EMPIRICAL TESTS OF ASSET PRICING MODELS DISSERTATION Presented in Partial Ful…llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Philip R. Davies, B.Sc., M.Sc. * * * * * The Ohio State University 2007 Dissertation Committee: Professor R.M. Stulz, Adviser Professor G.M. Allenby Professor G.A. Karolyi Approved by Adviser Graduate Program in Business Administration ABSTRACT The Capital Asset Pricing Model (CAPM) developed by Sharpe (1964) and Lint- ner (1965) is widely viewed as one of the most important contributions to our under- standing of …nance over the last 50 years. The CAPM predicts that non-diversi…able risk () is the only risk that matters for the pricing of assets, and that an asset’s expected return is a positive linear function of its non-diversi…able risk. However, the empirical p erformance of the CAPM has been poor. This poor performance may re‡ect theoretical failings. Alternatively, it may be due to di¢ culties in implementing valid tests of the model. This dissertation focuses on the second possibility. In the …rst essay I develop a Bayesian approach to test the cross-sectional predic- tions of the CAPM at the …rm level. Using a broad cross-section of NYSE, AMEX, and NASDAQ listed stocks over the period July 1927 - June 2005, I …nd evidence of a robust positive relation between  and average returns. Fama and French (1993) pro- pose two additional risk factors related to …rm size and book-to-market equity. I …nd no evidence that these additional risk factors help to explain the cross-sectional vari- ation in average returns. These results are consistent with the empirical predictions of the CAPM. The use of p ortfolios as test assets in cross-sectional tests of asset pricing models is widespread, principally to help mitigate statistical problems. However, there is a considerable theoretical literature showing that the use of portfolios can make bad ii models look good, and good models look bad. In the second essay I investigate whether inferences from portfolio level studies can be generalized to the …rm level. Using the Bayesian approach developed in the …rst essay, I …nd that inferences at the portfolio level are closely linked to the way in which portfolios are formed, rather than the underlying …rm level associations. These results raise questions about what we can really learn from empirical asset pricing studies that use portfolios as test assets. iii ACKNOWLEDGMENTS I wish to thank my adviser, René Stulz, for his helpful comments, patience, and advice during my dissertation research. Andrew Karolyi introduced the …eld of em- pirical asset pricing to me, and provided helpful comments and suggestions for my dissertation. I would also like to thank Greg Allenby for the time and e¤ort that he put into my education. His comments and encouragement have been invaluable. I hope that I will be able to inspire students in the same way that he has inspired me. Thanks also to Bernadette Minton for her help and advice throughout my time at Ohio State. My parents, Geo¤ and Eleanor Davies, and my sister, Jo Davies, have supported me every step of the way, and it goes without saying that I would not have made it through the PhD program without the help and support of my friends and colleagues, Rei-Ning Chen, Chuan Liao, An Chee Low, Taylor Nadauld, Haoqing Pan, Robyn Scholl, and Jérôme Taillard. I also wish to thank Cli¤ord Ball, Long Chen, Eugene Fama, Satadru Hore, An- drew Snell, Ashish Tiwari, and seminar participants at Michigan State University, the Ohio State University, Southern Methodist University, SUNY Bu¤alo, the University of Colorado at Boulder, the University of Connecticut, the University of Edinburgh, the University of Iowa, the University of Warwick, and Vanderbilt University for helpful comments and suggestions. iv VITA February 8, 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . Born — Bromley, United Kingdom 2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.Sc. Accounting and Finance — Uni- versity of Warwick 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M.Sc. Economics and Finance — Uni- versity of Warwick PUBLICATIONS Research Publications A. Abhyankar and P. Davies. "Market Timing and Economic Value: Evidence from the Short Rate Revisited". Finance Letters 3, 1-9, 2005. FIELDS OF STUDY Major Field: Business Administration Concentration: Finance v TABLE OF CONTENTS Page Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Chapters: 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Reviving the CAPM: A Bayesian approach for testing asset pricing models 6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 The CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Model Speci…cation . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Testing the CAPM . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.3 Model Estimation . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.4 Evaluating competing model speci…cations . . . . . . . . . . 20 2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.1 The CAPM at the …rm level using portfolio s . . . . . . . 22 2.4.2 The CAPM at the …rm level using …rm-speci…c s . . . . . 23 2.4.3 The Fama-French 3 Factor model at the …rm level using …rm- speci…c s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.4 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 vi 3. Testing Asset Pricing Models: Firms vs Portfolios . . . . . . . . . . . . . 42 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2.1 Model Speci…cation . . . . . . . . . . . . . . . . . . . . . . 47 3.2.2 Model Estimation . . . . . . . . . . . . . . . . . . . . . . . 47 3.2.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . 49 3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.4.1 The CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4.2 Alternate Asset Pricing Models . . . . . . . . . . . . . . . . 61 3.4.3 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Appendices: A. Estimation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 B. Additional Empirical Results for Chapter 2 . . . . . . . . . . . . . . . . . 99 C. Additional material for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 105 C.1 Portfolio Formation Procedures . . . . . . . . . . . . . . . . . . . . 105 C.2 Variation in …rm level s over time . . . . . . . . . . . . . . . . . . 106 vii LIST OF TABLES Table Page 2.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Empirical tests of asset pricing models: July 1927 - June 2005 . . . . 35 2.3 Empirical tests of asset pricing models: July 1927 - June 1963 . . . . 37 2.4 Empirical tests of asset pricing models: July 1963 - June 2005 . . . . 39 2.5 Empirical tests of asset pricing models: Variance-Covariance Matrix . 40 2.6 The fully conditional CAPM: July 1927 - June 2005 . . . . . . . . . . 41 3.1 Empirical tests of the CAPM . . . . . . . . . . . . . . . . . . . . . . 79 3.2 Empirical tests of the CAPM with Human Capital . . . . . . . . . . . 81 3.3 Empirical tests of the Consumption CAPM . . . . . . . . . . . . . . . 83 3.4 Empirical tests of the Fama-French 3 Factor Model . . . . . . . . . . 85 3.5 Empirical tests of the Fama-French 3 Factor Model . . . . . . . . . . 87 3.6 Firm characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.7 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 B.1 Empirical tests of asset pricing models: July 1927 - June 2005 . . . . 100 B.2 Empirical tests of asset pricing models: July 1927 - June 1963 . . . . 102 viii B.3 Empirical tests of asset pricing models: July 1963 - June 2005 . . . . 104 C.1 Transition Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 ix LIST OF FIGURES Figure Page 2.1 Posterior distribution plots for the risk premium, c m , after controlling for …rm size, at return horizons of 1 - 6 years . . . . . . . . . . . . . . 30 2.2 Posterior distributions for the intercept . . . . . . . . . . . . . . . . . 31 3.1 Posterior distribution plots for the risk premium, c m , in the simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2 Posterior distribution plots for the risk premium, c m , at a return horizon of 4 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.3 The distribution of s at a 4 year return horizon . . . . . . . . . . . . 73 3.4 The distribution of …rm level s at a 4 year return horizon . . . . . . 74 3.5 The distribution of …rm level HML s at a 4 year return horizon . . . 75 3.6 Price indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.7 Posterior distribution plots for the Fama-French 3 factor model: July 1965 - June 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 C.1 Di¤erences between pre-ranking and contemp oraneous s at a 4 year return horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 x [...]... test assets in cross-sectional tests of asset pricing models is to reduce the impact of measurement error problems However, cautions regarding the use of portfolios as test assets abound in the literature Theoretical work shows that the use of portfolios can make bad asset pricing models look good (Roll 1977) On the other hand, Kan (2004) shows that the use portfolios can also make good asset pricing models. .. portfolios as test assets rather than individual …rms I choose to examine the CAPM at the …rm level rather than the portfolio level for three reasons First, cautions regarding the use of portfolios as test assets abound in the literature For example, Kan (2004) demonstrates that the use portfolios can not only make good asset pricing models look bad, but also make bad asset pricing models look good Second,... speci…cations To compare the relative performance of di¤erent empirical speci…cations I compute the log marginal density using the importance sampling method of Newton and Raftery (1994) This is a Bayesian measure of model …t which includes an implicit penalty for models with a large number of parameters To get a better sense of how well di¤erent models perform in terms of in-sample explanatory power I also calculate... REVIVING THE CAPM: A BAYESIAN APPROACH FOR TESTING ASSET PRICING MODELS 2.1 Introduction The capital asset pricing model of Sharpe (1964), Lintner (1965), and Black (1972) has shaped the way that academics and practitioners think about risk and return The central prediction of the CAPM is that the aggregate wealth portfolio is mean-variance e¢ cient The e¢ ciency of the aggregate wealth portfolio implies that... conditional consumption CAPM Second, the empirical tests of the conditional models proposed by Jagannathan and Wang (1996) and Lettau and Ludvigson (2001) ignore the theoretical restrictions on cross-sectional slope coe¢ cients Lewellen and Nagel (2006) argue that imposing such restrictions could greatly reduce the explanatory power of the proposed asset pricing models Therefore it is not clear whether... associated with …rm size (SMB) and book-to-market equity (HML) They show that the empirical performance of their 3 factor model is superior to that of the CAPM The poor empirical performance of the CAPM may re‡ theoretical ect failings Alternatively, it may be caused by di¢ culties in implementing valid tests of the model The focus of my dissertation is on the latter possibility Researchers seeking to examine... heterogeneity are in the estimation of s, while explicitly controlling for the inherent uncertainty associated with time varying …rm-speci…c s Second, the Bayesian approach is able to overcome the problems with the classical two-step tests of asset pricing models identi…ed by Kan and Zhang (1999) In an extreme setting where a risk factor is useless, de…ned as being independent of all the asset returns, Kan and... e¢ ciency of the aggregate wealth portfolio implies that 1) the only risk that matters for the pricing of …nancial assets is non-diversi…able risk, and 2) a …nancial asset expected s return is a positive linear function of its non-diversi…able risk Today the CAPM is still widely used by academics and practitioners to estimate the cost of capital for …rms, and to evaluate the performance of investment... While much of the evidence presented in table 2.2 is consistent with the empirical predictions of the CAPM, …rm size is negatively related to average returns for all model speci…cations Berk (1995) argues that an asset pricing model should not be rejected solely on the basis of the …nding that …rm size is negatively related to average returns, since such a relation will exist if the asset pricing model...CHAPTER 1 INTRODUCTION Asset pricing refers to the process by which the prices of …nancial assets are determined, and the resulting relationships between expected returns and the risks associated with those returns Over four decades ago Sharpe (1964) and Lintner (1965) developed the Capital Asset Pricing Model (CAPM) Building on the pathbreaking work of Markowitz (1959), Sharpe (1964) and . Empirical tests of asset pricing models: July 1927 - June 1963 . . . . 37 2.4 Empirical tests of asset pricing models: July 1963 - June 2005 . . . . 39 2.5 Empirical tests of asset pricing models: . 89 B.1 Empirical tests of asset pricing models: July 1927 - June 2005 . . . . 100 B.2 Empirical tests of asset pricing models: July 1927 - June 1963 . . . . 102 viii B.3 Empirical tests of asset pricing. EMPIRICAL TESTS OF ASSET PRICING MODELS DISSERTATION Presented in Partial Ful…llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State