Evaluating the importance of missing risk factors using the optimal orthogonal portfolio approach

We apply the orthogonal portfolio approach to analyse the importance of risk factors potentially missing from the CAPM. We generalize the approach proposed by MacKinlay and Pastor (2000) [MacKinlay, A.C., Pastor, L., 2000. Asset pricing models: implications for expected returns and portfolio selection. Review of Financial Studies 13, 883-916] by estimating the Sharpe ratio of the optimal orthogonal portfolio. Our result, based on US industry portfolios for the period 1927-2002, reveals important risk factors missing from the CAPM during periods with high market volatility. We show that a priori fixing the Sharpe ratio, which is an assumption used by MacKinlay and Pastor (2000) [MacKinlay, A.C., Pastor, L., 2000. Asset pricing models: implications for expected returns and portfolio selection. Review of Financial Studies 13, 883-916], may produce less plausible estimates of the expected returns.