Knight Meets Sharpe: Capital Asset Pricing under Ambiguity

Yehuda Izhakian

Abstract

This paper extends the standard mean-variance preferences to mean-variance-ambiguity preferences by relaxing the assumption that probabilities are known, and instead assuming that probabilities are uncertain. The optimal portfolio is identified in general equilibrium, demonstrating that the two-fund separation theorem is preserved. Thereby, introducing ambiguity into the capital asset pricing model shows that the ambiguity premium corresponds to systematic ambiguity, which is distinguished from the systematic risk. With the closed-form measurable beta ambiguity, performance measures are generalized to account for ambiguity alongside risk. Use of this model can be extended to other applications including investment decisions and valuations.