Static and Dynamic Risk Capital Allocations With the Euler Rule

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