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