Risk Prudence Premia

We show that risk prudence - the aversion to downside risk - is the common source of three features of asset markets: a negative variance risk premium, a downward-sloping implied-volatility skew, and a downside-risk premium in the cross-section of stock returns. Embedding the skew-normal distribution in a minimum-divergence stochastic discount factor, we derive the prudence premia in closed form; a single parameter that aggregates the skewness of the priced factors signs them. In a Gaussian economy the variance premium vanishes for any degree of risk aversion. Estimating the discount factor from U.S. characteristic-managed portfolios - using no option data - we decompose it into a symmetric Gaussian factor and an asymmetric downside-risk factor, and reproduce the salient features of equity-index option markets: option-implied variance exceeds its realized counterpart, and out-of-the-money puts trade at higher implied volatilities than out-of-the-money calls.