Return-Based Risk Management for Hedge Fund Investments

Return-based methods are frequently used by risk managers to estimate the exposures of hedge funds because of the limited transparency offered by such investment schemes. This paper proposes a method to assess the limitations of such methods using the Posterior Cramer-Rao Bound (PCRB). This PCRB allows one to quantify the achievable accuracy of exposure estimates without having to compare computed estimates to actual exposures. This approach is particularly useful in situations where exposure data is unavailable. The main determinants of the PCRB are shown to be the variance of the hedge fund exposures and the ratio of market variance to idiosyncratic error variance. The paper also discusses the effects of asset correlation, return frequency, and the use of return contributions on the PCRB. To illustrate the application of the methodology, we provide four examples in which we compare the PCRB to the computed estimation error using real hedge fund data.