Time-varying betas and the cross-sectional return–risk relation: evidence from the UK

The seminal study by Fama and MacBeth in 1973 initiated a stream of papers testing for the cross-sectional relation between return and risk. The debate as to whether beta is a valid measure of risk was reanimated by Fama and French and subsequent studies. Rather than focusing on exogenous variables that have a larger explanatory power than an asset's beta in cross-sectional tests, the matrix of variances-covariances is assumed to follow a time varying ARCH process. Using monthly data from the UK market from February 1975 to December 1996, the cross-sectional return–risk relations obtained with an unconditional specification for assets’ betas are compared to those obtained when the estimated betas are based on an ARCH model. The approach taken by Pettengill, Sundaram and Mathur, which allows a negative cross sectional return–risk relation in periods in which the market portfolio yields a negative return relative to the risk free rate, was also investigated. These tests are also carried out on samples pertaining to a specific month and on samples from which a particular month is removed. Results suggest that the CAPM holds better in downward moving markets than in upward moving markets hence beta is a more appropriate measure of risk in bear markets.