EFF/KRF: We have written papers on this issue. The answer is consistently the same. Higher market betas tend to be associated with higher average returns, but the historical beta premium is much lower than predicted by the CAPM, and it is not statistically distinguishable from zero. Because of the high volatility of stock returns, however, estimates of the beta premium leave substantial uncertainty about the true premium. It may be much higher, or lower, than the historical estimate.
Eugene Fama and Ken French are members of the Board of Directors of the general partner of, and provide consulting services to Dimensional Fund Advisors LP.