Adding Value Through Risk Measurement: Capital Allocation & Beyond
Risk diversification is at the heart of insurance. In a modern Enterprise Risk Management (ERM) approach, a company's entire risk profile - including risk diversification and concentration - must be considered in decision-making processes such as insurance pricing, product design, asset allocation and reinsurance. The impact on risk-oriented performance measures such as return on risk-adjusted capital (RORAC) and economic value added (EVA) must also be assessed.
For risk managers, it is therefore essential to assess not only the overall risk of the enterprise, but also the impact of individual risks, business units and hedging instruments on the overall risk. In this context, the term "capital allocation" is a widely discussed and used concept. The gradient (also known as Euler) capital allocation principle plays an important role. The principle is directly linked to “marginal capital requirements” and is compatible with the performance measures mentioned above.
However, the proper implementation of capital allocation in risk management, risk limiting, and decision making often imposes significant challenges. On the computational side, the gradient allocation principle requires determining the derivative of the risk measure—typically Value-at-Risk or Expected Shortfall—with respect to business volumes or other decision variables. Obtaining these derivatives is numerically challenging, especially when risk measurement relies on Monte Carlo simulations. We demonstrate methods to enhance the stability of these estimations, such as kernel estimation. In addition, the allocation has the limitation of accounting only for the risk diversification effects of the current portfolio, which can easily become invalid if the portfolio changes and new risk concentration and diversification patterns emerge. To tackle this issue, we present a recently developed methodology called "Orthogonal Convexity Scenarios" (OCS), which helps to proactively identify potentially adverse portfolio shifts and integrate them into risk management and business steering.