Robust Benchmark Design

Recent scandals over the manipulation of LIBOR, foreign exchange benchmarks, and other financial benchmarks have spurred policy discussions over their appropriate design. We characterize the optimal fixing of a benchmark as an estimator of a market value or reference rate. The fixing data are the reports or transactions of agents whose profits depend on the fixing, and who may therefore have incentives to manipulate it. If the benchmark administrator cannot detect or deter the strategic splitting of trades, we show that the best linear unbiased fixing is the commonly used volume-weighted average price (VWAP).