Risk Management with Benchmarking

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 pre-specified 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 over-performs a target benchmark under different economic conditions, depending on his attitude towards risk and choice of the benchmark. The analysis therefore illustrates how investors can achieve their desired gain/loss characteristics for funds under management through an appropriate combined choice of the benchmark and money manager. We consider a variety of extensions, and also highlight the ability of our setting to shed some light on documented return patterns across segments of the money management industry.