Knight Meets Sharpe: Capital Asset Pricing under Ambiguity

Abstract

This paper extends the classical mean-variance preferences to mean-variance-ambiguity preferences by relaxing the assumption that probabilities are known, and instead assuming that probabilities are uncertain. In general equilibrium, the two-fund separation theorem is preserved and the market portfolio is identified as efficient. Thereby, introducing ambiguity into the capital asset pricing model indicates that the \emph{ambiguity premium} corresponds to systematic ambiguity, which is distinguished from systematic risk. Using the measurable closed-form beta ambiguity, well-known performance measures are generalized to account for ambiguity alongside risk. The introduced capital asset pricing model is empirically implementable and provides insight into empirical asset pricing anomalies. The model can be extended to other applications, including investment decisions and valuations.

Keywords: Ambiguity Measurement, Perceived Probabilities, Mean-Variance, Optimal Portfolio, Investment Decisions

JEL Classification: D81, G4, G11, G12