Optimal Portfolio Choice with Estimation Risk: No Risk-free Asset Case
61 Pages Posted: 10 Feb 2016 Last revised: 23 Mar 2020
Date Written: March 21, 20
For the popular mean-variance portfolio choice problem in the case without a risk-free asset, we develop a new portfolio strategy to mitigate estimation risk. We show that in both calibrations and real datasets, optimally combining the sample global minimum variance portfolio with a sample zero-investment portfolio is a more effective strategy to deal with estimation risk than alternative strategies proposed in the literature. In addition, the newly derived optimal combining strategy can be readily combined with some existing strategies, such as using the shrinkage covariance matrix estimators of Ledoit and Wolf (2004, 2017) or imposing the factor structure of MacKinlay and Pastor (2000), to further improve portfolio performance. For the combining portfolios, we further obtain the exact distribution of the out-of-sample returns and explicit expressions of the expected out-of-sample utilities, which provide a fast and accurate way of evaluating the portfolios and offer analytical insights into portfolio construction and performance evaluation.
Keywords: portfolio choice, estimation risk, mean-variance optimization, optimal combining
JEL Classification: G11, G12, C11
Suggested Citation: Suggested Citation