Cost gap, Shapley, or nucleolus allocation: Which is the best game‐theoretic remedy for the low‐risk anomaly?

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.