The Correlations and Volatilities of Stock Returns: The CAPM Beta and the Fama-French Factors

Abstract

This paper conducts time-series tests on the Capital Asset Pricing Model (CAPM) and the Fama-French three-factor (FF3) model in the context of market beta estimation for the cost of equity capital. We find that the market index is by far the most consistent and powerful systematic risk factor throughout the sample period, for both large- and micro-cap stocks, in FF3 model as well as CAPM specifications, and across industry sectors. Most of market beta estimates are statistically significant and appear to be economically consistent with the systematic risk exposure of individual stocks. Consistent with the theory, virtually all alpha estimates are statistically zero. Market volatilities are critical for beta estimates. When the market is highly volatile, beta estimates breakdown as do the correlations of stock returns with the market index. For small-cap stocks and in a highly volatile market, SMB and HML stabilize the market beta and improve the statistical explanatory power; for large-cap and in a relatively stable market, SMB and HML add little to the CAPM beta. Model diagnostics show that the CAPM and the FF3 model are practically equivalent. Parameter estimates of the CAPM are generally superior to those of the FF3 model, except for some small-cap stocks and in a highly volatile market. On the other hand, statistical explanatory power of the FF3 model is generally superior to that of the CAPM.