Underestimation Bias of Risk on Optimized Portfolio by Multifactor Risk Model - Risk of Long Short Portfolio can be Underestimated

Existence of underestimation bias on risk for optimized portfolio is well known to quantitative fund managers who construct their portfolio from optimizer (mathematical software) by using multi factor risk model. There are some reasons for underestimation of portfolio risk. One of the reasons of underestimation lays in sampling bias of covariance matrix of factor returns. It is important for quantitative fund managers to know which portfolio has large underestimation bias. This study shows that risk of long short portfolio without constraint and with large number of stocks in investable universe can be largely underestimated. On the other hand, minimum variance portfolio with long only constraint can not be largely underestimated