Optimal portfolio choice with benchmark

When a benchmark model is inefficient, including additional assets to the benchmark portfolios can improve its performance. In reality, however, the efficiency of a benchmark model relative to a given set of test assets is ex ante unknown, and the optimal portfolio is constructed based on estimated parameters. Given the unknown value of including test assets and the estimation risk, whether and how to include the test assets becomes a critical question faced by 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. In particular, our proposed combining strategy addresses two layers of estimation errors: those in the estimated optimal portfolios and those in the implementable combining coefficients