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Recovering Risk Aversion from Option Prices and Realized Returns

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Author Info
Jens Carsten Jackwerth (Haas School of Business, University of California, Berkeley)

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Abstract

A relationship exists between aggregate risk-neutral and subjective probability distributions and risk aversion functions. Using a variation of the method developed by Jackwerth and Rubinstein (1996), we estimate risk-neutral probabilities reliably from option prices. Subjective probabilities are estimated from realized returns. This paper then introduces a technique to empirically derive risk aversion functions implied by option prices and realized returns simultaneously. These risk aversion functions dramatically change shapes around the 1987 crash: Precrash, they are positive and decreasing in wealth and thus consistent with standard economic theory. Postcrash, they are partially negative and increasing and irreconcilable with the theory. Overpricing of out-of-the-money puts is the most likely cause. A simulated trading strategy exploiting this overpricing shows excess returns even after accounting for the possibility of further crashes and transaction costs.

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Paper provided by EconWPA in its series Finance with number 9803002.

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Date of creation: 13 Mar 1998
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Handle: RePEc:wpa:wuwpfi:9803002

Note: Revision, October 1997; postscript
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References listed on IDEAS
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  1. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December. [Downloadable!] (restricted)
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  2. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(01), pages 91-115, March. [Downloadable!]
  3. Joshua V. Rosenberg & Robert F. Engle, 1997. "Option Hedging Using Empirical Pricing Kernels," NBER Working Papers 6222, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn. [Downloadable!] (restricted)
  5. Hayne E. Leland., 1996. "Beyond Mean-Variance: Performance Measurement of Portfolios Using Options or Dynamic Strategies," Research Program in Finance Working Papers RPF-263-rev, University of California at Berkeley. [Downloadable!]
  6. Jens Carsten Jackwerth., 1996. "Implied Binomial Trees: Generalizations and Empirical Tests," Research Program in Finance Working Papers RPF-262, University of California at Berkeley. [Downloadable!]
  7. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February. [Downloadable!] (restricted)
  8. Brennan, M.J. & Solanki, R., 1981. "Optimal Portfolio Insurance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(03), pages 279-300, September. [Downloadable!]
  9. Constantinides, George M, 1982. "Intertemporal Asset Pricing with Heterogeneous Consumers and without Demand Aggregation," Journal of Business, University of Chicago Press, vol. 55(2), pages 253-67, April. [Downloadable!] (restricted)
  10. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  11. Rubinstein, Mark E, 1973. "A Comparative Statics Analysis of Risk Premiums," Journal of Business, University of Chicago Press, vol. 46(4), pages 605-15, October. [Downloadable!] (restricted)
  12. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04. [Downloadable!] (restricted)
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  13. Leland, Hayne E, 1980. " Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-94, May. [Downloadable!] (restricted)
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  14. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," Journal of Business, University of Chicago Press, vol. 51(4), pages 653-72, October. [Downloadable!] (restricted)
  15. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December. [Downloadable!] (restricted)
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