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The Value of a Probability Forecast from Portfolio Theory

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  • D. Johnstone

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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  • D. Johnstone, 2007. "The Value of a Probability Forecast from Portfolio Theory," Theory and Decision, Springer, vol. 63(2), pages 153-203, September.
    • Handle: RePEc:kap:theord:v:63:y:2007:i:2:p:153-203
    DOI: 10.1007/s11238-006-9023-1
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    2. D. J. Johnstone, 2009. "Discussion of Penman," Abacus, Accounting Foundation, University of Sydney, vol. 45(3), pages 372-378, September.
    3. Jingni Yang, 2020. "The uniqueness of local proper scoring rules: the logarithmic family," Theory and Decision, Springer, vol. 88(2), pages 315-322, March.

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