Calibrating risk preferences with the generalized capital asset pricing model based on mixed conditional value-at-risk deviation

Konstantin Kalinchenko, Stan Uryasev and R. Tyrrell Rockafellar

Abstract

ABSTRACT

The generalized capital asset pricing model based on mixed conditional value-at-risk (CVaR) deviation is used for calibrating the risk preferences of investors. Risk preferences are determined by coefficients in the mixed CVaR deviation. The corresponding new generalized beta is designed to capture the tail performance of S&P 500 returns. Calibration of the coefficients is done by extracting information about risk preferences from put-option prices on the S&P 500. Actual market option prices are matched with the estimated prices from the pricing equation based on the generalized beta. Calibration is done for 153 moments in time with intervals of approximately one month. Results demonstrate that the risk preferences of investors change over time, reflecting investors' concern about potential tail losses. A new index of fear is introduced, calculated as a sum of several coefficients in the mixed CVaR deviation.