Risk-Adjusted Option-Implied Moments

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may Risk-Adjusted Option-Implied Moments AbstractOption-implied moments, like implied volatility, contain useful information about an underlying asset's return distribution, but are derived under the risk-neutral probability measure. This paper shows how to convert risk-neutral moments into the corresponding physical ones. The main theoretical result expresses moments under the physical probability measure in terms of observed option prices and the preferences of a representative investor. Based on this result, we investigate several empirical questions. We show that a model of a representative investor with CRRA utility can explain the variance risk premium for the S&P500 index but fails to capture variance and skewness risk premiums simultaneously. Moreover, we present methods to estimate forward-looking market risk premiums and investors' disappointment aversion implied in market prices. JEL Classification: G13, G17, C51, C53 1 I IntroductionThe use of option prices to gain information about the underlying's return distribution is an important idea in finance. Certainly, the most prominent example is implied volatility that goes back to Latané and Rendleman (1976) Option-implied moments have the drawback that they are formed under the riskneutral probability measure, whereas many applications require moments under the physical (real-world, actual, subjective) probability measure. Ideally, one would exploit all information contained in current option prices and have a simple but economically justified method to adjust for risk, i.e., to move from the risk-neutral moment to the corresponding physical moment. This paper provides such a method by showing explicitly how the risk adjustment depends on current option prices and risk preferences. This result has many potential uses. A specific one is to express ex-ante return moments under the physical measure, which we call risk-adjusted implied moments, in terms of observed option prices and preferences. The presented methodology 2 is very general. It applies to implied moments as in Neuberger (2012), implied moments as in Bakshi, Kapadia, and Madan (2003), which refer to log returns, and to the corresponding moments of discrete returns. It can deal with both central and non-central moments and is not restricted to a narrow class of utility functions.The empirical contributions of the paper refer to different applications of the presented methodology for the S&P500 index....

Which Beta Is Best? On the Information Content of Option‐implied Betas

“…(), also assuming constant relative risk aversion, show that the difference in the n th moment of the risk‐neutral and physical distribution depends on the (n +1) st moment of the physical distribution . Brinkmann and Korn () provide exact formulas for the difference between risk‐neutral and physical moments under quite general utility functions. However, since these results are limited to index options and do not consider covariances with individual stocks, we cannot easily draw conclusions about risk‐adjusted implied betas.…”