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Empirical risk aversion functions-estimates and assessment of their reliability

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  • Kang, Byung Jin
  • Kim, Tong Suk

Abstract

In this paper, we examine investor's risk preferences implied by option prices. In order to derive these preferences, we specify the functional form of a pricing kernel and then shift its parameters until realized returns are best explained by the subjective probability density function, which consists of the ratio of the risk-neutral probability density function and the pricing kernel. We examine, alternatively, pricing kernels of power, exponential, and higher order polynomial forms. Using S&P 500 index options, we find surprising evidence of risk neutrality, instead of risk aversion, in both the power and exponential cases. When extending the underlying assumption on the specification of the pricing kernel to one of higher order polynomial functions, we obtain functions exhibiting 'monotonically decreasing' relative risk aversion (DRRA) and anomalous 'inverted U-shaped' relative risk aversion. We find, however, that only the DRRA function is robust to variation in sample characteristics, and is statistically significant. Finally, we also find that most of our empirical results are consistent, even when taking into account market imperfections such as illiquidity.

Suggested Citation

  • Kang, Byung Jin & Kim, Tong Suk, 2008. "Empirical risk aversion functions-estimates and assessment of their reliability," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 1123-1138, December.
  • Handle: RePEc:eee:finana:v:17:y:2008:i:5:p:1123-1138
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    4. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    5. Kang, Byung Jin & Kim, Tong Suk, 2006. "Option-implied risk preferences: An extension to wider classes of utility functions," Journal of Financial Markets, Elsevier, vol. 9(2), pages 180-198, May.
    6. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    7. Nikkinen, Jussi, 2003. "Normality tests of option-implied risk-neutral densities: evidence from the small Finnish market," International Review of Financial Analysis, Elsevier, vol. 12(2), pages 99-116.
    8. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, February.
    9. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March.
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