO/ATA Dependent variable = Ret1yr  All Firms (N=74,364) December Firms (N=38,691) Small Firms (N=49,648) Large Firms (N=24,716) Growth Firms (N=43,662) Value Firms (N=30,702)  Panel A: Association of returns with O-Score before controlling for CFO/ATA  Intercept 15.06***  14.96***  15.54***  14.36***  12.01***  19.35***  (3.55) (3.75) (3.19) (4.35) (2.87) (4.30)  O-ScoreD −6.11***  −5.80**  −7.89***  −2.29  −5.90***  −2.92  (−3.37) (−2.51) (−3.82) (−0.99) (−2.85) (−1.27)  BetaD −1.70  −1.38  −0.04  −4.52  −2.90  0.29  (−0.35) (−0.30) (−0.01) (−0.94) (−0.59) (0.06)  MED −2.39  −1.81  −3.56  1.57  0.34  −6.30  (−0.52) (−0.40) (−1.02) (0.68) (0.08) (−1.40)  BE/MED 13.17***  13.94***  14.53***  5.91**  11.63***  1.66  (3.95) (3.98) (4.13) (2.06) (4.73) (0.61)  Avg. Adj. R2 (%) 4.05 4.54 3.31 6.29 4.72 2.13  Panel B: Association of returns with O-Score after controlling for CFO/ATA  Intercept 15.06***  14.96***  15.54***  14.36***  12.01***  19.35***  (3.55) (3.75) (3.19) (4.35) (2.86) (4.30)  O-ScoreD −2.57  −2.11  −4.49**  0.25  −1.54  −1.61  (−1.16) (−0.80) (−2.10) (0.09) (−0.57) (−0.67)  CFO/ATAD 10.24***  10.75***  9.94***  7.56***  10.24**  6.72**  (3.42) (3.06) (2.77) (3.45) (2.73) (2.50)  BetaD −0.06  0.46  1.43  −2.91  −1.10  1.03  (−0.01) (0.11) (0.33) (−0.66) (−0.26) (0.23)  MED −4.28  −4.09  −4.36  1.02  −1.28  −7.10  (−1.05) (−1.03) (−1.31) (0.45) (−0.33) (−1.69)  BE/MED 13.82***  14.58***  14.37***  8.02**  12.15***  2.21  (4.07) (4.12) (4.23) (2.49) (4.87) (0.78)  Avg. Adj. R2 (%) 4.65 5.29 3.91 7.07 5.47 2.53  Note to Table 2.10: This table presents the results of Fama-MacBeth regressions using 74,364 firm-years (8,594 firms), span- ning 30 years from 1978 to 2007. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables, each year. The regression coefficient reported here is the mean of the coefficient estimates over 30 sample years and t-statistic reported in parenthesis is the mean of the coefficient estimates divided by time-series standard error of the coefficient estimates. Variable  57 definitions are in Table 2.6, except O-Score whose definition is in Table 2.1. Superscript D (D) denotes decile ranks. December Firms are firms with a December 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (larger) than the first quintile of NYSE size distribution. Growth (Value) Firms include firms whose book-to-market is smaller (larger) than the median of NYSE book-to- market distribution. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  58 Table 2.11: Returns across FFO/TL and O-Score quintile portfolios after controlling for CFO/ATA Panel A: Returns across FFO/TL quintile portfolios after controlling for CFO/ATA   CFO/ATA quintile FFO/TL quintile lowest 2 3 4 highest CFO/ATA highest − lowest  lowest 6.92  15.03  11.83  13.56  18.24  11.32***  [318] [94] [38] [22] [23] (3.59)  2 9.72  15.30  16.55  18.28  14.41  4.69*  [87] [172] [133] [71] [34] (1.71)  3 9.52  16.68  16.90  18.77  17.81  8.29**  [39] [103] [148] [142] [64] (2.07)  4 21.21  18.74  16.06  17.85  18.44  −2.77  [26] [71] [103] [156] [140] (−0.42)  highest 7.63  11.57  15.41  17.16  16.72  9.09***  [26] [56] [74] [105] [235] (3.17)   0.71  −3.46  3.58  3.61  −1.52  FFO/TL highest – lowest (0.19) (−1.18) (0.75) (0.80) (−0.28)  Panel B: Returns across O-Score quintile portfolios after controlling for CFO/ATA   CFO/ATA quintile O-Score quintile lowest 2 3 4 highest CFO/ATA highest − lowest  lowest 10.34  12.65  16.07  15.95  16.39  6.06**  [28] [69] [85] [115] [198] (2.15)  2 15.53  16.96  15.32  17.40  17.35  1.82  [39] [89] [112] [136] [120] (0.41)  3 9.59  15.54  16.76  19.25  19.38  9.79***  [62] [112] [123] [118] [80] (3.22)  4 13.65  18.75  18.49  20.11  16.33  2.69  [110] [132] [115] [83] [56] (0.65)  highest 4.63  11.96  10.98  16.82  15.59  10.97***  [256] [93] [61] [44] [41] (3.05)   5.71**  0.68  5.10  −0.88  0.80  O-Score lowest – highest (2.23) (0.22) (1.05) (−0.19) (0.26)  Note to Table 2.11: This table presents average annual returns (in percent) for each of 25 portfolios. Portfolios are formed according to the independent rankings of FFO/TLt (O-Scoret) and CFO/ATAt at the end of June of each year t from 1978 to 2007 in Panel A (Panel B). The average number of firms over the sample years for each of 25 portfolios is reported in bracket. The number in parenthesis represents a time-series t-statistic. *,  59 ** , ***  denote two-tail significance at the 10%, 5%, and 1% level, respectively.  60 Table 2.12: Sensitivity tests using post-SFAS No. 95 observations Dependent variable = Ret1yr  All Firms (N=47,948) December Firms (N=26,448) Small Firms (N=32,138) Large Firms (N=15,810) Growth Firms (N=27,845) Value Firms (N=20,103)  Panel A: Repeat of Table 2.7 using post-SFAS No. 95 observations  CFOSCF/ATAD 10.84***  9.75**  11.12**  7.92***  9.89**  7.85**  (3.26) (2.52) (2.48) (3.58) (2.56) (2.36)  Panel B: Repeat of Panel B in Table 2.9 using post-SFAS No. 95 observations  FFO/TLD 2.33  2.19  3.23  2.54  4.31  1.38  (1.15) (0.89) (0.96) (0.75) (1.63) (0.49)  CFOSCF/ATAD 9.26**  8.17*  8.93**  6.44*  6.73  7.01**  (2.77) (1.95) (2.37) (2.08) (1.49) (2.64)  Panel C: Repeat of Panel B in Table 2.10 using post-SFAS No. 95 observations  O-ScoreD −2.09  0.47  −3.14  −0.69  −1.94  −0.43  (−0.64) (0.12) (−1.08) (−0.18) (−0.47) (−0.16)  CFOSCF/ATAD 10.10**  10.13*  9.75*  8.00**  9.11*  7.66**  (2.43) (2.05) (1.95) (2.70) (1.78) (2.20)  Note to Table 2.12: This table presents the replication of Tables 2.7, 2.9, and 2.10 using post-SFAS No. 95 observations. The sample consists of 47,948 firm-years (6,309 firms), spanning 19 years from 1989 to 2007. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables, each year. The regression coefficient reported here is the mean of the coefficient estimates over 19 sample years and t-statistic reported in parenthesis is the mean of the coefficient estimates divided by time-series standard error of the coefficient estimates. For brevity, only the results for the variables of interest are provided in the table. CFOSCF is defined as cash flows from operations minus the cash portion of discon- tinued operations and extraordinary items. Definitions of the remaining variables are in Table 2.6, except O-Score whose definition is in Table 2.1. Subscript SCF (SCF) denotes the statement of cash flows. Super- script D (D) denotes decile ranks. December Firms are firms with a December 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (larger) than the first quintile of NYSE size distribution. Growth (Value) Firms include firms whose book-to-market is smaller (larger) than the me- dian of NYSE book-to-market distribution. *, **, *** denote two-tail significance at the 10%, 5%, and 1%  61 level, respectively.    62 Table 2.13: Sensitivity tests using Sloan’s (1996) original accrual measure Dependent variable = Ret1yr  All Firms (N=74,364) December Firms (N=38,691) Small Firms (N=49,648) Large Firms (N=24,716) Growth Firms (N=43,662) Value Firms (N=30,702)  Panel A: Association of returns with O-Score after controlling for ACC/ATA  O-ScoreD −6.93***  −6.81***  −8.91***  −2.59  −6.47***  −3.86  (−3.71) (−3.08) (−4.41) (−1.08) (−3.09) (−1.61)  ACC/ATAD −3.26*  −4.15**  −3.71*  −2.51  −1.70  −5.36**  (−1.97) (−2.44) (−1.96) (−1.67) (−1.05) (−2.15)  Panel B: Association of returns with ACC/ATA after controlling for CFO/ATA  ACC/ATAD 3.43  2.13  4.06  1.73  4.24*  −0.80  (1.28) (0.71) (1.28) (0.75) (1.88) (−0.18)  CFO/ATAD 12.94***  12.57***  13.64***  8.13***  12.81***  6.86  (3.66) (3.05) (3.16) (3.06) (3.57) (1.46)  Panel C: Association of returns with O-Score after controlling for ACC/ATA and CFO/ATA  O-ScoreD −1.68  −1.67  −3.95  0.88  0.42  −2.53  (−0.51) (−0.51) (−1.19) (0.26) (0.11) (−0.78)  ACC/ATAD 2.70  1.44  2.42  1.91  4.35  −1.87  (0.76) (0.41) (0.59) (0.63) (1.45) (−0.36)  CFO/ATAD 12.04**  11.76**  11.54*  8.71**  13.05**  5.73  (2.47) (2.26) (2.04) (2.34) (2.56) (1.02)  Note to Table 2.13: This table presents the results of sensitivity tests using Sloan’s (1996) original accrual measure. The results provided are based on Fama-MacBeth regressions using 74,364 firm-years (8,594 firms), spanning 30 years from 1978 to 2007. Beta, ME, and BE/ME are included in the regression but their results are not reported here for brevity. The dependent variable is regressed on scaled decile ranks, ranging from −0.5 to 0.5, of the independent variables, each year. The regression coefficient reported here is the mean of the coefficient estimates over 30 sample years and t-statistic reported in parenthesis is the mean of the coeffi- cient estimates divided by time-series standard error of the coefficient estimates. Variable definitions are in Tables 1 and 6, except ACC/ATA, which represents accruals divided by average total assets, where accruals are defined as the change in non-cash current assets minus the change in current liabilities ex- cluding the current portion of long-term debt and taxes payable minus depreciation expense. Superscript  63 D (D) denotes decile ranks. December Firms are firms with a December 31 year-end. Small (Large) Firms include those firms with market capitalization smaller (larger) than the first quintile of NYSE size distri- bution. Growth (Value) Firms include firms whose book-to-market is smaller (larger) than the median of NYSE book-to-market distribution. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  64 Figure 2.1: Returns to zero-investment trading strategy using FFO/TL and CFO/ATA Panel A: Equal-weighted portfolio -60% -45% -30% -15% 0% 15% 30% 45% 60% 19 78 19 79 19 80 19 81 19 82 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 N et  re tu rn s Year FFO/TL CFO/ATA  Panel B: Value-weighted portfolio -60% -45% -30% -15% 0% 15% 30% 45% 60% 19 78 19 79 19 80 19 81 19 82 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07N et  re tu rn s Year FFO/TL CFO/ATA     65 Chapter 3: Implementability of trading strategies based on account- ing information: Piotroski (2000) revisited 3.1 Introduction Chapter 2’s investigation of the bankruptcy risk anomaly makes use of standard research design elements that are common to tests of return predictability. Generally, this “anomalies literature” explores whether firm characteristics such as book-to-market, bankruptcy risk measures, ratio of accruals to total assets, etc., can be used to identify mispriced stocks. Although the literature is now fairly voluminous, there are still differences in opinion as to why detected mispricing persists. One explanation for detected mispricing is that excess re- turns represent compensation for risk (e.g., French, Schwert, and Stambaugh, 1987; Chan, 1998; Ball and Kothari, 1989; Kim and Kim, 2003; Khan, 2008). As noted in Fama (1970), this expla- nation is particularly difficult to prove or disprove because market efficiency must be tested jointly with a model for expected returns: in order to test whether returns are anomalous, one must know what expected returns should be in the absence of mispricing. Skeptics have also explored the degree to which excess returns documented by researchers are obtainable in practice due to institutional constraints such as short-sale constraints (e.g., Jones and Lamont, 2002; Boehme, Danielsen, and Sorescu, 2006) or transaction costs (e.g., Bhushan, 1994; Mashruwala, Rajgopal, and Shevlin, 2006; Ng, Rusticus, and Verdi, 2008). Finally, some critics point to re- search design choices or flaws that over- or understate the degree to which excess returns can be  66 earned (e.g., Lo and MacKinlay, 1990; Kothari, Shanken, and Sloan, 1995; Kothari, Sabino, and Zack, 2005; Kraft, Leone, and Wasley, 2006). This study contributes to this last research stream. It investigates the effects of two poten- tially problematic research design choices that are often made in accounting-based studies of anomalies. Both of these research design choices are relevant to the class of studies that employ zero-investment hedge portfolios to measure the economic significance of anomalous returns and do not apply to the alternative methodology that relates, via regression, future returns to current information. The two implementation issues are: 1) the use of equal- versus value-weights in forming the portfolios and 2) the selection of return accumulation periods based on firm specific fiscal year-ends, rather than establishing a common investment date for all firms in the hedge portfolio. I will argue that equal weighting of stocks within the hedge portfolios can be called into question. This first issue, coupled with transaction costs, implies that the returns earned on equal- ly weighted stocks within an assumed portfolio generated for research purposes are not likely to mimic real-world returns on the same set of stocks. The second issue revolves around the fact that if a money manager were to sort firms on the variable of interest such as book-to-market she cannot determine the total number of firms in each side of the hedge portfolio until the account- ing information of the entire portfolio becomes available. Therefore, she is unable to decide the applicable weight for an individual firm within the portfolio. For this reason, I label the imple-  67 mentability issue related to the return accumulation period as the problem of unknown portfolio weights. This study explores these two issues by re-examining the results in Piotroski (2000). That study investigates whether a simple, accounting-based fundamental analysis strategy can en- hance the returns to so-called value investing (i.e., investing in high book-to-market firms) doc- umented by Fama and French (1992) and Lakonishok, Shleifer, and Vishny (1994), among others. Piotroski’s study is motivated by the observation that while the value investing strategy, on average, yields positive abnormal returns, the success of that strategy relies on the strong performance of a small fraction of firms and thus, value investors must tolerate poor perform- ance from a large fraction of the firms in their portfolios. Given the diverse outcomes realized within high book-to-market firms, Piotroski asks whether a simple, financial statement-based heuristic, when applied to a subset of firms with high book-to-market ratios, can discriminate between the firms that will eventually provide high returns and those that will be poor perform- ers. To identify the firms that will eventually be strong value firms, Piotroski (2000) estab- lishes a trading heuristic that is based on nine fundamental signals to measure the financial con- dition of value firms. The nine signals are based on widely used measures of profitability,  68 financial leverage/liquidity, and operating efficiency.20 He classifies each firm’s realized signal as either “good” or “bad” depending on the signal’s implication for future performance. He as- signs one (zero) to an indicator variable if the signal’s realization is good (bad) and then defines the aggregate signal measure, F-Score, as the sum of the nine binary signals. With a subset of firms with high book-to-market ratios, he finds that firms with high F-Scores earn higher average subsequent returns than those with low F-Scores during his sample period of 1976 to 1999. It is worth noting that Piotroski (2000) is not the only study that is subject to the two is- sues of trading strategy implementability raised in this study. However, there are additional rea- sons that make revisiting Piotroski a worthy exercise. First, if the purpose of a study is to enhance the value investing strategy, then the methodology used in the study should be consis- tent with prior studies that document excess returns from value investing. Piotroski does not follow this general principle. Specifically, all three finance studies cited in Piotroski on value investing (i.e., Rosenberg, Reid, and Lanstein, 1984; Fama and French, 1992; and Lakonishok, Shleifer, and Vishny, 1994) start accumulating returns of individual firms at a common date (i.e., July 1 of each year). In contrast, Piotroski accumulates returns starting four months after each firm’s fiscal year-end. Thus, the question arises, would he have obtained similar results even if he had followed the approach used in these finance studies upon which he relied? Second, Pi-   20  Piotroski identifies nine fundamental signals based on his own reading of the professional and academic articles, not based on statistical techniques such as factor analysis.  69 otroski’s research question leads him to employ a subset of firms that are likely to be particularly vulnerable to the portfolio weighting issue raised in this study. To investigate the impact of the unknown portfolio weights problem, I replicate the anal- ysis in Piotroski (2000), which I refer to as Analysis 1, and then adjust the return accumulation period such that returns of individual firms are accumulated with a common starting date, which I refer to as Analysis 2. To isolate the impact of this problem on Piotroski’s results, equal weighting is applied to both analyses. The comparison of returns to zero-investment trading strategies reveals that the trading strategy in Analysis 1 outperforms that in Analysis 2 in 22 out of 32 years from 1976 to 2007. The difference in mean and median are significantly different from zero. Taken together, my results suggest that the return accumulation methodology typi- cally used in accounting studies is likely to result in inflated excess returns relative to the one used in the finance literature. To investigate the effect of portfolio weighting on the evidence of market inefficiency, I apply value weighting to Analysis 2, where the weight assigned to a firm is determined based on its market capitalization at the beginning of return accumulation date. In contrast to Piotroski (2000), which finds a mean annual return of 9.70 percent over 21 years from 1976 to 1996, I find that the F-Score-based zero-investment strategy only yields a mean annual return of 2.49 percent, insignificantly different from zero, over 32 years from 1976 to 2007. I also find that firms with high F-Scores only outperform those with low F-Scores in 20 out of 32 years and the accompa-  70 nying Z-statistic shows that the proportion of positive returns is not likely to be greater than 50 percent. Taken as a whole, my results highlight that when value-weighted returns are examined, the evidence of stock market inefficiency shrinks significantly and becomes statistically unreli- able. Thus, they remind researchers of the importance of a value-weighting scheme as a robust- ness check at a minimum, if not the focus of the main analysis. 3.2 Background and motivation 3.2.1 Equal- versus value-weighting Most accounting studies that challenge market efficiency, including Piotroski (2000), exclusively rely on equal-weighting when forming portfolios. Equal-weighting by itself does not pose any econometric problems. However, if the objective is to show market inefficiency by generating profits from a trading strategy, then the adopted methodology should reflect the economic cir- cumstances under which trades are executed in practice. Academic researchers often use the NYSE-Amex-NASDAQ universe to maximize sam- ple size and statistical power. However, the majority of firms in this universe are small firms, calling into question the real-world potential of implementing an equal-weighting scheme. Ac- cording to Fama and French (2008), microcaps, which they define as stocks with market capitali- zation below the 20th NYSE percentile, are on average about 3 percent of the NYSE-Amex- NASDAQ universe in value, but they account for about 60 percent of the total number of stocks. Although researchers implicitly assume that there would have been a large enough supply of  71 shares at a particular price at a particular point in time, this assumption is more likely to be vio- lated if the shares under consideration are from small firms because these shares tend to be illiq- uid. Furthermore, documented profits from trading strategies are reported gross of transaction costs. These costs are important in determining the performance of the strategies and can sub- stantially reduce documented returns to an investment strategy (Keim and Madhavan, 1997). While an equal-weighting scheme implicitly assumes equal transaction costs across firms, this is not the case in the real world. For example, Lesmond, Ogden, and Trzcinka (1999) estimate that average round-trip transaction costs from 1963 to 1990 are 1.2 percent and 10.3 percent for the largest and smallest NYSE-Amex decile firms, respectively. Prior research in finance has proposed value-weighting as a superior alternative to equal- weighting. Nonetheless, most accounting studies that challenge market efficiency have exclu- sively relied on equal-weighting when forming portfolios. In response to this, Lewellen (2010), in his review of recent empirical work on market inefficiency, proposes that “empirical studies should focus on value-weighted returns in addition to (or instead of) equal-weighted returns (p. 462).” 3.2.2 The problem of unknown portfolio weights Accounting studies that raise doubts about the informational efficiency of stock markets tend to document positive returns on zero-investment portfolios constructed on the basis of publicly available information. These studies typically accumulate returns for individual firms starting  72 three or four months after their fiscal year-ends. The gap between fiscal year-end and return accumulation period starting date ensures that (1) the financial accounting information of a firm becomes publicly available before its returns are accumulated and (2) accounting information used is not stale. Finance studies, meanwhile, accumulate returns with a common starting date each year regardless of the fiscal year-end of individual firms. For example, Lakonishok, Shleifer, and Vishny (1994) in their study of the value anomaly accumulate returns starting at the end of April each year for all observations with fiscal years ending in the prior calendar year and thus, the gap between fiscal year-end and the common starting date is four months for firms with De- cember fiscal year-ends, but this gap could be as much as 15 months for firms with January fiscal year-ends. Regression analyses that relate future returns to current accounting information are also commonly used to identify anomalies because one can extract the marginal effects of the variable of interest using multiple regression slopes. As long as researchers limit their analyses to regres- sion, the approach used in accounting studies with respect to return accumulation does not pose any problem. However, researchers oftent extend their analyses into portfolio analyses (1) to provide a simple picture of how returns vary across the spectrum of the variables of interest and (2) to facilitate gauging the economic significance of identified anomalies. The typical approach in portfolio analyses is to form decile portfolios by sorting stocks on the variable of interest. Though returns for individual deciles are typically shown, it is common to focus on the hedge  73 portfolio return obtained from long-short positions in the extreme deciles. This is where the problem of unknown portfolio weights arises. Hedging long-short positions requires the same amount of investment in each position. To achieve this, one has to know how many and which firms belong to each position, which, in turn, determines the amount of investment in individual firms in each position. If a money man- ager were to sort firms on the variable of interest such as book-to-market, she cannot determine the number and identity of firms in each side of the hedge portfolio until the accounting informa- tion of the entire portfolio becomes available. Therefore, she cannot decide an applicable weight for an individual firm within the portfolio. I illustrate the problem of unknown portfolio weights in the context of Piotroski (2000) to enhance understanding of this problem. Suppose there are 100 firms in the market of interest and that 40 of these have June fiscal year-ends and the remainder have December year-ends. For the sake of simplicity, assume each firm can only have an F-Score of zero or nine. A money manager will go long on firms with F- Scores of nine and short on firms with F-Scores of zero. She will take a total of $3,000 in each position and assign an equal weight to individual firms in each position. At the end of April of year t+1, accounting information for all 100 firms becomes available and thus, the fund manager can determine the number of individual firms within each F-Score group. This enables her to decide the amount of investment in the individual firms as shown in Figure 3.1. At the end of October of year t, by contrast, she has information on F-Scores of only the first 40 firms (those  74 with June fiscal year-ends). This makes it impossible to decide the amount of investment in the individual firms because the total number of individual firms in each side of the hedge portfolio is not yet available. Therefore, the analysis suffers from the problem of unknown portfolio weights if a researcher assumes knowledge of the number of individual observations within a hedge portfolio before the accounting information of the entire portfolio becomes publicly avail- able. 3.2.3 Survey of prior accounting studies related to accounting anomalies This section provides a focused survey of recent archival empirical literature related to account- ing anomalies because this study contributes to that literature to the extent that the implement- ability issues discussed are widespread in the accounting literature.21 My survey focuses on research studies published in The Accounting Review, Journal of Accounting and Economics, and Journal of Accounting Research within a 10-year period starting with the year 2000. Although my survey is limited only to studies published in three journals, the methodologies employed in these studies are often adopted by subsequent studies in other journals. Therefore, I believe my survey captures a broad picture of the methods used in recent studies on anomalies. I was able to identify 14 studies, including Piotroski (2000), that are related to accounting   21  The focus of my survey is to identify the implementability issues raised in this study. Refer to Richard- son, Tuna, and Wysocki (2010) for a more general survey of recent studies on anomalies.  75 anomalies. Of these 14 studies, three studies limit their analysis to regressions and thus, they are not subject to the implementability issues discussed in this study as noted above.22 Table 3.1 provides information about the remaining 11, including (1) portfolio formation methodology and (2) whether the particular study is subject to the problem of unknown portfolio weights. The second column of Table 3.1 confirms that unlike finance studies, in which value- weighted hedge portfolio returns are often shown along with equal-weighted returns, a signifi- cant proportion of accounting studies rely exclusively on equal-weighting. Among the articles identified, Hirshleifer, Hou, Teoh, and Zhang (2004) is the only study that provides value- weighted portfolio returns as well as equal-weighted returns. Equal-weighting by itself does not pose any econometric problems, but equal-weighted returns do not accurately capture the total wealth effects experienced by investors. Moreover, money managers are unlikely to be able to replicate an anomaly derived from equal-weighting. Whether the use of value-weighted returns would change the tenor of results concerning the remaining 10 studies remains an open question, but Fama (1998) provides a helpful insight as to the robustness of anomalies derived from equal-weighted returns. After re-examining anoma- lies documented in the finance literature, he concludes that   22  These three studies are Ali, Hwang, and Trombley (2003); Fairfield, Whisenant, and Yohn (2003); and Pincus, Rajgopal, and Venkatachalam (2007).  76 “Whenever value-weighted returns are examined, apparent anomalies shrink a lot and typically become statistically unreliable. At a minimum, this suggests that anomalies are largely limited to small stocks. But a reasonable alternative expla- nation is that small stocks are just a sure source of bad-model problems (p. 304).” Thus, Fama’s findings not only challenge the validity of 10 accounting studies that only rely on equal-weighting but also call for a robustness check using value-weighted returns. As shown in the third column of Table 3.1, only three of 11 studies are free of the prob- lem of unknown portfolio weights. These studies avoid this problem by limiting their samples to firms with December fiscal year-end (Beneish and Vargus, 2002; Mashruwala, Rajgopal, and Shevlin, 2006) or forming portfolios in every month (Hirshleifer, Hou, Teoh, and Zhang, 2004). Of the eight studies that are subject to the problem of unknown portfolio weights, three address this problem in their sensitivity analysis. For example, Xie (2001) states that “My sample includes both December fiscal year-end and non-December fiscal year-end firms. Accounting information for a given fiscal year will become avail- able to the market at different points in calendar time for firms with different fis- cal year-end months. Thus, one cannot directly implement the hedge-portfolio strategies reported in Table 3 (p. 367).” After acknowledging the problem, these studies repeat their analysis by forming portfolios in every month (Xie) or by limiting their sample to firms with December fiscal year-end (Penman and Zhang, 2002; Desai, Rajpogal, Venkatachalam, 2004). Thus, it is clear that many studies published in the three surveyed journals are subject to  77 the issues of implementability of trading strategies raised in this study. Given the influence of these journals on the literature, additional studies published in other journals can be expected to have the same implementability issues as well. Thus, the implications of my findings are not limited to the case of Piotroski (2000). 3.3 Description of the empirical tests To investigate the impact of the unknown portfolio weights problem, I replicate the analysis in Piotroski (2000), which I refer to as Analysis 1, and then change the return accumulation period such that returns of individual firms are accumulated with a common starting date, which I refer to as Analysis 2. To isolate the impact of this problem on Piotroski’s results, equal weighting is applied to both analyses. In the subsequent analysis, I apply value weighting to Analysis 2 to investigate the effect of portfolio weighting on the evidence of market inefficiency. Before I lay out the details of Analysis 1 and Analysis 2, I discuss how Piotroski constructs his F-Score using fundamental analysis. 3.3.1 F-Score Piotroski (2000) introduces F-Score to differentiate between financially strong and weak firms among value stocks. Specifically, he chooses nine fundamental signals to measure three areas of a firm’s financial condition: profitability, financial leverage/liquidity, and operating efficiency. A firm’s F-Score is the sum of nine binary signals and provides a measure of the strength of the  78 firm’s financial position. Piotroski classifies each firm’s signal realization as either “good” or “bad” depending on the signal’s implication for future performance. An indicator variable for the signal is equal to one (zero) if the signal’s realization is good (bad). Thus, a high (low) F-Score represents a firm with mostly (very few) good signals. Piotroski (2000) employs four measures of profitability because these measures provide information about the firm’s ability to generate funds internally: ROA, CFO, ∆ROA, and ACCRUAL. He defines these variables as follows:  ROAt  = net income before extraordinary items in year t scaled by total assets at the beginning of year t;    CFOt  = cash flows from operations in year t scaled by total assets at the beginning of year t;    ∆ROAt  = ROA in year t less ROA in year t−1;   ACCRUALt  = ROAt − CFOt. For ROA, CFO, and ∆ROA, he assigns one to F_ROA, F_CFO, and F_∆ROA, respectively, if each signal is positive and zero otherwise. He assigns one to F_ACCRUAL if ACCRUAL is negative and zero otherwise because earnings driven by positive accrual adjustments have been found to be a bad signal about future profitability (Sloan, 1996). To measure changes in capital structure and the firm’s ability to meet future debt obliga- tions, Piotroski (2000) uses these signals: ∆LIQUID, ∆LEVER, and EQ_OFFER, defined as follows:  79  ∆LIQUIDt  = change in the ratio of total current assets to total current liabili- ties between the end of year t−1 and year t;    ∆LEVERt   = change in the ratio of total long-term debt to total assets between the end of year t−1 and year t;    EQ_OFFERt  = an indicator variable equal to one if a firm did not issue common equity in the year t, zero otherwise.  Piotroski assigns one to F_∆LIQUID if ∆LIQUID is positive and zero otherwise because an improvement in liquidity is expected to be a good signal about the firm’s ability to service short- term debt obligation. He assigns one to F_∆LEVER if ∆LEVER is negative and zero otherwise. As noted in Piotroski, an increase in leverage itself is not necessarily a negative signal with re- spect to future performance, but he reasons that because value firms tend to be financially dis- tressed to some extent they are signaling their inability to generate sufficient internal funds by issuing debt (Myers and Majluf, 1984; Miller and Rock, 1985). Using similar reasoning, Piotro- ski views issuing common equity as a bad signal and thus assigns one to EQ_OFFER when a firm does not issue common equity.23   23  To identify equity offerings, Piotroski depends on COMPUSTAT data108 (SSTK in the fundamental file), sale of common and preferred stock, which includes 1) sale of common shares, 2) sale of preferred shares, 3) conversion of preferred shares and/or debt into common shares, and 4) exercise of stock options and/or warrants. Thus, a positive value in the above data item does not necessarily mean that a company has issued common equity. Nonetheless, I follow Piotroski because 1) this study is replicating Piotroski and 2) the impact of the measurement error is expected to be marginal because the main analysis in this study combines firms into two groups.  80 Piotroski (2000) uses two signals to measure changes in the efficiency of the firm’s op- erations: ∆MARGIN and ∆TURN, defined as follows:  ∆MARGINt  = change in the gross margin ratio between year t−1 and year t;   ∆TURNt  = change in the asset turnover ratio between year t−1 and year t. Piotroski assigns one to F_∆MARGIN and F_∆TURN, respectively, if each signal is positive and zero otherwise because an improvement in either ratio suggests an improvement in operational efficiency. Having defined these nine signals, F-Score is then simply the sum of these signals:  F-Score  = F_ROA + F_CFO + F__∆ROA + F_ACCRUAL + F_∆LIQUID + F_∆LEVER + EQ_OFFER + F_∆MARGIN + F_∆TURN.  3.3.2 Details on Analysis 1 and Analysis 2 Analysis 1 intends to closely replicate Piotroski (2000) and Analysis 2 intends to vary the return accumulation period such that returns of individual firms are accumulated with a common start- ing date. I perform the following steps for Analysis 1:  Step 1: I calculate book-to-market quintile cutoffs for each calendar year using all firms with sufficient data within the merged COMPUSTAT/CRSP annual fundamental file. To calculate the market value of equity, I use a firm’s fiscal year-end share price and the number of shares outstanding at the fiscal year- end.    81  Step 2: I calculate F-Score for all observations in the merged COMPUSTAT/CRSP annual fundamental file.    Step 3: I merge cutoffs from Step 1 and the dataset in Step 2 such that cutoffs in year t−1 are assigned to the dataset in year t. Then, I retain only firm-years in the highest book-to-market quintile. If F-Score for a particular firm-year is miss- ing due to the lack of required financial statement data, then the observation is dropped from the sample.    Step 4: I calculate one-year market-adjusted returns for all available observations using the CRSP monthly stock file, where market-adjusted return is defined as the buy-and-hold return less the value-weighted market return.    Step 5: Using the cross-reference file linking COMPUSTAT’s GVKEY to the his- torical perm number on CRSP (LPERMNO), I merge the dataset derived from Step 3 and the dataset from Step 4 such that firm-years have one-year market-adjusted returns starting at the end of the sixth month after the fiscal year-end.  Although Analysis 1 closely follows Piotroski (2000), there are a few differences. First, my approach combines firm-years with fiscal year-ends falling on the same calendar year as a unit of yearly analysis, whereas Piotroski defines years according to FYEAR in COMPUSTAT, which ends on May 31. This choice was made in order to allow for comparison with Analysis 2. Second, Analysis 1 accumulates returns for individual observations starting six months after their fiscal year-end, rather than four months used in Piotroski. I intentionally switch to a six-month gap based on the findings of Alford, Jones, and Zmijewski (1994) that 2 percent of the 10-K reports are not filed by the end of the fifth month after the fiscal year-end. Another reason for switching to a six-month gap is that Piotroski does not limit his sample to U.S. firms, so his sam-  82 ple includes a number of ADRs, which have six months after the fiscal year-end to file Form 20- F. Note that the final sample does not include firms with negative book-to-market ratios be- cause I use only firms in the highest book-to-market quintile. Nonetheless, the decision of whether to include negative book-to-market firms in Step 1 is not trivial in that it affects the quintile cut-offs used to determine the composition of the final sample. Piotroski (2000) is silent about the inclusion (or exclusion) of negative book-to-market firms with respect to the calcula- tion of cutoffs, but the replication done in this study suggests that firms with negative book-to- market ratios are included in his study. Hence, I include firms with negative book-to-market ratios in Step 1. Also note that I use the delisting return in the delisting month in Step 4. If a delisting is due to liquidation or a forced delisting by either the exchange or the Securities and Exchange Commission (SEC) (CRSP delisting codes 400 to 699) and the delisting return is miss- ing, the delisting return is set to negative 100 percent.24 If a firm delists within one year after return accumulation begins, then the one-year market-adjusted return is defined as the buy-and- hold return through the delisting month less the value-weighted market return over the corre- sponding time period.   24  By contrast, Piotroski assumes that a missing delisting return is zero. While I do not agree with Piotro- ski’s decision here, I find that setting the delisting return to zero does not change the tenor of my results quantitatively or qualitatively.  83 Analysis 2 requires the following steps (differences from Analysis 1 are underlined).  Step 1: I calculate book-to-market quintile cutoffs for each calendar year using all firms with sufficient data within the merged COMPUSTAT/CRSP annual fundamental file. To calculate the market value of equity, I use a firm’s fiscal year-end price and the number of shares outstanding at the fiscal year-end (the same as Step 1 in Analysis 1).    Step 2: I calculate F-Score for all observations in the merged COMPUSTAT/CRSP annual fundamental file (the same as Step 2 in Analysis 1).    Step 3: I merge cutoffs from Step 1 and the dataset in Step 2 such that cutoffs in year t are assigned to the dataset in year t. Then, I retain only firm-years in the highest book-to-market quintile. If F-Score for a particular firm-year is miss- ing due to the lack of required financial statement data, then the observation is dropped from the sample.    Step 4: I calculate one-year market-adjusted returns for all available observations using the CRSP monthly stock file, where market-adjusted return is defined as the buy-and-hold return less the value-weighted market return (the same as Step 4 in Analysis 1).    Step 5: Using the cross-reference file linking COMPUSTAT’s GVKEY to the his- torical perm number on CRSP (LPERMNO), I merge the dataset derived from Step 3 and the dataset from Step 4 such that firm-years have one-year market-adjusted returns starting at the end of June of the following year.  Note that Analysis 2 employs the current year book-to-market distribution in Step 3 be- cause necessary information to determine the current year distribution is available at the begin- ning of the applicable return accumulation period. Because this study retains only firms in the highest book-to-market quintile, the use of different cutoffs in Step 3 across Analysis 1 and Analysis 2 leads to the creation of different samples across the two analyses, which will be dis-  84 cussed in more detail in the next section. 3.4 Sample The empirical tests in this study are conducted using all firms in the intersection of the 2010 editions of the merged COMPUSTAT/CRSP annual fundamental file and the CRSP monthly stock file. To be included in the sample, (1) the firm-year must have the accounting information necessary to calculate its F-Score, (2) the firm-year’s book-to-market falls in the highest book-to- market quintile, and (3) the share price and number of shares outstanding are available from CRSP at the beginning of the applicable return accumulation period. The third requirement im- plies that included firms survived until the beginning of the applicable return accumulation pe- riod. For firms that fail after the return accumulation period begins, the delisting returns are used as explained above. Consistent with Piotroski (2000), the sample period in this study begins in 1976. Due to the need to accumulate returns up to 30 months following the end of a fiscal year, the sample period ends in 2007. For example, firm-years with fiscal year-ends falling in January to Decem- ber 2007 are grouped together and their returns are accumulated from July 2008 to June 2009. Taking into account the data restrictions discussed in Section 3.3, the final sample for Analysis 1 (Analysis 2) is 22,520 (23,118) firm-years representing 6,429 (6,297) firms. The intersection of the two samples is 19,889 firm-years representing 5,898 firms. Discrepancies between the two samples in the number of observations arise from the re-  85 quirements of Step 3 and Step 5. With regard to Step 3, Analysis 1 uses the previous year’s book-to-market distribution, whereas Analysis 2 uses the current year’s distribution. Thus, the increase or decrease in the highest quintile cutoff from year t−1 to year t results in some observa- tions being included in the final sample of one but not the other analysis.25 With respect to Step 5, there are two sources of differences in the final sample composition. First, Analysis 1 requires firms to survive until the end of six months after the fiscal year-end, whereas Analysis 2 requires firms to survive longer, with the exception of firms with December fiscal year-ends. Thus, if a firm delists between the beginning of the return accumulation period of Analysis 1 and that of Analysis 2, then the firm is only included in the sample for Analysis 1. Second, if a firm’s shares are suspended from trading at the beginning of the return accumulation period of Analysis 1 but trading is resumed on or before that of Analysis 2, the firm is only included in the sample of Analysis 2. To summarize the differences in the two samples, I decompose the final samples into those that are common across Analysis 1 and Analysis 2 and those that are unique to one or the   25  For example, assume the highest book-to-market quintile cutoff in year 2001 was 1.0 and the corre- sponding figure in year 2002 was 1.5. Then, firm-years with a book-to-market that falls between 1.0 and 1.5 in year 2002 will only be included in Analysis 1. On the other hand, if the cutoff declined from 1.5 in year 2001 to 1.0 in year 2002, then firm-years with book-to-market between 1.0 and 1.5 in year 2002 will only be included in Analysis 2.  86 other analysis. I further decompose each subsample based on F-Score. As can be seen in Table 3.2, all observations are heavily concentrated in the intermediate F-Scores. This holds true for the observations that are common to both samples as well as those that are unique to one sample. This result is expected because F-Score is a sum of random variables with finite means and vari- ances, so the distribution of F-Score should approach normal as the number of observations in- creases (Central Limit Theorem). Because the main empirical tests are performed on a yearly basis, differences in sample composition by year are also investigated. The results are shown in Table 3.3. The highest book- to-market quintile cutoff used in this study declines over my sample period from 1.83 in 1976 to 0.83 in 2007. This is consistent with Givoly and Hayn (2000), who find that the average book-to- market has decreased since the 1970s. Although there is an overall decreasing trend in book-to- market, the trend is not entirely monotonic year over year: out of the 32 years examined in this study, the quintile cutoff decreased 22 times from year t-1 to year t, but it also increased 10 times. The differences in sample composition reported in Table 3.3 are quite dramatic in some years because of a unique set of firm-years belonging only to the sample for Analysis 1 or that for Analysis 2. For example, in 1976 the number of firm-years in the sample for Analysis 2 is almost twice as large as that for Analysis 1.  87 3.5 Empirical results 3.5.1 The problem of unknown portfolio weights The main analyses start with replicating Table 3 of Piotroski (2000, p. 17): I calculate mean and median one-year market-adjusted returns of each F-Score group for the 32-year period spanning from 1976 to 2007 and report the results in Table 3.4. Consistent with Piotroski (2000), mean and median one-year market-adjusted returns are monotonically increasing in F-Score, including the exception of firms with F-Scores of zero. In addition, firms with F-Scores of eight or nine deliver economically and statistically higher re- turns than those with F-Scores of zero or one. In Table 3 of Piotroski, where the sample period spans 21 years from 1976 to 1996, mean and median difference in market-adjusted returns be- tween firms with F-Scores of 8 or 9 and those with F-Scores of zero or one are 23.0 and 20.0 percent, respectively. The results in Table 3.4 are comparable to those of Piotroski: mean and median differences are 20.59 and 24.56 percent, respectively. The results for Analysis 2, where the problem of unknown portfolio weights in Analysis 1 is eliminated, provide insight into whether unknown portfolio weights would impact conclusions drawn from Analysis 1. Compar- ing the results of Analysis 1 to those of Analysis 2, it is clear that returns of firms with F-Scores of five or greater decline with regard to both mean and median, but returns of firms with F- Scores of four or less provide mixed results. Nonetheless, the difference between firms with F- Scores of eight or nine and those with F-Scores of zero or one is still economically and statisti-  88 cally significantly different from zero whether I focus on Analysis 1 or Analysis 2. In his main analysis, Piotroski (2000) presents the gap between returns of firms with F- Scores of eight or nine and those with F-Scores of zero or one as evidence of stock market ineffi- ciency. However, the gap does not represent an excess return one could obtain over the period of 32 years from 1976 to 2007 by going long on firms with F-Scores of eight or nine and going short on firms with F-Scores of zero or one. The excess return and the corresponding statistical significance in Table 3.4 are calculated as if observations coexist in one year. However, that is not the case because the data spans 32 years. Thus, it is impossible to determine how much should be invested in each stock to form a zero-investment portfolio. Furthermore, the feasibility of the trading strategy that employs firms with F-Scores of eight or nine and those with F-Scores of zero or one is to some extent doubtful: there is no guarantee that firms with extreme scores will exist in a particular year. Following Piotroski’s (2000) yearly analysis and to address these two concerns, Tables 3.5 and 3.6 present results by year. I classify all firms in a particular year into two groups: one with F-Scores of five through nine and another with F-Scores of zero through four. As in Piotro- ski, I call the former Strong and the latter Weak for brevity. For each year from 1976 to 2007, I form equally-weighted portfolios for Weak and Strong under Analysis 1, as well as Analysis 2, and report the associated returns in Table 3.5. I also report the performance of All, which repre- sents all firms in both Strong and Weak. By construction, performance of All is the weighted  89 average of the performances of Strong and Weak. The performance of Weak is not significantly different from that of the market index across Analysis 1 and Analysis 2. Strong clearly outper- forms the market index as evidenced by the tests of mean, median, and proportion in each analy- sis. Table 3.6 formally investigates the impact of unknown portfolio weights. It reports and compares the profits of hedge portfolios derived under Analysis 1 and Analysis 2, using equally weighted returns in the hedge portfolios. Given the presence of short-sale constraints (Jones and Lamont, 2002; Boehme, Danielsen, and Sorescu, 2006), it is also important to compare the per- formance of Strong and that of All: the former represents the outcome of value investing refined with F-Score and the latter represents the outcome of value investing as originally conceived. Thus, I also report Strong minus All, in addition to Strong minus Weak. Under Analysis 1, the mean (median) annual return on Strong minus Weak is 8.33 percent with t-statistic of 6.22 (8.00 percent with significance at the 1 percent level). The profitability of the strategy is consistent: Strong outperforms Weak in 27 out of 32 years. Although the mean and median annual returns of  90 Strong minus All are smaller, they show similar statistical significance.26 As explained above, the returns reported under Analysis 1 rely on accounting information that is not available at the time of portfolio formation. Analysis 2 effectively removes this con- cern but with a trade-off of incorporating stale information. Implementing Analysis 2 reveals that the profitability of hedge portfolios under Analysis 1 (mean of 8.33 and median of 3.24 percent) is more than 40 percent higher relative to that under Analysis 2 (mean of 5.80 and median of 2.26 percent). The comparison of the trading strategy in the last two columns shows that the trading strategy in Analysis 1 produces higher returns than that in Analysis 2 in 22 out of 32 years and the differences in mean and median are significantly different from zero. Thus, Table 3.6 demonstrates that the relationship between Piotroski’s (2000) fundamental signals and subse- quent returns is attenuated if the portfolios are formed only after knowledge of the portfolio weights becomes available using a common date to accumulate returns, as is done in many stud- ies in the finance literature.   26  Note that the sign of Strong minus All should be the same as that of Strong minus Weak, and the mag- nitude of Strong minus All is equal to one minus the proportion of Strong to total firms multiplied by the magnitude of Strong minus Weak by construction. The numerical relationship between Strong minus All and Strong minus Weak is as follows:  Strong − All = Strong − [α*Strong + (1 − α)*Weak] = (1 − α)*(Strong − Weak),  where α is the proportion of Strong to total firms and 0 < α < 1.  91 3.5.2 Equal- versus value-weighting The results provided in Table 3.6 show that the unknown portfolio weights problem attenuates, but does not eliminate, the positive relationship between F-Score and subsequent returns. How- ever, the profit generated using the trading strategy is potentially unobtainable due to the issue of equal-weighting discussed earlier. As noted above, equal-weighting does not reflect the eco- nomic circumstances in which trades are executed. Thus, I revisit Analysis 2 with a value- weighting scheme. Table 3.7 reports one-year market-adjusted returns to value-weighted portfolios for each year from 1976 to 2007. This table is identical to Panel B of Table 3.5 with the exception of portfolio weighting. The weight assigned to a firm is determined based on its market capitaliza- tion at the beginning of the return accumulation date (i.e., July 1 each year). For brevity, I limit my discussion to the Strong portfolios because Table 3.5 shows that most of the excess returns derive from this side of the hedge portfolios. The mean annual return on Strong is 5.21 percent with t-statistic of 2.09, while the median annual return is 4.85 percent with significance at the 10 percent level. These figures are about half of the corresponding figures in Panel B of Table 3.5. Moreover, as shown in the bottom rows of Table 3.7, Strong outperforms the market index in only 18 of 32 years and the accompanying Z statistic shows that the proportion of positive mar- ket-adjusted returns is not significantly greater than 50 percent. Table 3.8 provides a formal test of excess hedge portfolio returns. As shown in the bot-  92 tom rows, the Strong minus Weak strategy only yields a mean annual return of 2.49 percent, insignificantly different from zero. While the median annual return is slightly higher than the mean return, it is also not significantly different from zero. Furthermore, Strong only outper- forms Weak in 20 of 32 years and the accompanying Z statistic shows that the proportion of positive returns is not significantly greater than 50 percent. The results in Table 3.8 thus demon- strate that firms with high F-Scores do not outperform those with low F-Scores when value- weighting is employed and the problem of unknown portfolio weights is corrected. Table 3.8 also compares returns to hedge portfolios under Analysis 1 with equal- weighting to those under Analysis 2 with value-weighting. Mean returns to hedge portfolios under the former are greater than those under the latter by 5.84 percent with t-statistic of 2.75. This difference represents the combined impact of the unknown portfolio weights problem and the change in portfolio weighting, demonstrating that these research design choices can have substantial consequences when exploring evidence of stock market inefficiency. Because Analy- sis 1 with equal-weighting is typical of those often employed in the accounting literature, the results in Table 3.8 suggest that evidence of profitable trading strategies and market inefficiency is likely to be overstated in a substantial number of studies. 3.5.3 Real-world implementation of F-Score-based trading strategy Analysis 2, the approach used in finance studies, provides a solution to the unknown portfolio weights problem but with a trade-off of using stale information in portfolio formation. Thus, this  93 approach is unlikely to be the approach used by money managers. Instead, they would implement a trading strategy multiple times, possibly every month, to better use current information. For example, by increasing the frequency of portfolio formation under Analysis 2 from once a year to twice a year, one can reduce the maximum gap between fiscal year-end and the beginning of the return accumulation period by six months (from 17 months to 11 months). In the extreme, one can entirely avoid incorporating stale information by forming portfolios every month. This section revisits the F-Score-based trading strategy by implementing the strategy multiple times a year.27 I start by implementing an F-Score-based trading strategy twice a year and report returns to hedge portfolios in Panel A of Table 3.9. To better reflect the economic circumstances in which trades are executed, I form value-weighted portfolios. Each year firms with fiscal year-end from January 1 to June 30 (July 1 to December 31) are grouped together and their returns are accumulated starting January 1 (July 1) of the following year. The mean annual return on the hedge portfolios is 2.70 percent with t-statistic of 1.30 and the median annual return is 4.54 per-   27  Another way to avoid incorporating stale information is to limit a sample to firms with December fiscal year-ends. When I repeat the analysis using only firms with December fiscal year-ends, profits to hedge portfolios are not materially different from those obtained under value-weighting in Table 3.8: mean (median) returns are 4.30 percent with t-statistic of 1.63 (5.22 percent with significance at the 10 percent level) and the proportion of positive returns is 21 out of 32 with Z-statistic of 1.77.  94 cent with significance at the 10 percent level. Compared to the results obtained under value- weighting in Table 3.8, results in Panel A suggest that implementing the strategy multiple times a year does not improve the profitability of hedge portfolios. I further increase the frequency of portfolio formation to four times a year and six times a year. Technically speaking, I could form portfolios every month, but I decide not to because of the small number of firms in the Weak group. Implementing the strategy four times a year pro- duces results that are similar to implementing the strategy twice a year. When the frequency is increased to six times a year, there is a marginal improvement in the profitability of the hedge portfolios. The mean annual return on the hedge portfolios is 3.38 percent with t-statistic of 1.71 and the median annual return is 2.36 percent with significance at the 5 percent level. The profit- ability of the trading strategy is marginally consistent: the proportion of positive returns is 109 of 192 iterations with Z-statistic of 1.88. However, the reported profits are not large enough to off- set related transaction costs. Thus, the information in Table 3.9 suggests that Piotroski’s (2000) trading strategy is unlikely to generate a reliable profit even if it is implemented by a money manager. 3.5.4 Replication of Xie (2001) Many prior accounting studies using trading strategies are subject to the issues of implementabil- ity raised in this study. I replicate and extend Piotroski (2000) because his research design em- ploys a subset of firms that are likely to be more vulnerable to the issue of implementability.  95 While this makes the test setting advantageous, this is a double-edged sword: I may not find similar results when I repeat the analyses with other subsets of firms or when I apply the analy- ses to other anomalies. To answer concerns about the true impact of the issues I have identified on studies other than Piotroski, I investigate the implementability issues in the context of Xie (2001). Xie (2001) is an extension of Sloan’s (1996) accrual anomaly. Xie estimates abnormal accruals with a cross-sectional version of the Jones (1991) model (DeFond and Jiambalvo, 1994; Subramanyam, 1996). Then he shows that the overpricing of total accruals documented by Sloan is due largely to abnormal accruals. I replicate Xie because this is the paper with the highest average citations per year among the 54 anomalies-related papers published in accounting jour- nals in the last 10 years (Richardson, Tuna, and Wysocki, 2010). In replicating Xie (2001), I limit my sample to firms with fiscal year-ends falling between 1971 and 1992 so that my sample period coincides with that of Xie. I closely follow Xie’s re- search design, but I make a few modifications. The gap between fiscal year-end and the begin- ning of the return accumulation period is three months in Xie, whereas I allow a six-month gap, as in my main analysis. Second, Xie uses COMPUSTAT definition of FYEAR for the year iden- tification (year t includes firm-years whose fiscal year-end falls between June 1, year t and May 31, year t+1), whereas I use the calendar year to be consistent with my main analysis. Third, Xie excludes NASDAQ observations prior to 1982 due to the lack of size-adjusted returns in the  96 1995 CRSP Indices file, whereas I include these observations because the 2010 CRSP Indices file supplies size-adjusted returns for these firms. Xie’s final sample consists of 56,692 firm- years (representing 7,506 firms), whereas my final sample consists of 68,549 firm-years (repre- senting 8,225 firms). Each year the hedge portfolio is formed by taking a long position in the lowest decile portfolio and a short position in the highest decile portfolio based on abnormal accruals. Annual returns to the hedge portfolios are reported in Table 3.10, which is directly comparable to Panel A of Table 3 of Xie (2001, p. 366). The mean return over the 22 year period from 1971 to 1992 in Table 3.10 is 7.50 percent with t-statistic of 7.16 and the corresponding figure in Xie is 11.0 percent with t-statistic of 8.43. The lowest decile outperforms the highest decile in 21 of 22 years in Table 3.10, whereas Xie reports that the lowest decile outperforms the highest decile in all 22 years. Overall, results provided in Table 3.10 are similar to those reported in Xie. As in my main analysis, I accumulate returns of individual firms starting July 1 of each year in order to eliminate the problem of unknown portfolio weights, and then I form equal- and value-weighted portfolios. When equal-weighted portfolios are formed, the mean and median return and the proportion of positive returns becomes smaller to some extent but they are still statistically significant at the 1 percent level. This is consistent with what I find in the context of Piotroski (2001) and also consistent with what Xie (2001) reports in his sensitivity test, in which he forms equal-weighted portfolios in every month.  97 The previously discussed analyses in Tables 3.7 to 3.9 show that value weighting dimin- ishes excess returns. In contrast, hedge portfolios formed based on abnormal accruals with value weighting still generate statistically significant profits, although the statistical significance is moderated. The mean annual return on the hedge portfolios is 5.56 percent with t-statistic of 2.16 and the median annual return is 6.59 percent with significance at the 10 percent level. The most striking difference when my results are compared to Xie’s (2001) is the proportion of positive returns. When value-weighted portfolios are formed (after eliminating the problem of unknown portfolio weights), the profitability of the trading strategy becomes much less consistent: the lowest decile outperforms the highest decile in only 15 of 22 years with Z-statistic of 1.71. Al- though the combined impact of the unknown portfolio weights problem and different portfolio weighting on Xie is not as dramatic as that on Piotroski (2000), Table 3.10, taken as a whole, demonstrates that the implementation issues raised in this study are not limited to Piotroski. 3.6 Conclusions This study investigates two aspects relating to the implementability of trading strategies used in studies on accounting-related anomalies. First, the return accumulation approach used in ac- counting studies cannot be replicated in a practical context because the number and identity of individual observations within a portfolio are assigned within a research context before the ac- counting information of all firms in the portfolio would actually be available in real time. Second, the fact that the majority of the firms in the NYSE-Amex-NASDAQ universe are small impedes  98 the implementation of an equal-weighting scheme. As discussed, equal weighting has been the approach used in most accounting studies. I examine these two issues by replicating and extending the analysis in Piotroski (2000). I find that the relationship between Piotroski’s fundamental signals and subsequent returns is part- ly driven by the choice of return accumulation periods and the use of equally weighted returns. When the research design controls for both problems, the relationship between F-Scores and subsequent returns disappears. Because the methods used in Piotroski are typical of those often employed in the accounting literature, my study suggests that evidence of profitable trading strategies and market inefficiency in the literature is likely to be overstated. This study contributes to a stream of research that proposes research design choices or flaws as an explanation of detected mispricing (e.g., Lo and MacKinlay, 1990; Kothari, Shanken, and Sloan, 1995; Kothari, Sabino, and Zack, 2005; Kraft, Leone, and Wasley, 2006). I demon- strate that two research design choices commonly made in accounting studies can bias the evi- dence in favor of finding stock market inefficiency. Of the two research design choices I examine, it appears that the decision to equal-weight rather than value-weight stocks within a portfolio can be the most influential.  99 Table 3.1: Implementability of trading strategies in prior accounting studies Authors (Year published) [Publication outlet]  Portfolio formation methodology  Subject to problem of unknown portfolio weights?*  Piotroski (2000) [Journal of Accounting Research]  Equal-weighting only  Yes  Xie (2001) [The Accounting Review]  Equal-weighting only  Yes#  Beneish and Vargus (2002) [The Accounting Review]  Equal-weighting only  No  Penman and Zhang (2002) [The Accounting Review]  Equal-weighting only  Yes#  Desai, Rajgopal, and Venkatachalam (2004) [The Accounting Review]  Equal-weighting only  Yes#  Hirshleifer, Hou, Teoh, and Zhang (2004) [Journal of Accounting and Economics]  Equal-weighting and value-weighting  No  Richardson, Sloan, Soliman, and Tuna (2005) [Journal of Accounting and Economics]  Equal-weighting only  Yes  Mashruwala, Rajgopal, and Shevlin (2006) [Journal of Accounting and Economics]  Equal-weighting only  No  Penman, Richardson, and Tuna (2007) [Journal of Accounting Research]  Equal-weighting only  Yes  Zhang (2007) [The Accounting Review]  Equal-weighting only  Yes  Dechow, Richardson, and Sloan (2008) [Journal of Accounting Research]  Equal-weighting only  Yes  Note to Table 3.1: This table compiles the results of a survey of recent archival empirical literature related to accounting anomalies. The survey focuses on research studies published in The Accounting Review, Journal of Ac- counting and Economics, and Journal of Accounting Research within a 10-year period starting the year 2000. # denotes a case where a sensitivity test in a particular study addresses problem of unknown portfo- lio weights. *  I classify a particular study as being subject to the problem of unknown portfolio weights when (1) the study accumulates returns for individual firms starting three or four months after their fiscal year-ends and (2) it does not limit its sample to firms with December fiscal year-end.  100 Table 3.2: The sample composition across Analysis 1 and Analysis 2 by F-Score   Unique to Analysis 1 Unique to Analysis 2  F-Score Due to increase in cutoff from year t-1 to year t Due to subse- quent delisting Common to Analysis 1 and Analysis 2 Due to decrease in cutoff from year t-1 to year t Due to suspen- sion of trading  0 11 1 56 7 0 1 64 16 553 66 0 2 150 46 1,593 211 4 3 308 85 2,768 351 6 4 412 112 3,546 528 4 5 401 102 3,816 586 3 6 369 74 3,283 630 8 7 230 52 2,486 485 2 8 141 22 1,428 256 5 9 29 6 360 76 1  Total 2,115 516 19,889 3,196 33  Note to Table 3.2: This table reports the number of observations by F-Score in the final samples of Analysis 1 and Analysis 2. Spanning 32 years from 1976 to 2007, the final sample of Analysis 1 (Analysis 2) is 22,520 (23,118) firm-years representing 6,429 (6,297) firms. In Analysis 1, following Piotroski (2000), returns of individ- ual observations are accumulated starting six months after the fiscal year-end, whereas returns under Analysis 2 are accumulated with a common starting date (i.e., July 1 each year), which is consistent with the approach used in finance studies. Analysis 1 (Analysis 2) employs firm-years in the highest quintile of the previous (current) year’s book-to-market distribution. Thus, the increase (decrease) in the highest quintile cutoff from year t−1 to year t results in unique observations in the final sample of Analysis 1 (Analysis 2). There are two additional sources of differences in the sample composition. First, Analysis 1 requires firms to survive until the end of six months after the fiscal year-end, whereas Analysis 2 requires firms to survive longer, with the exception of firms with December fiscal year-ends. Thus, if a firm delists between the beginning of the return accumulation period of Analysis 1 and that of Analysis 2, then the firm is only included in the sample for Analysis 1. Second, if a firm’s shares are suspended from trading at the beginning of the return accumulation period of Analysis 1 but trading is resumed on or before that of Analysis 2, the firm is only included in the sample of Analysis 2. F-Score represents a summary meas-  101 ure of a firm’s financial condition introduced by Piotroski and it is the sum of the following nine binary signals: (1) F_ROA is equal to one if ROA is positive, and zero otherwise, where ROA is net income before extraordinary items scaled by total assets at the beginning of the year, (2) F_CFO is equal to one if CFO is positive, and zero otherwise, where CFO is cash flows from operations scaled by total assets at the beginning of the year, (3) F_∆ROA is equal to one if ∆ROA is positive, and zero otherwise, where ∆ROA is current year ROA minus prior year ROA, (4) F_ACCRUAL is equal to one if ACCRUAL is negative, and zero otherwise, where ACCRUAL is ROA minus CFO, (5) F_∆LIQUID is equal to one if ∆LIQUID is positive, and zero otherwise, where ∆LIQUID is change in the ratio of total current assets to total cur- rent liabilities from prior year to current year, (6) F_∆LEVER is equal to one if ∆LEVER is negative, and zero otherwise, where ∆LEVER is change in the ratio of total long-term debt to total assets from prior year to current year, (7) EQ_OFFER is equal to one if a firm does not issue common equity, and zero otherwise, (8) F_∆MARGIN is equal to one if ∆MARGIN is positive, and zero otherwise, where ∆MARGIN is change in the gross margin ratio from prior year to current year, and (9) F_∆TURN is equal to one if ∆TURN is positive, and zero otherwise, where ∆TURN is change in the asset turnover ratio from prior year to current year.  102 Table 3.3: The sample composition across Analysis 1 and Analysis 2 by year   Unique to Analysis 1 Unique to Analysis 2  Year Due to increase in cutoff from year t-1 to year t Due to subse- quent delisting Common to Analysis 1 and Analysis 2 Due to decrease in cutoff from year t-1 to year t Due to suspen- sion of trading  1976 0 4 329 298 0 1977 0 10 564 50 1 1978 0 3 544 63 3 1979 0 8 550 63 1 1980 0 12 592 34 2 1981 0 12 595 57 1 1982 0 18 607 42 4 1983 0 4 242 426 3 1984 118 23 727 0 1 1985 0 18 585 155 3 1986 0 15 653 76 1 1987 174 9 687 0 0 1988 0 19 660 9 0 1989 0 21 640 14 0 1990 438 10 645 0 2 1991 0 23 507 175 0 1992 0 11 514 249 3 1993 0 12 564 109 0 1994 112 12 677 0 0 1995 0 17 684 102 0 1996 0 22 775 155 0 1997 0 28 801 177 0 1998 450 29 904 0 0 1999 180 23 853 0 0 2000 276 32 826 0 1 2001 0 23 702 161 1 2002 59 28 895 0 1 2003 0 17 376 441 0 2004 0 11 469 262 0 2005 53 18 701 0 2 2006 0 16 526 78 2 2007 255 8 495 0 1  Total 2,115 516 19,889 3,196 33  Note to Table 3.3: This table reports the number of observations by year in the final samples of Analysis 1 and Analysis 2. Spanning 32 years from 1976 to 2007, the final sample of Analysis 1 (Analysis 2) is 22,520 (23,118) firm-years representing 6,429 (6,297) firms. In Analysis 1, following Piotroski (2000), returns of individ- ual observations are accumulated starting six months after the fiscal year-end, whereas returns under  103 Analysis 2 are accumulated with a common starting date (i.e., July 1 each year). Analysis 1 (Analysis 2) employs firm-years in the highest quintile of the previous (current) year’s book-to-market distribution. Thus, the increase (decrease) in the highest quintile cutoff from year t−1 to year t results in unique obser- vations in the final sample of Analysis 1 (Analysis 2). There are two additional sources of differences in the sample composition. First, Analysis 1 requires firms to survive until the end of six months after the fiscal year-end, whereas Analysis 2 requires firms to survive longer, with the exception of firms with December fiscal year-ends. Thus, if a firm delists between the beginning of the return accumulation pe- riod of Analysis 1 and that of Analysis 2, then the firm is only included in the sample for Analysis 1. Second, if a firm’s shares are suspended from trading at the beginning of the return accumulation period of Analysis 1 but trading is resumed on or before that of Analysis 2, the firm is only included in the sam- ple of Analysis 2.  104 Table 3.4: One-year market-adjusted returns by F-Score   Analysis 1 Analysis 2  F-Score mean median n n% mean median n n%  0 4.64% −24.67% 68 0.3% 13.85% −29.02% 63 0.3% 1 −4.10 −20.50 633 2.8% −7.46 −20.02 619 2.7% 2 4.27 −12.82 1,789 7.9% 0.54 −13.70 1,808 7.8% 3 9.36 −8.81 3,161 14.0% 6.60 −10.22 3,125 13.5% 4 8.46 −6.97 4,070 18.1% 8.11 −5.96 4,078 17.6% 5 11.06 −2.95 4,319 19.2% 8.88 −2.84 4,405 19.1% 6 13.85 −0.38 3,726 16.5% 11.29 −1.74 3,921 17.0% 7 14.76 0.87 2,768 12.3% 12.18 0.30 2,973 12.9% 8 15.83 1.91 1,591 7.1% 13.78 1.91 1,689 7.3% 9 23.41 6.70 395 1.8% 13.74 3.98 437 1.9%  All 10.84 −4.36 22,520 100% 8.64 −4.36 23,118 100%  F-Score 1&2 [A] −3.26 −21.40 701 3.1% −5.49 −21.59 682 3.0% F-Score 8&9 [B] 17.34 3.17 1,986 8.8% 13.78 2.29 2,126 9.2%  [B] − [A] 20.59*** 24.56***   19.27*** 23.89***  Note to Table 3.4: This table presents one-year market-adjusted returns (in percent) over the period of 1976-2007 by F-Score, where the market-adjusted return is the buy-and-hold return less the value-weighted market return. F- Score represents a summary measure of a firm’s financial condition introduced by Piotroski (2000). See Table 3.2 for more details on F-Score. In Analysis 1, following Piotroski, returns of individual observa- tions are accumulated starting six months after the fiscal year-end, whereas returns under Analysis 2 are accumulated with common starting date (i.e., July 1 each year). Differences in mean and median are tested with two-sample t-test and signed rank test, respectively. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.   105 Table 3.5: One-year market-adjusted returns to F-Score-based equal-weighted portfolios Panel A: Returns to Weak, Strong, and All portfolios under Analysis 1   Strong portfolios Weak portfolios All portfolios  Year n one year market-adjusted return n one year market-adjusted return n one year market-adjusted return  1976 261 33.32% 72 28.74% 333 32.33% 1977 404 21.61 170 15.53 574 19.81 1978 376 −0.50 171 −11.03 547 −3.80 1979 372 22.64 186 6.18 558 17.15 1980 420 13.41 184 0.15 604 9.37 1981 426 35.34 181 24.67 607 32.16 1982 382 30.30 243 20.99 625 26.68 1983 174 −1.70 72 −26.38 246 −8.92 1984 563 −4.65 305 −19.06 868 −9.72 1985 323 6.52 280 −11.82 603 −2.00 1986 351 10.68 317 2.69 668 6.89 1987 524 6.35 346 −4.37 870 2.09 1988 392 −9.57 287 −15.91 679 −12.25 1989 359 −11.00 302 −7.94 661 −9.60 1990 614 20.32 479 16.05 1093 18.45 1991 306 26.43 224 18.42 530 23.04 1992 339 32.75 186 18.67 525 27.76 1993 333 14.22 243 11.08 576 12.90 1994 453 2.22 348 2.93 801 2.53 1995 396 −2.65 305 −17.01 701 −8.90 1996 441 −0.33 356 −12.67 797 −5.84 1997 451 −12.35 378 −15.18 829 −13.64 1998 665 18.64 718 28.51 1383 23.76 1999 535 22.51 521 8.69 1056 15.69 2000 604 35.50 530 28.07 1134 32.03 2001 344 12.29 381 15.51 725 13.98 2002 479 59.49 503 61.33 982 60.43 2003 208 23.18 185 −1.18 393 11.71 2004 274 15.45 206 6.51 480 11.61 2005 405 10.05 367 3.48 772 6.93 2006 282 −9.06 260 −16.23 542 −12.50 2007 343 −4.89 415 −9.40 758 −7.36  Mean 13.02***  4.69  9.77*** (t)  (4.37)  (1.41)  (3.19)       Median 12.85***  3.21  10.49*** (signed rank)         (189)           (64)          (150)       No. of positive 22/32**  19/32  21/32* (Z)  (2.12)  (1.06)  (1.77)     106 Table 3.5: One-year market-adjusted returns to F-Score-based equal-weighted portfolios (cont.) Panel B: Returns to Weak, Strong, and All portfolios under Analysis 2   Strong portfolios Weak portfolios All portfolios  Year n one year market-adjusted return n one year market-adjusted return n one year market-adjusted return  1976 502 38.79% 125 35.57% 627 38.15% 1977 427 9.98 188 −0.71 615 6.71 1978 416 −5.47 194 −10.04 610 −6.92 1979 410 30.06 204 23.26 614 27.80 1980 433 11.68 195 0.67 628 8.26 1981 462 45.89 191 44.65 653 45.53 1982 397 9.32 256 1.94 653 6.43 1983 480 −2.71 191 −24.13 671 −8.81 1984 465 −3.50 263 −13.54 728 −7.13 1985 400 9.27 343 −5.04 743 2.66 1986 390 9.44 340 0.26 730 5.16 1987 409 2.94 278 −4.74 687 −0.17 1988 389 −8.78 280 −19.80 669 −13.39 1989 356 −2.64 298 −7.51 654 −4.86 1990 349 17.04 298 17.23 647 17.13 1991 406 31.61 276 12.48 682 23.87 1992 494 18.68 272 16.51 766 17.91 1993 389 6.33 284 5.14 673 5.83 1994 383 2.24 294 9.40 677 5.35 1995 440 −9.62 346 −25.77 786 −16.73 1996 522 −5.14 408 −6.88 930 −5.90 1997 540 −19.39 438 −15.95 978 −17.85 1998 444 12.17 460 26.72 904 19.58 1999 425 33.00 428 14.52 853 23.73 2000 432 38.65 395 27.09 827 33.13 2001 411 11.92 453 12.31 864 12.12 2002 439 51.68 457 45.41 896 48.48 2003 468 8.70 349 6.10 817 7.59 2004 443 11.90 288 9.96 731 11.14 2005 366 7.97 337 5.21 703 6.64 2006 322 −12.91 284 −19.55 606 −16.02 2007 216 −8.92 280 −6.28 496 −7.43  Mean 10.63***  4.83  8.37** (t)  (3.38)  (1.47)  (2.69)   Median 9.30***  3.54  6.53** (signed rank)          (155)            (64)           (118)   No. of positive 22/32**  19/32  21/32* (Z)  (2.12)  (1.06)  (1.77)  Note to Table 3.5: This table presents one-year market-adjusted returns (in percent) to equal-weighted portfolios, where  107 portfolios are formed based on F-Score. F-Score represents a summary measure of a firm’s financial condition introduced by Piotroski (2000). See Table 3.2 for more details on F-Score. Strong (Weak) rep- resents firms with F-Scores of 5 or greater (0 through 4) and All represents all firms. In Analysis 1, fol- lowing Piotroski, returns of individual observations are accumulated starting six months after the fiscal year-end, whereas returns under Analysis 2 are accumulated with a common starting date (i.e., July 1 each year). Differences in mean and median are tested with two-sample t-test and signed rank test, respectively. * , ** , ***  denote two-tail significance at the 10%, 5%, and 1% level, respectively.   108 Table 3.6: The impact of the unknown portfolio weights problem on the profitability of hedge portfolios   Piotroski (2000) replicated Unknown portfolio weights problem eliminated   Analysis 1 under equal-weighting Analysis 2 under equal-weighting Impact of unknown portfolio weights problem  Year   Strong − Weak [A]   Strong − All [B]   Strong − Weak [A*]   Strong − All [B*]  [A] − [A *] [B] − [B*]  1976 4.58% 0.99% 3.22% 0.64% 1.36% 0.35% 1977 6.08 1.80 10.68 3.27 −4.61 −1.47 1978 10.53 3.29 4.57 1.45 5.96 1.84 1979 16.46 5.49 6.80 2.26 9.67 3.23 1980 13.26 4.04 11.01 3.42 2.25 0.62 1981 10.67 3.18 1.24 0.36 9.44 2.82 1982 9.32 3.62 7.38 2.89 1.94 0.73 1983 24.68 7.22 21.41 6.10 3.27 1.13 1984 14.41 5.06 10.04 3.63 4.37 1.44 1985 18.34 8.52 14.32 6.61 4.02 1.91 1986 7.99 3.79 9.18 4.28 −1.19 −0.48 1987 10.73 4.27 7.68 3.11 3.04 1.16 1988 6.34 2.68 11.02 4.61 −4.68 −1.93 1989 −3.06 −1.40 4.87 2.22 −7.93 −3.62 1990 4.27 1.87 −0.20 −0.09 4.46 1.96 1991 8.02 3.39 19.12 7.74 −11.11 −4.35 1992 14.08 4.99 2.17 0.77 11.92 4.22 1993 3.14 1.33 1.19 0.50 1.96 0.83 1994 −0.71 −0.31 −7.15 −3.11 6.44 2.80 1995 14.36 6.25 16.15 7.11 −1.79 −0.86 1996 12.33 5.51 1.75 0.77 10.59 4.74 1997 2.83 1.29 −3.44 −1.54 6.27 2.83 1998 −9.87 −5.12 −14.55 −7.41 4.69 2.28 1999 13.82 6.82 18.48 9.27 −4.66 −2.46 2000 7.43 3.47 11.56 5.52 −4.13 −2.05 2001 −3.22 −1.69 −0.39 −0.21 −2.82 −1.48 2002 −1.84 −0.94 6.27 3.20 −8.11 −4.14 2003 24.35 11.46 2.61 1.11 21.75 10.35 2004 8.94 3.84 1.94 0.76 7.01 3.07 2005 6.57 3.12 2.76 1.32 3.81 1.80 2006 7.17 3.44 6.64 3.11 0.53 0.33 2007 4.50 2.46 −2.64 −1.49 7.14 3.96  Mean 8.33*** 3.24*** 5.80*** 2.26*** 2.53** 0.99* (t) (6.22) (5.75) (4.26) (3.83) (2.13) (1.89)  Median 8.00*** 3.41*** 5.57*** 2.24*** 3.15** 1.14* (signed rank) (232) (223) (194) (189) (105) (93)  No. of positive 27/32*** 27/32*** 26/32*** 26/32*** 22/32** 22/32** (Z) (3.89) (3.89) (3.54) (3.54) (2.12) (2.12)  Note to Table 3.6:  109 This table compares returns (in percent) to hedge portfolios, in which equal-weighted portfolios are formed based on F-Score. F-Score represents a summary measure of a firm’s financial condition intro- duced by Piotroski (2000). See Table 3.2 for more details on F-Score. Strong (Weak) represents firms with F-Scores of 5 or greater (0 through 4) and All represents all firms. In Analysis 1, following Piotroski, returns of individual observations are accumulated starting six months after the fiscal year-end, whereas returns under Analysis 2 are accumulated with a common starting date (i.e., July 1 each year). Differences in mean and median are tested with two-sample t-test and signed rank test, respectively. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  110 Table 3.7: One-year market-adjusted returns to F-Score-based value-weighted portfolios Returns to Weak, Strong, and All portfolios under Analysis 2   Strong portfolios Weak portfolios All portfolios  Year n one year market-adjusted return n one year market-adjusted return n one year market-adjusted return  1976 502 8.09% 125 22.11% 627 9.22% 1977 427 3.79 188 −6.01 615 1.67 1978 416 −4.92 194 −9.35 610 −6.37 1979 410 9.94 204 3.91 614 7.87 1980 433 9.89 195 4.94 628 8.38 1981 462 7.52 191 15.32 653 8.97 1982 397 10.62 256 19.77 653 15.34 1983 480 5.49 191 −6.45 671 2.47 1984 465 −2.71 263 −25.97 728 −9.81 1985 400 26.23 343 5.48 743 17.16 1986 390 7.29 340 10.60 730 8.32 1987 409 14.37 278 −2.34 687 6.86 1988 389 −12.34 280 −8.08 669 −11.02 1989 356 −5.03 298 −10.95 654 −7.08 1990 349 21.75 298 4.72 647 13.94 1991 406 12.77 276 0.35 682 7.56 1992 494 6.63 272 −5.93 766 1.62 1993 389 −0.09 284 −8.70 673 −3.71 1994 383 −8.21 294 −10.71 677 −8.94 1995 440 −8.91 346 −12.84 786 −10.07 1996 522 −2.24 408 −0.11 930 −1.50 1997 540 −10.47 438 −13.44 978 −11.33 1998 444 −22.16 460 11.90 904 −7.70 1999 425 46.01 428 41.13 853 43.71 2000 432 15.05 395 −7.78 827 0.52 2001 411 −8.67 453 6.61 864 −1.01 2002 439 36.62 457 22.56 896 28.32 2003 468 13.40 349 5.11 817 11.63 2004 443 4.21 288 7.07 731 4.72 2005 366 −0.29 337 25.90 703 7.45 2006 322 −0.44 284 8.81 606 3.06 2007 216 −6.42 280 −0.45 496 −3.91  Mean 5.21**  2.72  3.95* (t)  (2.09)  (1.11)  (1.89)   Median 4.85*  2.13  2.77 (signed rank)           (97)            (33)            (84)   No. of positive 18/32  17/32  20/32 (Z)  (0.71)  (0.35)  (1.41)  Note to Table 3.7: This table presents one-year market-adjusted returns (in percent) to value-weighted portfolios, where  111 portfolios are formed based on F-Score. The weight assigned to a firm is determined based on its market capitalization at the beginning of return accumulation date (i.e., July 1 each year). F-Score represents a summary measure of a firm’s financial condition introduced by Piotroski (2000). See Table 3.2 for more details on F-Score. Strong (Weak) represents firms with F-Scores of 5 or greater (0 through 4) and All represents all firms. Differences in mean and median are tested with two-sample t-test and signed rank test, respectively. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.  112 Table 3.8: The impact of the unknown portfolio weights problem and change in portfolio weighting on the profitability of hedge portfolios   Piotroski (2000) replicated Unknown portfolio weights problem eliminated and different portfolio weighting applied   Analysis 1 under equal-weighting Analysis 2 under value-weighting Impact of unknown portfolio weights problem and change in portfolio weighting  Year   Strong − Weak [A]   Strong − All [B]   Strong − Weak [A*]   Strong − All [B*]  [A] − [A *] [B] − [B*]  1976 4.58% 0.99% −14.02% −1.13% 18.60% 2.12% 1977 6.08 1.80 9.80 2.12 −3.73 −0.32 1978 10.53 3.29 4.43 1.45 6.10 1.85 1979 16.46 5.49 6.03 2.07 10.43 3.42 1980 13.26 4.04 4.95 1.51 8.31 2.53 1981 10.67 3.18 −7.80 −1.44 18.47 4.63 1982 9.32 3.62 −9.15 −4.72 18.47 8.34 1983 24.68 7.22 11.95 3.02 12.73 4.20 1984 14.41 5.06 23.26 7.10 −8.84 −2.03 1985 18.34 8.52 20.75 9.07 −2.41 −0.55 1986 7.99 3.79 −3.31 −1.03 11.30 4.82 1987 10.73 4.27 16.71 7.51 −5.98 −3.25 1988 6.34 2.68 −4.26 −1.32 10.59 4.00 1989 −3.06 −1.40 5.92 2.04 −8.98 −3.44 1990 4.27 1.87 17.03 7.81 −12.76 −5.94 1991 8.02 3.39 12.41 5.20 −4.39 −1.81 1992 14.08 4.99 12.56 5.01 1.52 −0.02 1993 3.14 1.33 8.61 3.62 −5.47 −2.30 1994 −0.71 −0.31 2.50 0.72 −3.21 −1.03 1995 14.36 6.25 3.93 1.15 10.43 5.09 1996 12.33 5.51 −2.13 −0.74 14.46 6.25 1997 2.83 1.29 2.96 0.85 −0.14 0.44 1998 −9.87 −5.12 −34.05 −14.46 24.19 9.34 1999 13.82 6.82 4.88 2.30 8.94 4.52 2000 7.43 3.47 22.84 14.53 −15.41 −11.06 2001 −3.22 −1.69 −15.29 −7.66 12.07 5.97 2002 −1.84 −0.94 14.06 8.30 −15.90 −9.24 2003 24.35 11.46 8.28 1.76 16.07 9.70 2004 8.94 3.84 −2.86 −0.51 11.80 4.35 2005 6.57 3.12 −26.19 −7.74 32.76 10.86 2006 7.17 3.44 −9.25 −3.50 16.42 6.94 2007 4.50 2.46 −5.97 −2.51 10.48 4.98  Mean 8.33*** 3.24*** 2.49 1.26 5.84*** 1.98** (t) (6.22) (5.75) (1.06) (1.28) (2.75) (2.15)  Median 8.00*** 3.41*** 4.65 1.48* 9.68*** 2.98** (signed rank) (232) (223)          (76)          (91) (135) (119)  No. of positive 27/32*** 27/32*** 20/32 20/32 20/32 20/32 (Z) (3.89) (3.89) (1.41) (1.41) (1.41) (1.41)   113 Note to Table 3.8: This table compares returns (in percent) to hedge portfolios, in which portfolios are formed based on F- Score. F-Score represents a summary measure of a firm’s financial condition introduced by Piotroski (2000). See Table 3.2 for more details on F-Score. Strong (Weak) represents firms with F-Scores of 5 or greater (0 through 4) and All represents all firms. In Analysis 1, following Piotroski, returns of individual observations are accumulated starting six months after the fiscal year-end, whereas returns under Analysis 2 are accumulated with a common starting date (i.e., July 1 each year). For value-weighting, the weight assigned to a firm is determined based on its market capitalization at the beginning of the return accumu- lation date. Differences in mean and median are tested with two-sample t-test and signed rank test, respec- tively. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.   114 Table 3.9: Profitability of implementing F-Score-based hedge portfolios multiple times a year Panel A: Profitability of implementing F-Score-based hedge portfolios twice a year   V-W Portfolios formed on January 1 [FYE1/31 to FYE6/30] V-W Portfolios formed on July 1 [FYE7/31 to FYE12/31]  Year n Strong:Weak:All Strong − Weak Strong − All n Strong:Weak:All Strong − Weak Strong − All  1976 135:31:166 25.42% 6.41% 362:97:459 −22.40% −1.51% 1977 118:48:166 12.79 2.58 323:132:455 8.94 1.87 1978 116:52:168 −18.42 −4.25 303:141:444 5.42 1.81 1979 121:70:191 5.37 1.88 294:136:430 7.23 2.50 1980 125:64:189 −36.31 −9.56 313:124:437 6.45 1.91 1981 141:66:207 2.08 0.47 330:136:466 −8.55 −1.70 1982 141:66:207 −4.25 −1.63 258:190:448 −9.90 −5.51 1983 133:71:204 14.85 4.56 357:124:481 12.48 3.23 1984 153:88:241 14.57 1.51 321:188:509 20.02 6.80 1985 132:94:226 −7.03 −4.39 272:254:526 20.61 8.55 1986 127:112:239 −17.49 −10.75 274:238:512 −6.58 −2.29 1987 132:113:245 −10.99 −2.61 291:182:473 22.38 10.19 1988 125:105:230 27.27 11.00 266:183:449 −9.02 −3.00 1989 119:106:225 −12.39 −5.12 248:200:448 5.75 1.93 1990 137:88:225 −19.39 −5.08 229:210:439 19.50 9.76 1991 115:120:235 22.73 14.90 296:170:466 16.13 5.94 1992 153:89:242 22.92 9.32 344:187:531 4.75 1.86 1993 136:82:218 3.37 1.31 260:202:462 6.93 3.38 1994 117:88:205 −35.48 −19.50 271:212:483 1.06 0.25 1995 115:103:218 −6.23 −3.26 324:245:569 2.24 0.61 1996 120:118:238 15.62 8.10 406:287:693 0.97 0.29 1997 160:97:257 10.90 2.34 371:351:722 −0.80 −0.26 1998 129:110:239 0.24 0.05 340:368:708 −39.71 −19.02 1999 102:109:211 20.95 13.64 331:323:654 −4.77 −2.05 2000 103:81:184 17.35 3.84 342:324:666 33.72 24.86 2001 88:99:187 24.22 10.37 327:363:690 4.32 2.11 2002 84:91:175 26.92 20.57 359:379:738 12.61 7.40 2003 100:71:171 3.68 0.79 365:261:626 17.62 2.78 2004 101:59:160 −16.77 −3.55 346:234:580 3.96 0.78 2005 73:70:143 6.96 4.09 284:273:557 −31.13 −7.91 2006 69:69:138 10.35 6.44 256:219:475 −12.39 −4.37 2007 61:65:126 −17.61 −5.32 172:225:397 −1.38 −0.57  Avg.  118:84:202   307:224:531     Strong − Weak Strong − All  Mean 2.70 1.56 (t) (1.30) (1.67)   Median 4.54* 1.66* (signed rank)                           (248)                              (269)   No. of positive 41/64** 41/64** (Z) (2.25) (2.25)   115 Table 3.9: Profitability of implementing F-Score-based hedge portfolios multiple times a year (cont.) Panel B: Profitability of implementing F-Score-based hedge portfolios four times a year  Average n (Strong:Weak:All)  V-W Portfolios formed on January 1 [FYE4/30 to FYE6/30] V-W Portfolios formed on April 1 [FYE7/31 to FYE9/30] V-W Portfolios formed on July 1 [FYE10/30 to FYE12/31] V-W Portfolios formed on October 1 [FYE1/31 to FYE3/31]  60:43:103 52:38:89 256:187:444 60:42:102    Strong − Weak Strong − All  Mean 1.89 0.99 (t) (0.97) (1.14)   Median 5.02* 1.39** (signed rank)                           (778)                              (879)   No. of positive 80/128*** 80/128*** (Z) (2.83) (2.83)  Panel C: Profitability of implementing F-Score-based hedge portfolios six times a year  Average n (Strong:Weak:All)  V-W Portfolios formed on January 1 [FYE5/31 & FYE6/30] V-W Portfolios formed on May 1 [FYE9/30 & FYE10/31] V-W Portfolios formed on September 1 [FYE1/31 & FYE2/28]   49:36:86 44:33:77 30:21:52   V-W Portfolios formed on March 1 [FYE7/31 & FYE8/31] V-W Portfolios formed on July 1 [FYE11/30 & FYE12/31] V-W Portfolios formed on November 1 [FYE3/31 & FYE4/30]   22:14:36 242:177:419 39:27:66    Strong − Weak Strong − All  Mean 3.38* 2.20** (t) (1.71) (2.46)   Median 2.36** 0.43** (signed rank)                         (1,534)                            (1,635)   No. of positive 109/192* 109/192* (Z) (1.88) (1.88)  Note to Table 3.9: This table reports returns (in percent) to hedge portfolios, in which F-Score-based value-weighted portfo- lios are formed multiple times a year. F-Score represents a summary measure of a firm’s financial condi- tion introduced by Piotroski (2000). See Table 3.2 for more details on F-Score. Strong (Weak) represents firms with F-Scores of 5 or greater (0 through 4) and All represents all firms. For value-weighting, the  116 weight assigned to a firm is determined based on its market capitalization at the beginning of the return accumulation date. Differences in mean and median are tested with two-sample t-test and signed rank test, respectively. *, **, *** denote two-tail significance at the 10%, 5%, and 1% level, respectively.   117 Table 3.10: The impact of the unknown portfolio weights problem and change in portfolio weighting on the profitability of hedge portfolios in the context of Xie (2001)   Xie (2001) replicated Unknown portfolio weights problem eliminated  Year n Lowest:Highest Lowest decile – Highest decile (equal-weighting) n Lowest:Highest Lowest decile – Highest decile (equal-weighting) Lowest decile – Highest decile (value-weighting)  1971 130:130 4.91% 130:130 2.83% 12.72% 1972 165:165 5.02 165:165 2.67 –5.88 1973 213:213 14.99 213:213 24.34 –10.90 1974 288:288 7.13 289:289 1.87 25.92 1975 319:319 6.80 320:320 2.23 16.31 1976 320:320 8.36 319:319 3.88 7.29 1977 311:311 12.64 308:308 8.40 –3.67 1978 300:300 4.33 297:297 2.46 0.99 1979 296:296 8.72 293:293 –2.10 0.55 1980 301:301 2.89 297:297 1.91 10.68 1981 302:302 12.59 298:298 12.97 –11.36 1982 320:320 0.34 316:316 3.51 16.48 1983 327:327 7.74 323:323 1.04 18.37 1984 339:339 6.38 332:332 4.50 30.24 1985 352:352 11.69 344:344 16.48 9.01 1986 345:345 5.81 338:338 5.19 2.83 1987 354:354 5.16 346:346 6.95 –3.04 1988 377:377 –3.30 369:369 –7.13 5.88 1989 373:373 5.59 365:365 4.08 –4.12 1990 370:370 14.23 364:364 10.57 10.31 1991 369:369 17.64 361:361 6.98 10.18 1992 373:373 5.31 369:369 –2.44 –16.59   Avg. 311:311  307:307    Mean  7.50***  5.05*** 5.56** (t)  (7.16)  (3.55) (2.16)    Median 6.59***  3.70*** 6.59* (signed rank)         (123.5)            (99.5)           (56.5)    No. of positive 21/22***  19/22*** 15/22* (Z)  (4.26)  (3.41) (1.71)  Note to Table 3.10: This table reports size-adjusted returns (in percent) to hedge portfolios originally documented in Xie (2001). Portfolio deciles are formed annually based on the ranking of abnormal accruals estimated from cross-sectional version of Jones’ (1991) model. The hedge portfolio is formed by taking a long position in the lowest decile portfolio and a short position in the highest decile portfolio. Differences in mean and  118 median are tested with two-sample t-test and signed rank test, respectively. *, **, *** denote two-tail sig- nificance at the 10%, 5%, and 1% level, respectively.  119 Figure 3.1: Illustration of the unknown portfolio weights problem    As of Oct. 30, year t   As of Apr. 30, year t+1 time       F-Score   0 9 Total Jun. 30 FYE firms 13 27 40 Dec. 31 FYE firms ? ? 60 Total position $3,000 short $3,000 long $0  Applicable weight  to individual firm ? ?  Individual position ? ? $0        F-Score       0 9 Total      Jun. 30 FYE firms 13 27 40      Dec. 31 FYE firms 12 48 60   Total position $3,000 short $3,000 long $0      Applicable weight  To individual firm 1/25 1/75    Individual position $120 short $40 long $0    120 Chapter 4: Conclusions In an informationally efficient market, future price changes cannot be forecasted because the current price already fully incorporates the information available to all market participants. Early capital market studies (e.g., Ball and Brown, 1968; Brown, 1968; Fama, Fisher, Jensen, and Roll, 1969) largely supported this notion of market efficiency but later studies (e.g., Foster, Olsen, and Shevlin, 1984; Bernard and Thomas, 1990; Sloan, 1996) with more refined data challenge mar- ket efficiency. This dissertation investigates explanations for stock market anomalies related to accounting information as documented by Dichev (1998) and Piotroski (2000). The bankruptcy risk anomaly, originally documented by Dichev (1998), refers to the em- pirical regularity in which a composite measure of bankruptcy risk predicts future returns. Taken as a whole, the first study of the dissertation demonstrates that Dichev’s bankruptcy risk anomaly is a manifestation of investors’ under (over)-pricing of cash flows (accrual) component of earn- ings, i.e., Sloan’s (1996) accrual anomaly. This study contributes to the existing research in sev- eral ways. First, it provides an alternative explanation for Dichev’s findings. In this sense, this study is complementary to the explanations provided by Griffin and Lemmon (2002) and George and Hwang (2010). Second, the study highlights that the choice of bankruptcy risk measure can lead to different conclusions. Third, by relating the bankruptcy risk anomaly to the accrual anomaly, it contributes to a stream of research that investigates the relationship between anoma- lies (e.g., Collins and Hribar, 2000; Desai, Rajgopal, and Venkatachalam, 2004).  121 One limitation of the first study is that my findings are limited to the case of Dichev (1998). Subsequent studies that follow Dichev use their own measures of bankruptcy risk and thus, this study cannot address their results. As shown in my first study, their findings could be a manifestation of other anomalies but such an assessment would be beyond the scope of this study. The second study of the dissertation investigates the effects of two potentially problem- atic research design choices that are often made in accounting-based studies of anomalies. I ex- plore these issues by re-examining the results in Piotroski (2000). I find that the relationship between Piotroski’s fundamental signals and subsequent returns is partly driven by the choice of return accumulation periods and the use of equally weighted returns. When the research design controls for both problems, the relationship between his fundamental signals and subsequent returns disappears. Because the methods used in Piotroski are typical of those often employed in the accounting literature, this study suggests that evidence of profitable trading strategies and market inefficiency in the literature is likely to be overstated. Therefore, it contributes to a stream of research that proposes research design choices or flaws as an explanation of detected mispricing (e.g., Lo and MacKinlay, 1990; Kothari, Shanken, and Sloan, 1995; Kothari, Sabino, and Zack, 2005; Kraft, Leone, and Wasley, 2006). Studies that document anomalies, to varying extent, are subject to criticisms that research design flaws or omitted risk factors are responsible for the anomalous returns. Such studies need to be especially careful to rule out explanations other than informational inefficiency in securities  122 markets, and in some cases, existing anomalies documented in prior research. This dissertation explores alternative explanations for stock market anomalies documented in two separate studies by Dichev (1998) and Piotroski (2000). In the case of Dichev, I find that what appeared initially to be a new anomaly related to bankruptcy risk is a manifestation of the anomaly previously documented by Sloan (1996). 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The Accounting Review 76 (3): 357−374. Zhang, X. F. 2007. Accruals, investment, and the accrual anomaly. The Accounting Review 82 (5): 1333−1363. Zmijewki, M. E. 1984. Methodological issues related to the estimation of financial distress pre- diction models. Journal of Accounting Research 22 (Supplement): 59−82.   130 Appendices Appendix A Estimation of Hillegeist et al.’s (2004) BSM-Prob  Hillegeist et al. (2004) modify the original option-pricing equation as follows: ( ) ( ) ( ) ,T rT TE A 1 2 AV V e N d Xe N d 1 e Vδ δ− − −= − + −  (A1) where N(d1) and N(d2) are the standard cumulative normal distribution of d1 and d2, respectively, and ln[ / ] ( ( / )) , 2 A A 1 A V X r 2 Td T δ σ σ + − + =  (A2) and ,2 1 Ad d Tσ= −  (A3) VE is the current market value of equity; VA is the current market value of assets; X is the face value of debt maturing at time T; r is the continuously compounded risk-free rate; δ is the divi- dend rate expressed in terms of VA; and σA is the standard deviation of assets returns. They make two modifications to the traditional option-pricing model. The VAe−δT term accounts for the re- duction in the value of the assets due to the dividends that are distributed before time T. The addition of the (1 − e−δT)VA term is necessary because it is the equity holders who receive the dividends. Under the BSM model, the probability of bankruptcy is simply the probability that the market value of assets, VA, is less than the face value of the liabilities, X, at time T. The BSM model assumes that the natural log of future asset values is distributed normally as follows: ln ( ) ln , , 2 2A A A AV t N V t t2 σµ δ σ  + − −      ∼  (A4) where µ is the continuously compounded expected return on assets. Then, as shown in McDonald (2002, p. 604), the probability that VA(T) < X is, as follows:  131 ln( / ) ( ( / )) - . 2 A A A V X 2 TN BSM Prob T µ δ σ σ  + − − − =      (A5) Equation (A5) shows that the probability of bankruptcy is a function of the distance between the current value of the firm’s assets and the face value of its liabilities ln(VA/X) adjusted for the expected growth in asset values (µ − δ) relative to asset volatility (σA). Note that the value of the call option in equation (A1) is not a function of µ because equation (A1) is derived under the assumption of risk-neutrality. However, the probability of bankruptcy depends upon the actual distribution of future asset values, which is a function of µ. To empirically estimate BSM-Prob from equation (A5), the market value of assets, VA, asset volatility, σA, and the expected return on assets, µ, need to be estimated because these val- ues are not directly observable. In the first step, Hillegeist et al. (2004) estimate the values of VA and σA by simultaneously solving equation (A1) and the following optimal hedge equation:28 ( ) .E E1 T A A VN d V e δ σ σ− =  (A6) VE is set equal to the total market value of equity at the end of the firm’s fiscal year ending in calendar year t−1. σE is computed using daily return data from the CRSP over the entire fiscal year ending in calendar year t−1. The strike price X is set equal to the book value of total liabili- ties, T equals one year, and r is the one-year Treasury bill rate. The dividend rate, δ, is the sum of common and preferred dividends divided by sum of market value of equity plus total liabilities at   28  There are cases where the iterative process can not solve the two equations. This occurs because of the boundary condition which requires solutions of the equations to be positive. Accordingly, few observa- tions with valid data are lost; the number of lost observations is less than 0.01 percent of the total number of firm-years in my sample. Thus, I do not expect that this deletion will make any change in the tenor of the results.  132 the end of the fiscal year. Note that all applicable accounting data are from financial statements with fiscal years ending calendar year t−1 so that BSM-Prob is estimated on an ex ante basis. In the second step, the expected market return on assets, µ, is estimated based on the ac- tual return on assets during the previous year as follows: ( )  ( )( ) ,( ) A A A V t dividends V t 1 t V t 1 µ + − −= −  (A7) where dividends is the sum of the common and preferred dividends declared during the year. Note that this process is based on the estimates of VA that were computed in the first step. When expected returns are below the risk-free rate (above one), Hillegeist et al. (2004) set them equal to the risk-free rate (one).  133 Appendix B An association of a variable with a score: An econometric interpretation  Without a loss of generality, suppose that there are n firms and each firm has its score S, which is a linear combination of k components (e.g., accounting variables). Using matrices, I can express scores for n firms as: =S Xα ,  (B1) where S = n × 1, X = n × k, and α = k × 1. Then, an association of a variable Y (e.g., returns) with the score S can be written as: ( ) 0β ′ ′= ≠-1S S S Y ,  (B2) where Y is an n × 1. Substituting (B1) into (B2), I obtain: ( ) 0β ′ ′ ′ ′= ≠-1α X Xα α X Y .  (B3) With respect to the numerator (α'X'Y), since α ≠ 0, the following holds: ′ ≠X Y 0 .  (B4) The denominator (α'X'Xα) is non-zero as long as X'X is positive definite (i.e., rank (X) = k). This condition is satisfied as long as one component of the score is not a linear combination of the other components. Thus, it follows that, in a regression of variable Y on X (the component of the score), the resulting coefficients is a non-zero vector: ( ) 1 2 k γ γ γ      ′ ′ = = ≠       -1X X X Y γ 0  .  (B5) Therefore, when there is an association between a variable and a score, it must be true that one or more components of the score have nontrivial associations with the variable, holding all other components constant. 

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