Risk Management with Benchmarking

Abstract

Portfolio theory must address the fact that in reality, portfolio managers are evaluated relative to a benchmark, and therefore adopt risk management practices to account for the benchmark performance. We capture this risk management consideration by allowing a prespecified shortfall from a target benchmark-linked return, consistent with growing interest in such practice. In a dynamic setting, we demonstrate how a risk averse portfolio manager optimally under- or overperforms a target benchmark under different economic conditions, depending on his attitude towards risk and choice of the benchmark. Investors can therefore achieve their desired gain/loss characteristics for funds under management through an appropriate combined choice of the benchmark and money manager.