The dynamic and stochastic instability of betas: Implications for forecasting stock returns

The purpose of this paper is to simultaneously investigate several important issues that feature the dynamic and stochastic behavior of beta coefficients for individual stocks and affect the forecasting of stock returns. The issues include randomness, nonstantionarity, and shifts in the mean and variance parameters of the beta coefficient, and are addressed within the framework of variable‐mean‐response (VMR) random coefficients models in which the problem of heteroscedasticity is present. Estimation is done using a four‐step generalized least squares method. The hypotheses concerning randomness and nonstationarity of betas are tested. The time paths, sizes, and marginal rates of mean shifts are determined. The issue of variance shift is examined on the basis of five special tests, called T*, B, S', G and W. Then the impacts of the dynamic and stochastic instability on the estimation of betas is tested by a nonparametric procedure. Finally, the VMR models' ability of forecasting stock returns is evaluated against the standard capital asset pricing model. The empirical findings shed new light on the continuing debate as to whether the beta coefficient is random and nonstationary and have important implications for modeling and forecasting the measurement of performance and the determination of stock returns.