Optimal versus naive diversification : do different loss functions improve portfolio choice?

Abstract

I estimate the out-of-sample performance of the equal weight, minimum variance and mean-variance model portfolios in different settings. In each setting, I vary the loss function used when estimating returns and covariances, length of the estimation window, and number of factors used in our estimation model. I find that when measuring performance by Sharpe ratio, choice of loss function strongly influences whether the mean-variance model portfolio outperforms the equal weight or minimum variance portfolio, and that the optimal loss function depends on the length of the estimation window and the dimension of the return model. It appears that we don't gain much by using more factors. The 3-factor model does a pretty good job based on Sharpe ratio, and the results are consistently the best for MVO(10). With more factors, it seems clear that we need longer estimation windows, but even then we do not gain anything in terms of Sharpe Ratio. However, when measuring performance by the certainty-equivalent return, I find that the mean-variance model portfolio does not outperform the minimum variance portfolio or the equal weight portfolio in any setting. This suggests that choosing a loss function carefully is imperative to managing estimation errors and that an investor's utility preferences and attitude towards risk should be taken into account when choosing a measure of performance.