Optimal Portfolio Choice with Unknown Benchmark Efficiency

When a benchmark model is inefficient, including test assets in addition to the benchmark portfolios can improve the performance of the optimal portfolio. In reality, the efficiency of a benchmark model relative to the test assets is ex ante unknown; moreover, the optimal portfolio is constructed based on estimated parameters. Therefore, whether and how to include the test assets becomes a critical question faced by real world investors. For such a setting, we propose a combining portfolio strategy, optimally balancing the value of including test assets and the effect of estimation errors. The proposed combining strategy can work together with some existing estimation risk reduction strategies. In both empirical data sets and simulations, we show that our proposed combining strategy performs well. This paper was accepted by Agostino Capponi, finance. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2021.01767 .