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

Abstract

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.

A Dynamic and Stochastic Beta and Its Implications in Global Capital Markets

“…Lin et al (1992) have analysed the trend variable case in great detail based on four hypotheses which were tested for domestic stocks in the US in terms of CAPM, in contrast to the present study directed to global stock markets in terms of ICAPM. Here we will simply make note of which countries have satisfied these four hypotheses.…”

The Stochastic Structure of the Time–Varying Beta: Evidence from UK Companies

“…The concept of the time-varying beta has induced interest in the stochastic structure of the beta (Lin et al, 1992). According to Lin et al (1992, p. 538) stationarity of a stock's beta has important implications for the measures of capital asset pricing and performance, the e¤cient markets hypothesis and, more importantly, the forecasting of stock returns.…”

“…These methods include treating the market model of the CAPM as a ¢rst-order autoregressive process, using di¡erent sets of data over various time horizons, a switching regression model with a prior knowledge of two regimes, a variablemean-response model of random coe¤cients etc. (see Lin et al, 1992). These studies tend to ¢nd the beta to be non-stationary (see Lin et al 1992;Lin and Lin, 2000).…”

“…(see Lin et al, 1992). These studies tend to ¢nd the beta to be non-stationary (see Lin et al 1992;Lin and Lin, 2000). This paper applies the fractional integration and structural break unit root test methods to study the stochastic structure of the time-varying beta.…”

“…1 Ohlson (1976), Fabozzi andFrancis (1978) and Bos and Newbold (1984) provide evidence that security betas not only are time-varying but can also be better described by some form of stochastic model. Fabozzi and Francis (1978) and Bollerslev et al (1988) provide tests of the CAPM that imply time-varying betas.The concept of the time-varying beta has induced interest in the stochastic structure of the beta (Lin et al, 1992). According to Lin et al (1992, p. 538) stationarity of a stock's beta has important implications for the measures of capital asset pricing and performance, the e¤cient…”