On the Choice of Covariance Specifications for Portfolio Selection Problems

Two crucial aspects to the problem of portfolio selection are the specification of the model for expected returns and their covariances, as well as the choice of the investment policy to be adopted. A common trade-off is to consider dynamic covariance specifications vis-a-vis static models such as those based on shrinkage methods. This work empirically shows that these two aspects are intrinsically attached to the impact of transaction costs. To address this question, we implement a broad range of covariance specifications to generate a set of 16 portfolio selection policies over a period of 25 years in a high dimensional sample composed of 69 stocks belonging to the S&P100 index. We find that, in the absence of transaction costs, GARCH-type dynamic covariances deliver portfolios with similar risk-adjusted performance with respect to those obtained with static covariance specifications. In more realistic scenarios involving alternative levels of transaction costs, portfolios based on static covariance models consistently outperform as they demand a much lower level of portfolio turnover. In particular, we find that a risk-averse investor with quadratic utility function is willing to pay an annualized fee of 291 basis points (bp) on average in order to switch from the dynamic covariance models to a benchmark static covariance specification when the level of transaction costs is 20 bp. Finally, portfolio policies that seek to alleviate estimation error by ignoring off-diagonal covariance elements such as those proposed in Kirby and Ostdiek (2012) are more robust specially in scenarios with higher transaction costs