Skip to main content

Time-Varying Beta and the Value Premium

  • Hui Guo, Chaojiang Wu and Yan Yu

We model conditional market beta and alpha as flexible functions of state variables identified via a formal variable-selection procedure. In the post-1963 sample, the beta of the value premium comoves strongly with unemployment, inflation, and the price–earnings ratio in a countercyclical manner. We also uncover a novel nonlinear dependence of alpha on business conditions: It falls sharply and even becomes negative during severe economic downturns but is positive and flat otherwise. The conditional capital asset pricing model (CAPM) performs better than the unconditional CAPM, but this does not fully explain the value premium. Our findings are consistent with a conditional CAPM with rare disasters.

Corresponding author
* Guo (corresponding author),, Lindner College of Business, University of Cincinnati and Research Center of Applied Finance, Dongbei University of Finance and Economics; Yu,, Lindner College of Business, University of Cincinnati; and Wu,, LeBow College of Business, Drexel University.
Hide All

We thank an anonymous referee, Hendrik Bessembinder (the editor), and Stefan Nagel for helpful comments. Guo acknowledges financial support from the Key Projects of the National Social Science Foundation of China (No. 16ZDA039).

Hide All
Akaike, H.A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control, 19 (1974), 716723.
Ang, A., and Chen, J.. “CAPM over the Long Run: 1926–2001.” Journal of Empirical Finance, 14 (2007), 140.
Ang, A., and Kristensen, D.. “Testing Conditional Factor Models.” Journal of Financial Economics, 106 (2012), 132156.
Bai, H.; Hou, K.; Kung, H.; and Zhang, L.. “The CAPM Strikes Back? An Investment Model with Disasters.” Working Paper, Ohio State University (2015).
Bansal, R., and Yaron, A.. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.” Journal of Finance, 59 (2004), 14811509.
Belo, F.; Lin, X.; and Bazdresch, S.. “Labor Hiring, Investment and Stock Return Predictability in the Cross Section.” Journal of Political Economy, 122 (2014), 129177.
Berger, D.; Dew-Becker, I.; Schmidt, L.; and Takahashi, Y.. “Layoff Risk, the Welfare Cost of Business Cycles, and Monetary Policy.” Working Paper, Northwestern University (2015).
Boguth, O.; Carlson, M.; Fisher, A.; and Simutin, M.. “Conditional Risk and Performance Evaluation: Volatility Timing, Overconditioning, and New Estimates of Momentum Alphas.” Journal of Financial Economics, 102 (2011), 363389.
Campbell, J. Y., and Cochrane, J. H.. “By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior.” Journal of Political Economy, 107 (1999), 205251.
Campbell, J. Y., and Shiller, R. J.. “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors.” Review of Financial Studies, 1 (1988), 195228.
Campbell, J. Y., and Vuolteenaho, T.. “Inflation Illusion and Stock Prices.” American Economic Review, 94 (2004), 1923.
Carroll, R. J.; Fan, J.; Gijbels, I.; and Wand, M. P.. “Generalized Partially Linear Single-Index Models.” Journal of the American Statistical Association, 92 (1997), 477489.
Carroll, R. J.; Wu, C. J. F.; and Ruppert, D.. “The Effect of Estimating Weights in Weighted Least Squares.” Journal of the American Statistical Association, 83 (1988), 10451054.
Chen, N.-F.; Roll, R.; and Ross, S. A.. “Economic Forces and the Stock Market.” Journal of Business, 59 (1986), 383403.
Chen, L., and Zhang, L.. “Do Time-Varying Risk Premiums Explain Labor Market Performance?Journal of Financial Economics, 99 (2011), 385399.
Cooper, M., and Gubellini, S.. “The Critical Role of Conditioning Information in Determining If Value Is Really Riskier than Growth.” Journal of Empirical Finance, 18 (2011), 289305.
Cui, X.; Härdle, W.; and Zhu, L.. “The EFM Approach for Single-Index Models.” Annals of Statistics, 39 (2011), 16581688.
Fama, E. F., and French, K. R.. “Business Conditions and Expected Returns on Stocks and Bonds.” Journal of Financial Economics, 25 (1989), 2349.
Fama, E. F., and French, K. R.. “The Value Premium and the CAPM.” Journal of Finance, 61 (2006), 21632185.
Fan, J.; Yao, Q.; and Cai, Z.. “Adaptive Varying-Coefficient Linear Models.” Journal of the Royal Statistical Society, Series B (Statistical Methodology), 65 (2003), 5780.
Ferson, W. E., and Harvey, C. R.. “Conditioning Variables and the Cross Section of Stock Returns.” Journal of Finance, 54 (1999), 13251360.
Ghysels, E.On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?Journal of Finance, 53 (1998), 549573.
Harvey, C.The Specification of Conditional Expectations.” Journal of Empirical Finance, 8 (2001), 573638.
Hastie, T., and Tibshirani, R.. Generalized Additive Models. New York, NY: Chapman and Hall (1990).
Jarrow, R.; Ruppert, D.; and Yu, Y.. “Estimating the Term Structure of Corporate Debt with a Semiparametric Penalized Spline Model.” Journal of the American Statistical Association, 99 (2004), 5766.
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.
Lewellen, J., and Nagel, S.. “The Conditional CAPM Does Not Explain Asset-Pricing Anomalies.” Journal of Financial Economics, 82 (2006), 289314.
Mammen, E.Bootstrap and Wild Bootstrap for High Dimensional Linear Models.” Annals of Statistics, 21 (1993), 255285.
Orphanides, A., and Williams, J.. “Robust Monetary Policy Rules with Unknown Natural Rates.” Brookings Papers on Economic Activity, 2 (2002), 63145.
Paye, B.‘Deja Vol’: Predictive Regressions for Aggregate Stock Market Volatility Using Macroeconomic Variables.” Journal of Financial Economics, 106 (2012), 527546.
Petkova, R., and Zhang, L.. “Is Value Riskier than Growth?Journal of Financial Economics, 78 (2005), 187202.
Petrosky-Nadeau, N.; Zhang, L.; and Kuehn, L.. “Endogenous Economic Disasters and Asset Prices.” Working Paper, Ohio State University (2013).
Ruppert, D.Selecting the Number of Knots for Penalized Splines.” Journal of Computational and Graphical Statistics, 11 (2002), 735757.
Ruppert, D.; Wand, M. P.; and Carroll, R. J.. Semiparametric Regression. New York, NY: Cambridge University Press (2003).
Schwarz, G.Estimating the Dimension of a Model.” Annals of Statistics, 6 (1978), 461464.
Staiger, D.; Stock, J.; and Watson, M.. “How Precise Are Estimates of the Natural Rate of Unemployment?” In Reducing Inflation: Motivation and Strategy, Romer, C. and Romer, D., eds. Chicago, IL: University of Chicago Press (1997).
Stock, J., and Watson, M.. “Forecasting Output and Inflation: The Role of Asset Prices.” Journal of Economic Literature, 41 (2003), 788829.
Taylor, J.Discretion versus Policy Rules in Practice.” Carnegie-Rochester Conference Series on Public Policy, 39 (1993), 195214.
Wang, K. Q.Asset Pricing with Conditioning Information: A New Test.” Journal of Finance, 58 (2003), 161196.
Welch, I., and Goyal, A.. “A Comprehensive Look at the Empirical Performance of Equity Premium Prediction.” Review of Financial Studies, 21 (2008), 14551508.
Wu, C. F. J.Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis (with Discussions).” Annals of Statistics, 14 (1986), 12611350.
Wu, T. Z.; Lin, H.; and Yu, Y.. “Single Index Coefficient Models for Nonlinear Time Series.” Journal of Nonparametric Statistics, 23 (2011), 3758.
Xia, Y., and Li, W. K.. “On Single-Index Coefficient Regression Models.” Journal of the American Statistical Association, 94 (1999), 12751285.
Yu, Y., and Ruppert, D.. “Penalized Spline Estimation for Partially Linear Single-Index Models.” Journal of the American Statistical Association, 97 (2002), 10421054.
Yu, Y.; Yu, K.; Wang, H.; and Li, M.. “Semiparametric Estimation for a Class of Time-Inhomogeneous Diffusion Processes.” Statistica Sinica, 19 (2009), 843867.
Zhang, L.The Value Premium.” Journal of Finance, 60 (2005), 67103.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Financial and Quantitative Analysis
  • ISSN: 0022-1090
  • EISSN: 1756-6916
  • URL: /core/journals/journal-of-financial-and-quantitative-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 1
Total number of PDF views: 383 *
Loading metrics...

Abstract views

Total abstract views: 1053 *
Loading metrics...

* Views captured on Cambridge Core between 29th June 2017 - 27th May 2018. This data will be updated every 24 hours.