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The Recovery Theorem

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  • Stephen A. Ross

Abstract

We can only estimate the distribution of stock returns but we observe the distribution of risk neutral state prices. Risk neutral state prices are the product of risk aversion - the pricing kernel - and the natural probability distribution. The Recovery Theorem enables us to separate these and to determine the market's forecast of returns and the market's risk aversion from state prices alone. Among other things, this allows us to determine the pricing kernel, the market risk premium, the probability of a catastrophe, and to construct model free tests of the efficient market hypothesis.

Suggested Citation

  • Stephen A. Ross, 2011. "The Recovery Theorem," NBER Working Papers 17323, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:17323
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    File URL: http://www.nber.org/papers/w17323.pdf
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    References listed on IDEAS

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    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
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    6. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    7. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    8. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    9. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    10. Dybvig, Philip H & Rogers, L C G, 1997. "Recovery of Preferences from Observed Wealth in a Single Realization," The Review of Financial Studies, Society for Financial Studies, vol. 10(1), pages 151-174.
    11. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
    12. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    13. Dybvig, Philip H. & Ross, Stephen A., 2003. "Arbitrage, state prices and portfolio theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 10, pages 605-637, Elsevier.
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    Cited by:

    1. Ivanova, Vesela & Puigvert Gutiérrez, Josep Maria, 2014. "Interest rate forecasts, state price densities and risk premium from Euribor options," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 210-223.
    2. Anisha Ghosh & Christian Julliard & Alex P. Taylor, 2017. "What Is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 30(2), pages 442-504.
    3. Jukka Sihvonen & Sami Vähämaa, 2014. "Forward‐Looking Monetary Policy Rules and Option‐Implied Interest Rate Expectations," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(4), pages 346-373, April.
    4. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.

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    More about this item

    JEL classification:

    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • G0 - Financial Economics - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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