Pricing kernel monotonicity and the conservativeness of risk-neutral forecasts

A monotone projected pricing kernel provides a sufficient condition for stochastic dominance between real-world and risk-neutral distributions.When the projected pricing kernel is weakly decreasing (increasing), risk-neutral forecasts are more conservative (optimistic) than the real-world counterparts.The empirical failure of pricing kernel monotonicity implies that conservativeness is not a general property, even for broad market indices.For some hedging assets, the risk-neutral forecasts may provide an optimistic bounds rather than conservative ones. 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. Copyright Infopro Digital Limited. All rights reserved. You may share this content using our article tools. As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (clause 2.4), an Authorised User may only make one copy of the materials for their own personal use. You must also comply with the restrictions in clause 2.5. If you would like to purchase additional rights please email info@risk.net