An Examination of the Time Series Properties of Beta in the Market Model
Abstract Understanding the stochastic behavior of beta is fundamental to portfolio risk management. We evaluate the time series properties of beta for oil industry stocks, machinery industry stocks, and a random sample of 100 stocks. Daily returns for stocks in each of these industries and the random sample are obtained from the Center for Research in Security Prices tapes for the period July 1962 through December 1986 and are grouped into 98 quarter-year, and also 49 half-year, nonoverlapping time intervals. Beta is estimated for each interval. Our analysis indicates that the time series of beta is consistent with ARMA(1, 1). We found that the autoregressive parameter of the time series of beta estimated using a half-year interval is equal to the square root of the autoregressive parameter of the time series of beta using a quarter-year interval. Thus, as the length of time interval chosen to estimate beta becomes longer, the time series behavior of beta becomes less autoregressive and more random in nature.