Chapter 16 Economic Credit Capital Allocation and Risk Contributions

Abstract Economic capital (EC) acts as a buffer for financial institutions to absorb large unexpected losses, thereby protecting depositors and other claim holders and providing confidence to external investors and rating agencies on the financial health of the firm. Once the amount of capital has been determined, it must be allocated equitably among the various components of a portfolio (e.g., activities, business units, obligors or individual transactions). Capital allocation is an important management decision support and business planning tool, required for pricing, profitability assessment and limits, building optimal risk-return portfolios and strategies, performance measurement and risk based compensation. This chapter provides a practical overview of the measurement of economic credit capital contributions and their application to capital allocation. We discuss the advantages and disadvantages of various risk measures and models, the interpretation of various allocation strategies as well as the numerical issues associated with this task. We stress four key points. First, marginal risk contributions provide a useful basis for allocating EC since they are additive and reflect the benefits of diversification within a portfolio. Second, the choice of the risk measure can have a substantial impact on capital allocation. In particular, Value at Risk (VaR) and expected shortfall (ES) contributions avoid the inconsistencies, and potentially inefficient allocations, associated with the widely-used volatility-based methods. The quantile level chosen for measuring risk can also have a significant impact on the relative amount of capital allocated to portfolio components. Third, VaR and ES contributions can be calculated analytically under certain simple models. These methods provide fast calculations and can be used to understand capital allocation strategies better, but they present important practical limitations, as well. Finally, Monte Carlo methods may be required to compute risk contributions in more realistic credit models. Computing VaR and ES contributions is challenging, especially at the extreme quantiles typically used for credit capital definition. The quality of contribution estimates can be improved by exploiting the conditional independence framework underlying the most common models, through the use of more sophisticated quantile estimators (especially for VaR) and through the use of variance reduction techniques, such as Importance Sampling.