Loss Aversion, Behavioral Finance, and the Asymmetry of Volatility and Returns

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M. Levy, “Loss aversion and the price of risk,” Quantitative Finance (forthcoming):

Abstract: This paper derives a simple theoretical relationship between the degree of loss aversion, the concavity/convexity of the value function, and the equilibrium market price of risk. We show that while the degree of loss aversion is key in determining the market price of risk, the convexity/concavity of the value function is much less important in this respect. The theoretical relationship obtained is tested empirically by using international data from 16 different countries during over 100 years, as documented by Dimson et al. [Triumph of the Optimists: 101 Years of Global Investment Returns, 2002 (Princeton University Press)]. The empirical data yield an estimate of ?=2.3 for the loss aversion index. This value is in striking agreement with estimates obtained in the very different methodology of laboratory experiments of individual decision-making.

I couldn’t find a preprint of this anywhere for those without database access, unfortunately, but the result is what matters, anyway: people seem to be about as loss-averse empirically as they are expected to be based on smaller studies. One reason this feature of human psychology is so important is that it is one probable cause of the persistence of the variance/volatility risk premium, which is, as some of you know, the foundation of everything I do.

A. Hibbert, R. Daigler, & B. Dupoyet, “A behavioral explanation for the negative asymmetric return–volatility relation,Journal of Banking & Finance 32:10 (2008), pp. 2254-2266. (alt link)

Abstract: We examine the short-term dynamic relation between the S&P 500 (Nasdaq 100) index return and changes in implied volatility at both the daily and intraday level. Neither the leverage hypothesis nor the volatility feedback hypothesis adequately explains the results. Alternatively, we propose that the behavior of traders (from the representativeness, affect, and extrapolation bias concepts of behavioral finance) is consistent with our empirical results of a strong daily and intraday negative return–implied volatility relation. Moreover, both the presence and magnitude of the negative relation and the asymmetry between return and implied volatility are most closely associated with extreme changes in the index returns. We also show that the strength of the relation is consistent with the implied volatility skew.

The argument here is that neither of the classic explanations for the negative correlation between returns and volatility (the leverage and feedback hypotheses) are sufficient to explain the intraday effects that the authors observe. They posit some behavioral factors as an alternate explanation, and while I’m intuitively sympathetic to those elements, I’m not sure whether they are well motivated. So, the shorter abstract: there are negative return-volatility correlations, even intraday, the old explanations aren’t good enough, and here are some new ones.

Photo: Daniel Kahneman looking pleased, courtesy of Flickr user eirisko.

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Jared Woodard specializes in trading volatility as an asset class. With over a decade of experience trading options and other volatility products ... Read More

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