Option‐Implied Risk Aversion Estimates

Abstract

Using a utility function to adjust the risk-neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options, and both power and exponential-utility functions, we estimate the representative agent's relative risk aversion (RRA) at different horizons. The estimated coefficients of RRA are all reasonable. The RRA estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of RRA declines broadly with the forecast horizon and is lower during periods of high market volatility.ESTIMATING THE REPRESENTATIVE AGENT'S or the market's degree of risk aversion from securities prices has a long history. However, it is only recently that scholars have begun using options data to do so. Options provide a particularly promising context for studying risk preferences. Stocks are infinitely lived and so inferences must be drawn from the discounted stream of cash f lows over an indefinite horizon. Usually this involves additional assumptions as to how those cash f lows evolve (e.g., constant growth of dividends). Since only one value, the discounted present value of all cash f lows, is known, no inferences are possible about variations in preferences over different horizons. Options on the other hand have a fixed expiry date at which payoffs are realized. 1 Furthermore, options contracts exist for different investment horizons. Options thus permit studying preferences over specific horizons and simultaneously over multiple horizons. Futures contracts also share this fixed-horizon characteristic. Options * Bliss is with the Federal Reserve Bank of Chicago and Panigirtzoglou is with the Bank of England. We are particularly grateful for helpful discussions with Lars Hansen; for comments for the guidance and suggestions of the editor Richard Green; and the referee. We thank Darrin Halcomb for his excellent research assistance. The views expressed herein are those of the authors and do not necessarily ref lect those of the Federal Reserve Bank of Chicago or the Bank of England. This paper was previously titled "Recovering Risk Aversion from Options." Any remaining errors are our own. 1 American options present a somewhat more complicated investment horizon, but only to the extent that early exercise is optional. Still, even in that case, American options allow a greater specificity of investment horizon than stocks do. furthermore, several central banks track monthly changes in implied PDFs to infer changes in market sentiment. Though to be absolutely fair, this evidence is indirect and not necessarily conclusive. We know of no study that has directly tested whether it is possible to reject the stationarity of implied risk-neutral PDFs over various time intervals. 10 Of course, "failure to reject" does not mean we should "accept." Our use of the term a "good forecast" is merely an expositional convenience and should be understood as such.11 Short Sterling options were also examined but failed to produc...

Single Stock Call Options as Lottery Tickets

“…11 Similarly, if investors are rational, their subjective density functions should be consistent, on average, with the empirical density function. Bliss and Panigirtzoglou (2004) find that subjective density functions, produced from RND adjusted by two types of representative investors' utility functions (power and exponential) with plausible relative risk aversion parameters, outperform RND on forecasting density functions.…”

“…This is a key step for testing the hypothesis that the CPT helps explaining overpricing of OTM options because we build on the assumption that investors' subjective density estimates should correspond on average 8 , to the distribution of realizations (Bliss and Panigirtzoglou, 2004). Thus, testing whether the CPT's weighting function explains the overpricing of OTM options, ultimately, relates to how the subjective density function produced by CPT's preferences matches empirical returns.…”

“…Thus, CPT-biased agents assess probability distributions as if their tails would contain more weight than in reality they do. In other words, CPT-biased 9 Anagnou et al (2002) and Bliss and Panigirtzoglou (2004) have tested the consistency between RNDs and physical densities estimated from historical data and found such distributions are inconsistent, i.e., RNDs are poor forecasters of the distribution of realizations. 10 The condition necessary for Eq.…”

“…Following Ait-Sahalia and Lo (2000) and Bliss and Panigirtzoglou (2004), Eq. (7) can be manipulated so that the constant of the pricing kernel vanishes, producing Eq.…”

“…The Figlewski (2010) method is close to the one by Bliss and Panigirtzoglou (2004), where body and tails are also extracted separately. Bliss and Panigirtzoglou (2004) use a weighed natural spline algorithm for interpolation, which has the same decreasing-noise effect in RNDs of using splines in the absence of knots, as done in Figlewski (2010).…”