In this article, we illustrate that cooperative game theory may have the potential to solve the low‐risk puzzle, which has become one of the most important in modern finance because its implication of a negative risk‐return trade‐off poses a challenge to traditional models of asset prices. Using several simulation settings, we highlight that quantifying risk by means of assets' Shapley values, that is, assets' contributions to overall portfolio risk, instead of classic measures supplies a (more) positive risk‐return relationship in many practically relevant cases. This is partially attributable to the fact that the game‐theoretic risk measure captures more investment‐relevant information than commonly used alternatives.

Empirical research in investment management has discovered the puzzling phenomenon that, contrary to established capital market theory, low-risk assets tend to earn larger returns than their high-risk counterparts. In a recent contribution, Auer and Hiller (2019) emphasize that an inadequate quantification of risk may be the root of this problem. By interpreting a portfolio as a cooperative game, they arrive at the interesting finding that using assets' risk-based Shapley values instead of classic stand-alone risk measures has the potential to solve the low-risk puzzle. In this article, we extend their study first by considering additional game-theoretic risk allocation schemes, namely, the cost gap technique and the nucleolus method, and then by improving their simulation design via a larger number of assets and a supplementary determination of risk-return slopes. We find that the Shapley method outperforms the alternatives with respect to the generation of positive risk-return slopes. JEL CLASSIFICATIONG10; G11; C71 INTRODUCTIONFinancial research has revealed many capital market phenomena, which challenge the validity of the traditional asset pricing theory

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