Why do rational investors like variance at the peak of a crisis? A learning-based explanation

Abstract

Investors’ learning can drastically alter the dynamics of the variance risk premium: it no longer increases as economic conditions deteriorate but exhibits a highly nonlinear pattern, occasionally even turning negative. We demonstrate this intuition using a model where investors rationally form their belief about the hidden economic state. When the “bad” state becomes probable, investors start liking high future variance because it overwhelmingly correlates with lower marginal utility. This mechanism rationalizes the puzzling observation that risk-neutral volatility falls short of physical volatility at the peak of a severe crisis. Our results shed light on the interpretation of good economic uncertainty.