Optimal Benchmarks from a Trader's Perspective

Abstract

The problem of benchmarking in financial markets is an important one. It could be a mutual fund looking to meet its cash inflows and outflows or a brokerage that has been contracted a benchmark price. There is also often incentive to manipulate benchmark. We introduce a discrete-time market model to analyze the trade-off between attainability of a benchmark and its resistance to manipulation. In our setting with a single asset and temporary price impact, an honest trader tries to minimize the costs and deviation to the benchmark while a manipulator pushes the benchmark price up. The resulting optimal benchmark is very similar to the VWAP (volume weighted average price) in that prices are weighted by traded volumes. We find another VWAP-like benchmark in a market that includes an auction with an imbalance announcement that has a permanent price impact.