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A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, vis-à-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently-popularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionally-integrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management. JEL Klassifikation: C1, G1
Traditional tests of the CAPM following the Fama / MacBeth (1973) procedure are tests of the joint hypotheses that there is a relationship between beta and realized return and that the market risk premium is positive. The conditional test procedure developed by Pettengill / Sundaram / Mathur (1995) allows to independently test the hypothesis of a relation between beta and realized returns. Monte Carlo simulations show that the conditional test reliably identifies this relation. In an empirical examination for the German stock market we find a significant relation between beta and return. Previous studies failed to identify this relationship probably because the average market risk premium in the sample period was close to zero. Our results provide a justification for the use of betas estimated from historical return data by portfolio managers.