Portfolio optimization for an investor with a benchmark

摘要

The most common equity mandate in the financial industry is to try to outperform an externally given benchmark with known weights. The standard quantitative approach to do this is to optimize the portfolio over short time horizons consecutively, using one-period models. However, it is not clear that this approach actually yields good performance in the long run. We provide a theoretical justification to this methodology by verifying that applying the one-period benchmark-relative mean-variance portfolio, i.e., the industry standard optimal portfolio, continuously is in fact the solution to a specific continuous time portfolio optimization problem: a maximum expected utility problem for an investor who is compared against a benchmark and evaluates her performance based on exponential utility at a deterministic future date.