We develop a methodology for improving the estimate of the risk premia calculated jointly with the asset sensitivities, extending the McElroy-Burmeister approach for estimating the Arbitrage Pricing Theory (Ross 1976) as a restricted nonlinear multivariate regression model using observed macroeconomic risk factors. This allows us to use multiple samples of stocks to estimate and test common risk premia. This simpler expression for the variance-covariance matrix of the estimated parameter allows easier estimate and testing. With large number of stocks and a small number of observations, we use different samples of stocks to estimate vectors of risk premia which are then combined so that a final improved estimate of the risk premium vector is asymptotically unbiased and has minimum variance. We also derive the variance -covariance matrix of the final estimate of the risk premium. We apply the methodology to UK data, using FTSE-350 assets and observed macroeconomic risk factors.
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