Can unpredictable risk exposure be priced?

We study the link between beta predictability and the price of risk. An investor who desires exposure to a certain risk factor needs to predict what next period’s beta will be. We use a simple model to show that an ambiguity averse agent’s demand is lower when betas are hard to predict, leading to a reduction in risk premiums. We test the implications for downside betas and VIX betas. We find that they have economically and statistically small prices of risk once we account for the fact that an investor cannot observe ex-post realized betas when determining asset demand.