Aggregation of preferences for skewed asset returns

This paper characterizes the equilibrium demand and risk premiums in the presence of skewness risk. In a model with a single time period, we extend the classical mean-variance two-fund separation theorem to a three-fund separation theorem. The additional fund is the skewness portfolio, i.e. a portfolio that gives the optimal hedge of the squared market return; it contributes to the skewness risk premium through co-variation with the squared market return and supports a stochastic discount factor that is quadratic in the market return. When the skewness portfolio does not replicate the squared market return, a tracking error appears; this tracking error contributes to risk premiums through kurtosis and pentosis risk. In addition to the common powers of market returns, this tracking error shows up in stochastic discount factors as priced factors that are products of the tracking error and market returns. Extending the one-period to a two-period framework introduces an additional volatility-based risk factor in the stochastic discount factor as well as a hedging demand in individual asset allocations due to volatility risk.