Static and Dynamic Risk Capital Allocations With the Euler Rule

Abstract

Risk capital allocations are of central importance in performance measurement. A popular solution concept in the academic literature is the Euler rule. This paper studies the volatility of the Euler rule for capital allocation in static and dynamic empirical applications with a simulated history. The Euler rule is not continuous in small changes of the underlying risk capital allocation problem, and we show that the Euler rule in combination with the Value-at-Risk is very sensitive to empirical measurement error. The use of a known distribution with estimated parameters helps to reduce this error. The Euler rule with an Expected Shortfall risk measure is less volatile, but still more volatile than the proportional rule.

Keywords: Dynamic Capital Allocation, Euler Rule, Proportional Rule, Simulation, Value-at-Risk

JEL Classification: G32, G22