Enhancing gradient capital allocation with orthogonal convexity scenarios

Gradient capital allocation, also known as Euler allocation, is a technique used to redistribute diversified capital requirements among different segments of a portfolio. The method is commonly employed to identify dominant risks, assessing the risk-adjusted profitability of segments, and installing limit systems. However, capital allocation can be misleading in all these applications because it only accounts for the current portfolio composition and ignores how diversification effects may change with a portfolio restructuring. This paper proposes enhancing the gradient capital allocation by adding "orthogonal convexity scenarios" (OCS). OCS identify risk concentrations that potentially drive portfolio risk and become relevant after restructuring. OCS have strong ties with principal component analysis (PCA), but they are a more general concept and compatible with common empirical patterns of risk drivers being fat-tailed and increasingly dependent in market downturns. We illustrate possible applications of OCS in terms of risk communication and risk limits.