Risk Pricing Under Gain–Loss Asymmetry

We propose a novel gain–loss asymmetric utility model—losses relative to a reference point incur discontinuously more disutility than comparable gains—under which we derive closed-form asset pricing solutions within the workhorse “long-run risk” asset pricing model. Our formal analysis reveals gain–loss asymmetry has a dual impact on risk prices. First, a level effect: the expected excess returns of risky assets are made higher and the risk-free rate lower by the kink in the preferences. Second, a cross-sectional effect: the increase in expected returns for an additional unit of risk is higher (lower) for safer (riskier) assets, so expected returns increase nonlinearly with risk exposures. This second effect, absent in standard smooth utility models, can help rationalize, both qualitatively and quantitatively, key puzzles in empirical finance—the fit of the security market line and the downward-sloping term structure of equity risk premia—without compromising on the model’s ability to match the equity premium in the data.

This paper was accepted by Tomasz Piskorski, finance.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2025.02286.