Quantification of Risk and Return for Portfolio Optimization

Traditional portfolio optimization performed in the mean-variance framework critically depends on how accurately the first and second moments of the asset return distribution can be estimated. Of greater importance in portfolio analysis is the covariance matrix that captures the co-movement of the assets. In particular, the risk for a portfolio depends not only on individual variances but also on the correlation structure of assets returns. In general, it is argued that the portfolio performance is more sensitive to changes in the expected return than changes in the covariance matrix. Thus, estimation errors in the predicted returns are more influential on portfolio performance than errors in the variance and covariances predictions (Best and Grauer 1991; Pojarliev and Polasek 2001). The portfolio optimization process typically allocates the largest fraction of capital to assets with the largest estimation error in their expected returns. The difficulty in estimating expected return implies that improvement in portfolio optimization is feasible via an accurate estimation of the expected covariance matrix. Therefore, the selection of the appropriate variance-covariance model is crucial for the estimation of the portfolio weights and the overall portfolio performance.