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Using Stocks or Portfolios in Tests of Factor Models

Published online by Cambridge University Press:  01 April 2019

Andrew Ang ,
Jun Liu  and
Krista Schwarz Open the ORCID record for Krista Schwarz [Opens in a new window]
Andrew Ang
Affiliation:
Ang, [email protected], Blackrock Incorporated
Jun Liu
Affiliation:
Liu, [email protected], University of California San Diego Rady School of Management
Krista Schwarz*
Affiliation:
Schwarz, [email protected], University of Pennsylvania Wharton School
*
Schwarz (corresponding author), [email protected]
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Abstract

We examine the efficiency of using individual stocks or portfolios as base assets to test asset pricing models using cross-sectional data. The literature has argued that creating portfolios reduces idiosyncratic volatility and allows more precise estimates of factor loadings, and consequently risk premia. We show analytically and empirically that smaller standard errors of portfolio beta estimates do not lead to smaller standard errors of cross-sectional coefficient estimates. Factor risk premia standard errors are determined by the cross-sectional distributions of factor loadings and residual risk. Portfolios destroy information by shrinking the dispersion of betas, leading to larger standard errors.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 55 , Issue 3 , May 2020 , pp. 709 - 750
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2019

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Footnotes

We thank Hendrik Bessembinder (the editor), Wayne Ferson (the referee), Rob Grauer, Cam Harvey, Bob Hodrick, Raymond Kan, Bob Kimmel, Georgios Skoulakis, Yuhang Xing, and Xiaoyan Zhang for helpful discussions, and seminar participants at the American Finance Association, Columbia University, CRSP forum, Texas A&M University, and the Western Finance Association for comments. The usual disclaimer applies.

References

Ang, A.; Chen, J.; and Xing, Y.. “Downside Risk.” Review of Financial Studies, 19 (2006), 1191–1239.Google Scholar
Ang, A.; Hodrick, R. J.; Xing, Y.; and Zhang, X.. “The Cross Section of Volatility and Expected Returns.” Journal of Finance, 61 (2006), 259–299.Google Scholar
Bekaert, G.; Hodrick, R. J.; and Zhang, X.. “Aggregate Idiosyncratic Volatility.” Journal of Financial and Quantitative Analysis, 47 (2012), 1155–1185.Google Scholar
Berk, J. B.“Sorting Out Sorts.” Journal of Finance, 55 (2000), 407–427.Google Scholar
Black, F.; Jensen, M.; and Scholes, M.. “The Capital Asset Pricing Model: Some Empirical Test.” In Studies in the Theory of Capital Markets, Jensen, M., ed. New York, NY: Praeger (1972), 79–121.Google Scholar
Blume, M. E.“Portfolio Theory: A Step Toward Its Practical Application.” Journal of Business, 43 (1970), 152–173.Google Scholar
Brennan, M. J.; Chordia, T.; and Subrahmanyam, A.. “Alternative Factor Specifications, Security Characteristics, and the Cross-Section of Expected Stock Returns.” Journal of Financial Economics, 49 (1998), 345–373.Google Scholar
Burnside, A. C.“Identification and Inference in Linear Stochastic Discount Factor Models with Excess Returns.” Journal of Financial Econometrics, 14 (2016), 295–330.Google Scholar
Campbell, J. Y.; Lettau, M.; Malkiel, B. G.; and Xu, Y.. “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk.” Journal of Finance, 56 (2001), 1–43.Google Scholar
Campbell, J. Y.; Lo, A. W.; and MacKinlay, A. C.. The Econometrics of Financial Markets. New Jersey, NJ: Princeton University Press (1997).Google Scholar
Cochrane, J. H.Asset Pricing. New Jersey, NJ: Princeton University Press (2005).Google Scholar
Cramér, H.Mathematical Methods of Statistics. New Jersey, NJ: Princeton University Press (1946).Google Scholar
Daniel, K., and Titman, S.. “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns.” Journal of Finance, 52 (1997), 1–34.Google Scholar
Fama, E. F., and French, K. R.. “The Cross-Section of Expected Stock Returns.” Journal of Finance, 47 (1992), 427–465.Google Scholar
Fama, E. F., and French, K. R.. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33 (1993), 3–56.Google Scholar
Fama, E. F., and French, K. R.. “Dissecting Anomalies.” Journal of Finance, 63 (2008), 1653–1678.Google Scholar
Fama, E. F., and MacBeth, J. D.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 71 (1973), 607–636.Google Scholar
Ferson, W. E.; Simin, T.; and Sarkissian, S.. “The Alpha Factor Asset Pricing Model: A Parable.” Journal of Financial Markets, 2 (1999), 49–68.Google Scholar
Ferson, W. E.; Simin, T.; and Sarkissian, S.. “Spurious regressions in Financial Economics?” Journal of Finance, 58 (2003), 1393–1414.Google Scholar
Gibbons, M. R.“Multivariate Tests of Financial Models: A New Approach.” Journal of Financial Economics, 10 (1982), 3–27.Google Scholar
Gibbons, M. R.; Ross, S.; and Shanken, J.. “A Test of the Efficiency of a Given Portfolio.” Econometrica, 57 (1989), 1121–1152.Google Scholar
Grauer, R. R., and Janmaat, J. A.. “The Unintended Consequences of Grouping in Tests of Asset Pricing Models.” Journal of Banking and Finance, 28 (2004), 2889–2914.Google Scholar
Hou, K., and Kimmel, R. L.. “On Estimation of Risk Premia in Linear Factor Models.” Working Paper, Ohio State University (2006).Google Scholar
Huberman, G., and Kandel, S.. “Mean-Variance Spanning.” Journal of Finance, 42 (1987), 873–888.Google Scholar
Jagannathan, R.; Skoulakis, G.; and Wang, Z.. “The Analysis of the Cross Section of Security Returns.” In Handbook of Financial Econometrics, Aït-Sahalia, Y. and Hansen, L. P., eds. Amsterdam: Elsevier (2002).Google Scholar
Jagannathan, R., and Wang, Z.. “The Conditional CAPM and the Cross-Section of Expected Returns.” Journal of Finance, 51 (1996), 3–53.Google Scholar
Jagannathan, R., and Wang, Z.. “An Asymptotic Theory for Estimating Beta-Pricing Models using Cross-Sectional Regression.” Journal of Finance, 53 (1998), 1285–1309.Google Scholar
Jagannathan, R., and Wang, Z.. “Empirical Evaluation of Asset Pricing Models: A Comparison of the SDF and Beta Methods.” Journal of Finance, 57 (2002), 2337–2367.Google Scholar
Jegadeesh, N.; Noh, J.; Pukthuanthong, K.; Roll, R.; and Wang, J.. “Empirical Tests of Asset Pricing Models with Individual Assets: Resolving the Errors-in-Variables Bias in Risk Premium Estimation.” Working Paper, Emory University (2017).Google Scholar
Jobson, D., and Korkie, R.. “Potential Performance and Tests of Portfolio Efficiency.” Journal of Financial Economics, 10 (1982), 433–436.Google Scholar
Kan, R.“On the Explanatory Power of Asset Pricing Models Across and Within Portfolios.” Working Paper, University of Toronto (2004).Google Scholar
Kan, R., and Robotti, C.. “Specification Tests of Asset Pricing Models Using Excess Returns.” Journal of Empirical Finance, 15 (2008), 816–838.Google Scholar
Kan, R., and Zhang, C.. “Two-Pass Tests of Asset Pricing Models with Useless Factors.” Journal of Finance, 54 (1999), 203–235.Google Scholar
Kan, R., and Zhou, G.. “A Critique of Stochastic Discount Factor Methodology.” Journal of Finance, 54 (1999), 1221–1248.Google Scholar
Kim, D.“The Errors in the Variables Problem in the Cross-Section of Expected Stock Returns.” Journal of Finance, 50 (1995), 1605–1634.Google Scholar
Lettau, M., and Ludvigson, S.. “Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia are Time Varying.” Journal of Political Economy, 109 (2001), 1238–1287.Google Scholar
Lewellen, J.; Nagel, S.; and Shanken, J.. “A Skeptical Appraisal of Asset-Pricing Tests.” Journal of Financial Economics, 96 (2010), 175–194.Google Scholar
Litzenberger, R. H., and Ramaswamy, K.. “The Effects of Personal Taxes and Dividends on Capital Asset Prices: Theory and Empirical Evidence.” Journal of Financial Economics, 7 (1979), 163–195.Google Scholar
Lo, A. W., and MacKinlay, A. C.. “Data-Snooping Biases in Tests of Financial Asset Pricing Models.” Review of Financial Studies, 3 (1990), 431–468.Google Scholar
MacKinlay, A. C.“On Multivariate Tests of the CAPM.” Journal of Financial Economics, 18 (1987), 341–372.Google Scholar
Mehra, R., and Prescott, E.. “The Equity Premium: A Puzzle.” Journal of Monetary Economics, 15 (1985), 145–161.Google Scholar
Pástor, L., and Stambaugh, R. F.. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy, 111 (2003), 642–685.Google Scholar
Rao, C. R.“Information and the Accuracy Attainable in the Estimation of Statistical Parameters.” Bulletin of the Calcutta Mathematical Society, 37 (1945), 81–89.Google Scholar
Santos, T., and Veronesi, P.. “Labor Income and Predictable Stock Returns.” Review of Financial Studies, 19 (2006), 1–44.Google Scholar
Shanken, J.“On the Estimation of Beta-Pricing Models.” Review of Financial Studies, 5 (1992), 1–33.Google Scholar
Shanken, J., and Zhou, G.. “Estimating and Testing Beta Pricing Models: Alternative Methods and Their Performance in Simulations.” Journal of Financial Economics, 84 (2007), 40–86.Google Scholar
Velu, R., and Zhou, G.. “Testing Multi-Beta Asset Pricing Models.” Journal of Empirical Finance, 6 (1999), 219–241.Google Scholar
Zhou, G.“Small Sample Tests of Portfolio Efficiency.” Journal of Financial Economics, 30 (1991), 165–191.Google Scholar