Optimal Benchmarking for Active Portfolio Managers under Linear or Affine Compensation Schemes

Within an agency theoretic framework adapted to the portfolio delegation issue, we show how to construct optimal benchmarks. In accordance with U.S. regulations, the benchmark-adjusted compensation scheme is taken to be symmetric. The investor’s only control is to force the manager to adopt the appropriate benchmark. Solving simultaneously the manager’s and the investor’s dynamic optimization programs in a fairly general framework, we characterize the optimal benchmark. We then provide explicit solutions when the investor’s and the manager’s utility functions exhibit different CRRA parameters. We find that, even under optimal benchmarking, it is never optimal for the manager, and therefore for the investor, to follow exactly the benchmark, except in a very restrictive case. We finally assess by simulation the practical importance, in particular in terms of the investor’s welfare, of selecting a sub-optimal benchmark.