A note on ambiguity-adjusted asset pricing

This paper presents an asset pricing formula that accounts for risk and ambiguity, assuming these two factors drive the representative investor’s decision-making. While properly controlling for risk is paramount for any decision-maker, precisely defining the probabilities associated with risky events poses a significant challenge in many real-world situations. Rarely is there a single agreed-upon probability distribution that captures future uncertainty. Instead, many candidate probability models often need clarification and adjustment from the decision-maker based on their beliefs and information. The perceived probability measure is a derived concept that incorporates this set of possible probability distributions along with the decision-maker’s attitude toward ambiguity. It allows for a flexible representation of uncertainty by distorting the probabilities according to how the decision-maker views the ambiguity in each scenario. This paper presents the asset pricing formula based on this perceived probability so that the resulting asset prices naturally incorporate the combined effects of risk and ambiguity aversion. Crucially, we further show that the overall premium in expected market returns can be decomposed into separate risk premium and ambiguity premium components. This disentanglement clearly interprets how much each factor contributes to the total premium investors demand. By grounding the analysis in the perceived probabilities, the formula provides a theoretically consistent way to quantify the ambiguity portion of the premium beyond just risk compensation. Furthermore, our formulation helps clarify the methodological inconsistency identified in previous works, notably in Izhakian (J. Econ. Theory 187, 105001, 2020), and aligns with the perspective advanced by Fu et al. (J. Econ. Theory 207, 105573, 2023).