Pricing kernel monotonicity and the conservativeness of risk-neutral forecasts

This paper studies the relationship between option-implied, risk-neutral forecasts and their real-world counterparts through the lens of stochastic dominance and pricing kernel monotonicity. We show that when the pricing kernel is weakly decreasing in asset payoffs, the real-world distribution first-order stochastically dominates the risk-neutral one, implying that the risk-neutral forecast is more conservative. The situation is reversed when the pricing kernel is weakly increasing, implying that risk-neutral forecasts may be more optimistic than conservative. We further show that this monotonicity is closely linked to the dependence between asset payoffs and aggregate consumption. Our results provide a new perspective on the pricing kernel puzzle (that is, the empirical finding that pricing kernels for major market indexes are often nonmonotonic). Our results, together with the pricing kernel puzzle, suggest that the commonly held belief in the conservativeness of risk-neutral forecasts is not generally warranted, even for broad market indexes.