Abstract
We generalize an asset pricing model based on the Arbitrage Pricing Theory (APT) allowing beta to be time-varying. Making beta a random variable adds flexibility to the model because permits a non-linear relation between individual returns and the set of factors, and accounts for the effect of possible omitted variables. We integrate the conditional APT with a general linear stochastic process for beta. We analyze the behavior of the conditional expected return, the conditional variance and conditional covariance of individual asset returns as functions of the conditional moments of beta. On considering time-varying betas we introduce another source of uncertainty (risk) independent of the factors. We need to disentangle if this extra risk is systematic or non-systematic. To this end, we introduce a modified conditional APT model that rationalizes why the time variation of beta may represent extra systematic risk. For a sample of individual stocks, we test the hypothesis of time-varying beta and the feasibility of the modified conditional APT. We present a test for time-varying beta based on the conditional second moments of returns. We find that there is strong evidence against constancy of betas in favor of a random coefficient model, and that the time variation of beta is due to non-systematic behavior of the firms and investors should be able to diversify this risk away.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bollerslev T, Wooldridge J (1992) Quasi-maximum likelihood estimation and inference in dynamic models with time varying covariances. Econometrics Reviews 11:143–72
Bos T, Newbold P (1984) An empirical investigation of the possibility of stochastic systematic risk in the market model. Journal of Business 57:35–41
Brooks R, Faff R, Lee J (1992) The form of time variation of systematic risk: Some Australian evidence. Applied Financial Economics 2:191–198
Chen S-N, Keown A (1981) Risk decomposition and portfolio diversification when beta is nonstationary: A note. Journal of Finance 36:941–947
Collins D, Ledolter J, Rayburn J (1987) Some further evidence on the stochastic properties of systematic risk. Journal of Business 60:425–448
Engle R, Kroner K (1995) Multivariate simultaneous, generalized ARCH. Econometric Theory 11(1):122–150
Fabozzi F, Francis J (1978) Beta as a random coefficient. Journal of Financial and Quantitative Analysis 13:101–116
Ferson W, Harvey C (1991) The variation of economic risk premiums. Journal of Political Economy 99:385–415
Gallant A (1987) Nonlinear statistical models. John Wiley and Sons Inc., New York
González-Rivera G (1996) Time-varying risk. The case of the American computer industry. Journal of Empirical Finance 2:333–342
Hildreth C, Houck J (1968) Some estimators for a linear model with random coefficients. Journal of the American Statistical Association 63:584–595
King M (1987) Towards a theory of point optimal testing. Econometric Reviews 6:169–218
Leusner J, Akhavein J, Swamy P (1996) Solving an empirical puzzle in the capital asset pricing model. mimeographed
Ng V, Engle RF, Rothschild M (1992) A multi-dynamic factor model for stock returns. Journal of Econometrics 52:245–266
Ohlson J, Rosenberg B (1982) Systematic risk of the CRSP equal-weighted common stock index: A history estimated by stochastic parameter regression. Journal of Business 55:121–145
Pagan A (1984) Regressions with generated regressors. International Economic Review 25:221–247
Raj B, Ullah A (1981) Econometrics: A varying parametric approach. St. Martin Press
Ross S (1976) The arbitrage theory of capital asset pricing. Journal of Economic Theory 13:343–362
Schwert G, Seguin P (1990) Heteroskedasticity in stocks returns. Journal of Finance 45:1129–55
Sharpe W (1964) Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19:425–442
White H (1980) A heteroscedasticity-consistent covariance matrix and a direct test for heteroscedasticity. Econometrica 48:817–838
Author information
Authors and Affiliations
Additional information
I gratefully acknowledge the Intramural Research Grant of the Academic Senate of the University of California, Riverside. My thanks to Taradas Bandyopadhyay, Stephen Cullenberg and Jang-Ting Guo for carefully reading the manuscript, and to the editor, Dr. Baldev Raj, and to two anonymous referees whose comments have helped to improve the writing. An earlier version of this paper was presented at the University of California, Santa Barbara, University of Southern California, University of California, Riverside, Bank of Spain, Universidad Autonoma de Barcelona and Universidad Pompeu Fabra, Barcelona. The usual caveat applies.