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

50 Pages Posted: 18 Apr 2019 Last revised: 20 Mar 2020

See all articles by Valery Polkovnichenko

Valery Polkovnichenko

Federal Reserve Board - Divison of Research and Statistics

Date Written: February 20, 2020

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

Suggested Citation

Polkovnichenko, Valery, On the (Im)Possibility of Estimating Expected Return from Risk-Neutral Variance (February 20, 2020). Available at SSRN: https://ssrn.com/abstract=3357656 or http://dx.doi.org/10.2139/ssrn.3357656

Valery Polkovnichenko (Contact Author)

Federal Reserve Board - Divison of Research and Statistics ( email )

20th and C Streets, NW
Washington, DC 20551
United States

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