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The Value of a Probability Forecast from Portfolio Theory

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  • D. Johnstone

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    Abstract

    A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “marketâ€\x9D (all available forecasts). A forecast is seen to be more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easyâ€\x9D trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honestâ€\x9D alternative to the ruse of reporting conservative probability assessments. Copyright Springer Science+Business Media, LLC 2007

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    File URL: http://hdl.handle.net/10.1007/s11238-006-9023-1
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    Bibliographic Info

    Article provided by Springer in its journal Theory and Decision.

    Volume (Year): 63 (2007)
    Issue (Month): 2 (September)
    Pages: 153-203

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    Handle: RePEc:kap:theord:v:63:y:2007:i:2:p:153-203

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    Web page: http://www.springerlink.com/link.asp?id=100341

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    Keywords: forecast evaluation; portfolio theory; probability forecast; probability score;

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    1. Daniel Friedman, 1983. "Effective Scoring Rules for Probabilistic Forecasts," Management Science, INFORMS, vol. 29(4), pages 447-454, April.
    2. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    3. R. Winkler & Javier Muñoz & José Cervera & José Bernardo & Gail Blattenberger & Joseph Kadane & Dennis Lindley & Allan Murphy & Robert Oliver & David Ríos-Insua, 1996. "Scoring rules and the evaluation of probabilities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 5(1), pages 1-60, June.
    4. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    5. Robert T. Clemen & Robert L. Winkler, 1990. "Unanimity and Compromise Among Probability Forecasters," Management Science, INFORMS, vol. 36(7), pages 767-779, July.
    6. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    7. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-30, June.
    8. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-17, June.
    9. Leonard MacLean & Yonggan Zhao & William Ziemba, 2011. "Mean-variance versus expected utility in dynamic investment analysis," Computational Management Science, Springer, vol. 8(1), pages 3-22, April.
    10. Epstein, Larry G, 1985. "Decreasing Risk Aversion and Mean-Variance Analysis," Econometrica, Econometric Society, vol. 53(4), pages 945-61, July.
    11. Murphy, Allan H. & Winkler, Robert L., 1992. "Diagnostic verification of probability forecasts," International Journal of Forecasting, Elsevier, vol. 7(4), pages 435-455, March.
    12. Mark Grinblatt & Sheridan Titman, . "Portfolio Performance Evaluation: Old Issues and New Insights," Rodney L. White Center for Financial Research Working Papers 22-88, Wharton School Rodney L. White Center for Financial Research.
    13. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. " Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    14. Borch, Karl, 1969. "A Note on Uncertainty and Indifference Curves," Review of Economic Studies, Wiley Blackwell, vol. 36(105), pages 1-4, January.
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