On the (Im)Possibility of Estimating Expected Return from Risk-Neutral Variance

Abstract

I investigate the possibility of estimating expected return on a stock from a linear equation with known coefficients using only risk-neutral variance of return and reach a negative conclusion. The formula is not viable because: (i) its coefficients are indeterminate (unknown) and are not identified jointly; (ii) its approximation error, when the relative risk aversion exceeds one, has the same order of magnitude as the expected excess return it is intended to estimate; (iii) it requires one-factor structure (perfect/high correlation) of the time-series of conditional idiosyncratic variances for all stocks, which is rejected empirically and is hard to justify theoretically. For some stocks, risk-neutral variance determines upper or lower bound on expected return, independently of the risk aversion in the underlying economy.

Keywords: cross-section of expected returns, risk-neutral distribution

JEL Classification: G12