Skip to main content Accessibility help
×
Home
Hostname: page-component-59b7f5684b-z9m8x Total loading time: 0.527 Render date: 2022-09-25T22:16:28.475Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Beta Matrix and Common Factors in Stock Returns

Published online by Cambridge University Press:  19 March 2018

Abstract

We consider the estimation methods for the rank of a beta matrix corresponding to a multifactor model and study which method would be appropriate for data with a large number of assets. Our simulation results indicate that a restricted version of Cragg and Donald’s (1997) Bayesian information criterion estimator is quite reliable for such data. We use this estimator to analyze some selected asset pricing models with U.S. stock returns. Our results indicate that the beta matrix from many models fails to have full column rank, suggesting that risk premiums in these models are underidentified.

Type
Research Article
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

We are grateful to Stephen Brown (the editor), Raymond Kan (the referee), George Korniotis, Alok Kumar, Todd Pronno, Richard Roll, Aurelio Vazquez, and the participants at Columbia University, Instituto Tecnológico Autónomo de México, Universidad Autónoma de Nuevo León, Sogang University, Hofstra University, Arizona State University, the University of Miami, Hitotsubashi University, and numerous conferences at which we presented this paper. We also thank Laura Xiaolei Liu, Jonathan Lewellen, and Stefan Nagel for sharing their data with us.

References

Ahn, S. C.; Perez, M. F.; and Gadarowski, C.. “Two-Pass Estimation of Risk Premiums with Multicollinear and Near-Invariant Betas.” Journal of Empirical Finance, 20 (2013), 117.CrossRefGoogle Scholar
Al-Sadoon, M. M.“A General Theory of Rank Testing.” Barcelona GSE Working Paper 750 (2015).Google Scholar
Anderson, T. W.Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions.” Annals of Mathematical Statistics, 22 (1951), 327351.CrossRefGoogle Scholar
Bai, J., and Ng, S.. “Determining the Number of Factors in Approximate Factor Models.” Econometrica, 70 (2002), 191221.CrossRefGoogle Scholar
Brown, S. J.The Number of Factors in Security Returns.” Journal of Finance, 44 (1989), 12471262.CrossRefGoogle Scholar
Burnside, C.Identification and Inference in Linear Stochastic Discount Factor Models with Excess Returns.” Journal of Financial Econometrics, 14 (2016), 295330.CrossRefGoogle Scholar
Carhart, M. M.On Persistence in Mutual Fund Performance.” Journal of Finance, 52 (1997), 5782.CrossRefGoogle Scholar
Chamberlain, G., and Rothschild, M.. “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets.” Econometrica, 51 (1983), 12811304.CrossRefGoogle Scholar
Chen, N.; Roll, R.; and Ross, S. A.. “Economic Forces and the Stock Market.” Journal of Business, 59 (1986), 383403.CrossRefGoogle Scholar
Cragg, J. G., and Donald, S. G.. “Inferring the Rank of a Matrix.” Journal of Econometrics, 76 (1997), 223250.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33 (1993), 356.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “A Five-Factor Asset Pricing Model.” Journal of Financial Economics, 116 (2015), 122.CrossRefGoogle Scholar
Gospodinov, N.; Kan, R.; and Robotti, C.. “Misspecification-Robust Inference in Linear Asset-Pricing Models with Irrelevant Risk Factors.” Review of Financial Studies, 27 (2014), 21392170.CrossRefGoogle Scholar
Harvey, C. R.; Liu, Y.; and Zhu, H.. “…and the Cross-Section of Expected Returns.” Review of Financial Studies, 29 (2015), 568.CrossRefGoogle Scholar
Hou, K.; Xue, C.; and Zhang, L.. “Digesting Anomalies: An Investment Approach.” Review of Financial Studies, 28 (2015), 650705.CrossRefGoogle Scholar
Jagannathan, R., and Wang, Z.. “The Conditional CAPM and the Cross-Section of Expected Returns.” Journal of Finance, 51 (1996), 353.CrossRefGoogle Scholar
Jegadeesh, N., and Titman, S.. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance, 48 (1993), 6591.CrossRefGoogle Scholar
Kan, R., and Zhang, C.. “Two-Pass Tests of Asset Pricing Models with Useless Factors.” Journal of Finance, 54 (1999a), 203235.CrossRefGoogle Scholar
Kan, R., and Zhang, C.. “GMM Tests of Stochastic Discount Factor Models with Useless Factor.” Journal of Financial Economics, 54 (1999b), 103127.CrossRefGoogle Scholar
Kleibergen, F., and Paap, R.. “Generalized Reduced Rank Tests Using the Singular Value Decomposition.” Journal of Econometrics, 133 (2006), 97126.CrossRefGoogle 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), 12381287.CrossRefGoogle Scholar
Lewellen, J.; Nagel, S.; and Shanken, J.. “A Skeptical Appraisal of Asset Pricing Tests.” Journal of Financial Economics, 96 (2010), 175194.CrossRefGoogle Scholar
Li, Q.; Vassalou, M.; and Xing, Y.. “Sector Investment Growth Rates and the Cross Section of Equity Returns.” Journal of Business, 79 (2006), 16371665.CrossRefGoogle Scholar
Lintner, J.The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economic and Statistics, 47 (1965), 1337.CrossRefGoogle Scholar
Liu, L. X., and Zhang, L.. “Momentum Profits, Factor Pricing, and Macroeconomic Risk.” Review of Financial Studies, 21 (2008), 24172448.CrossRefGoogle Scholar
Lustig, H. N., and Nieuwerburgh, S. V.. “Housing Collateral, Consumption Insurance, and Risk Premia: An Empirical Perspective.” Journal of Finance, 60 (2005), 11671219.CrossRefGoogle Scholar
Merton, R.An Intertemporal Capital Asset Pricing Model.” Econometrica, 41 (1972), 867887.CrossRefGoogle Scholar
Mossin, J.Equilibrium in a Capital Asset Market.” Econometrica, 35 (1966), 768783.CrossRefGoogle Scholar
Onatski, A.Determining the Number of Factors from Empirical Distribution of Eigenvalues.” Review of Economic and Statistics, 92 (2010), 10041016.CrossRefGoogle Scholar
Robin, J. M., and Smith, R. J.. “Tests of Rank.” Econometric Theory, 16 (2000), 151175.CrossRefGoogle Scholar
Ross, S. A.The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory, 13 (1976), 341360.CrossRefGoogle Scholar
Santos, T., and Veronesi, P.. “Labor Income and Predictable Stock Returns.” Review of Financial Studies, 19 (2006), 144.CrossRefGoogle Scholar
Sharpe, W.Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (1964), 425442.Google Scholar
Treynor, J.“Toward a Theory of Market Value and Risky Assets.” Working Paper, available at http://ssrn.com/abstract=628187 (1962).Google Scholar
White, H. Asymptotic Theory for Econometricians. San Diego, CA: Academic Press (1984).Google Scholar
Yogo, M.A Consumption-Based Explanation of Expected Stock Returns.” Journal of Finance, 61 (2006), 539580.CrossRefGoogle Scholar
19
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Beta Matrix and Common Factors in Stock Returns
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Beta Matrix and Common Factors in Stock Returns
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Beta Matrix and Common Factors in Stock Returns
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *