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 in a high dimensional sample composed by the 50 most traded stocks of the S\&P100 index. We find that GARCH-type dynamic covariances yield portfolios with superior risk-adjusted performance only in the absence of transaction costs. In more realistic scenarios involving alternative levels of transaction costs, portfolios based on static covariance models outperform. In particular, we find that a risk-averse investor with quadratic utility function is willing to pay an annualized fee of 368 basis points (bp) on average in order to switch from the dynamic covariance models to a 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 as those proposed in \citet{kirby2012s} are more robust specially in scenarios with higher transaction costs.