Risk Management with Benchmarking

TLDR

Portfolio theory must account for benchmark‑based evaluation, prompting managers to adjust risk practices accordingly. The study introduces a model that permits a specified shortfall from a benchmark‑linked target return to capture risk‑management considerations. The framework allows a prespecified shortfall from a benchmark‑linked return and is extended to analyze return patterns across money‑management segments. The model shows that a risk‑averse manager can optimally under‑ or over‑perform a benchmark depending on risk attitude and benchmark choice, enabling investors to tailor performance profiles by selecting appropriate benchmarks and managers, and it also explains observed return patterns across money‑management segments.

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. The analysis therefore illustrates how investors can achieve their desired performance profile 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.