Optimal Portfolio Choice with Estimation Risk: No Risk-Free Asset Case

We propose an optimal combining strategy to mitigate estimation risk for the popular mean-variance portfolio choice problem in the case without a risk-free asset. We find that our strategy performs well in general, and it can be applied to known estimated rules and the resulting new rules outperform the original ones. We further obtain the exact distribution of the out-of-sample returns and explicit expressions of the expected out-of sample utilities of the combining strategy, providing not only a fast and accurate way of evaluating the performance, but also analytical insights into the portfolio construction.