Factor Models of Stock Returns: GARCH Errors versus Autoregressive Betas

The Single Factor Model (SFMT) of stock returns in its simplest form, namely the one that assumes time-invariant beta and homoskedastic error has been found to be empirically inadequate.The beta coefficient and the error process exhibit significant time-variation and dynamic conditional heteroskedasticity, respectively. Out of these empirical failures, two extended versions of SFMT have emerged: the first (SFMT-AR) assumes that the beta coefficient is an autoregressive process, whereas the second (SFMT-GARCH) maintains the assumption of time-invariant beta but assumes that the error follows a GARCH process. The purpose of this paper is twofold: first to show that SFMT-AR is capable of reproducing the most important stylized facts of stock returns, namely conditional heteroskedasticity and leptokurtosis, even in the case in which the factor is an independent process; second to compare SFMT-GARCH and SFMT-AR in terms of their in-sample and out-of-sample performance. The most important result from these comparisons is that SFMT-AR dominates SFMT-GARCH in terms of forecasting the second moments of stock returns.