Beta Nonstationarity, Portfolio Residual Risk and Diversification

Abstract

Over the past years the beta coefficient has been widely used as a measure of systematic risk in investment and portfolio analysis. The validity of using the beta coefficient as the proper measure of systematic risk is dependent upon the assumption that the beta coefficient is stationary over time. Unfortunately, this assumption has been challenged by a number of empirical studies which have found the beta coefficient to be unstable over time. Examples of such empirical investigations are those documented by Blume [4], Levy [12], Levitz [11], Baesel [2], Altman, Jacquillat, and Levasseur [1], and Roenfelt, Griepentrong, and Pflaum [16]. Most recently, Fabozzi and Francis [9] reported that some security beta coefficients tend to be random over time. Their findings also support the regression tendency of the beta coefficients towards the mean over time, as found by Blume [4]. Thus, because the beta coefficient is changing over time, the use of the ordinary least-squares (OLS) method in investment and portfolio analysis will yield an inefficient estimate of systematic risk. Furthermore, the OLS estimates of security and portfolio residual risks will be influenced by the variability of beta coefficient. Therefore, the purpose of this paper is to investigate the relationship between the variability of the beta coefficient and portfolio residual risk, and hence to provide a real picture of the process of portfolio diversification under the condition of beta nonstationarity. It is shown that the use of the OLS method to estimate security and portfolio residual risks will produce an incorrect conclusion that larger residual risks tend to be associated with higher variability in the beta coefficient.