The Coskewness Puzzle and Stochastic Discount Factor Volatility

In this paper, we propose a novel test of the 3M-CAPM under a positivity constraint on the estimated stochastic discount factor (SDF) and, more importantly, an upper bound on its volatility. The positivity constraint rules out arbitrage opportunities, while the restriction on SDF volatility rules out unduly large Sharpe ratios and is based on a sensible upper bound on investors’ risk aversion. Together, these restrictions reduce the risk of spurious estimates of the 3M-CAPM parameters without having to impose Dittmar’s (2002) overly-restrictive assumption that the representative investor’s utility function is concave in wealth. Under these restrictions, the 3M-CAPM is empirically admissible in the cross-section of excess returns on industry-sorted portfolios (and both the covariance and coskewness premia retain large part of their explanatory power) but it is rejected when the set of test asset payoffs is augmented to include portfolios managed using conditioning information.