The importance of dynamic risk constraints for limited liability operators

TL;DR

This paper demonstrates that dynamic risk constraints can effectively limit excessive risk-taking in portfolio optimization with S-shaped utility, unlike static constraints, but may be ineffective if derivatives are accessible.

Contribution

It introduces the importance of dynamic risk constraints in portfolio optimization with S-shaped utility, highlighting their effectiveness and limitations compared to static measures.

Findings

Dynamic risk constraints can effectively limit risk in certain conditions.

Static risk measures are ineffective for tail-risk-seeking traders.

Access to derivatives can undermine the effectiveness of dynamic risk constraints.

Abstract

Previous literature shows that prevalent risk measures such as Value at Risk or Expected Shortfall are ineffective to curb excessive risk-taking by a tail-risk-seeking trader with S-shaped utility function in the context of portfolio optimisation. However, these conclusions hold only when the constraints are static in the sense that the risk measure is just applied to the terminal portfolio value. In this paper, we consider a portfolio optimisation problem featuring S-shaped utility and a dynamic risk constraint which is imposed throughout the entire trading horizon. Provided that the risk control policy is sufficiently strict relative to the asset performance, the trader's portfolio strategies and the resulting maximal expected utility can be effectively constrained by a dynamic risk measure. Finally, we argue that dynamic risk constraints might still be ineffective if the trader has access to a derivatives market.