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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

This paper proposes a new novel to calculate tail risks incorporating risk-neutral information without dependence on options data. Proceeding via a non parametric approach we derive a stochastic discount factor that correctly price a chosen panel of stocks returns. With the assumption that states probabilities are homogeneous we back out the risk neutral distribution and calculate five primitive tail risk measures, all extracted from this risk neutral probability. The final measure is than set as the first principal component of the preliminary measures. Using six Fama-French size and book to market portfolios to calculate our tail risk, we find that it has significant predictive power when forecasting market returns one month ahead, aggregate U.S. consumption and GDP one quarter ahead and also macroeconomic activity indexes. Conditional Fama-Macbeth two-pass cross-sectional regressions reveal that our factor present a positive risk premium when controlling for traditional factors.