Linking Risk Management Under Expected Shortfall to Loss-Averse Behavior

Abstract

We introduce and solve an optimal asset allocation problem under a weighted expected shortfall (WES) constraint, which contains the risk management problem under an expected shortfall constraint of Basak and Shapiro (2001) as a special case. Furthermore, we link our risk management problem under the WES constraint with an optimal asset allocation with a multiple-reference-based preference (MRBP) and find that the optimal wealth with MRBP owns the same form as the optimal solution under the WES constraint. For the degenerate case with a fixed reference level, we are able to determine the critical maximal allowed expected shortfall constraint as a function of the loss aversion parameters to achieve equivalence. It is interesting to observe that, while no equivalence can be in general obtained between the WES
and the MRBP solution, the optimal terminal wealth of the WES can be made to coincide with the
MRBP terminal wealth in the most favorable and in the worst market states.
In addition, we carry out a general equilibrium analysis in the presence of a WES/MRBP risk manager.

Keywords: risk management, (weighted) expected shortfall, asset allocation, multiple-reference-based preferences

JEL Classification: G11, G12