Applications of nonlinear stochastic discount factors in performance analysis and tail risk

Abstract

We propose a new class of performance measures for Hedge Fund (HF) returns based on a family of empirically identi able stochastic discount factors (SDFs). These SDF-based measures incorporate no-arbitrage pricing restrictions and naturally embed information about higher-order mixed moments between HF and benchmark factors returns. We provide full asymptotic theory for our SDF estimators that allows us to test for the statistical signi cance of each fund's performance and for the relevance of individual benchmark factors in identifying each proposed measure. Empirically, we apply our methodology to a large panel of individual hedge fund returns, revealing sizable di erences across performance measures implied by di erent exposures to higher-order mixed moments. Moreover, when we compare SDF-based measures to the traditional linear regression approach (Jensen's alpha), our measures identify a signi cantly smaller fraction of funds in the cross-section of HFs with statistically signi cant performances