A number of authors have found that firm size and book-to-market-value capture the cross-sectional variation in average stock returns. More importantly, these variables have been shown to out-perform the CAPM's β coefficient in explaining the cross-section of US stock returns. However, these studies all employ variants of the two-step estimator due to Fama and MacBeth (Fama, E.F., MacBeth, J.D., 1973. Risk, return and equilibrium: Empirical tests. Journal of Political Economy 71, 607–636), which impose implicitly the restriction that idiosyncratic returns are uncorrelated. In this paper we use a one-step estimator due to McElroy et al. (McElroy, M.B., Burmeister, E., Wall, K.D., 1985. Two estimators for the APT model when factors are measured. Economics Letters 19, 271–275) and find a highly significant role for β risk in the UK stock market when we allow for correlation amongst idiosyncratic returns.

We test both the unconditional and conditional Mean Variance Efficiency of the UK stockmarket, paying particular attention to choosing a suitable set of instruments for the conditional version of the model. By considering more carefully than previous authors the pricing of economic risk within the mean-variance framework we show that certain instruments can enhance the basic model structure. Given the tendency for financial market data to display non-constancy in variance and non-normality we employ the GMM procedure described in Hansen (1982), which requires much weaker distributional assumptions than the more traditional OLS techniques. We discuss forming portfolios of stocks using both size and dividend yield as a criterion to achieve a suitable spread of risk and return, and find that our conclusions are sensitive both to the method of portfolio formation and to the choice of estimator. This is an important finding given the problem of thin trading associated with the size ordering of UK stocks. We find some support for both the unconditional and conditional version of the CAPM, though we are cautious about our conclusions given the instability of the parameter estimates.