Models for Risk Aggregation and Sensitivity Analysis: Application to Bank Economic Capital

A central challenge to the practice of enterprise risk measurement and management faced by diversified financial institutions (e.g., an internationally active bank or insurance company) is developing a coherent approach to aggregating different risk types.  This has been motivated by rapid financial innovation, developments in supervisory standards (Basel 2) and recent financial turmoil.  The main risks faced - market, credit and operational – have distinct distributional properties, and historically have been modeled in differing frameworks.   We contribute to the modeling effort along three dimensions, providing tools and insights to practitioners and regulators.  First, we extend the scope of the analysis for these three risks that have been the focus of the literature, analyzing proxies for A/L mismatch and liquidity risk, which has implications for Pillar II of Basel IRB framework.  Second, we utilize actual data representative of major banking institutions’ loss experience, extracted from call reports, submitted by banks to supervisory agencies.  This allows us to explore the impact of business mix and inter-risk correlations on total risk.  Third, we estimate alternative copula models, an established framework for capturing realistic distributional features of different risk types (e.g., non-normality) and cohesively combining such, on the same data-set.  We then compare our models to several conventional approaches to computing risk amongst practitioners.  Through differences observed across the three largest banks, we find the effect of business mix to exert an impact on total integrated risk above and beyond exposure to, and correlation amongst, underlying risk factors.  In regard to different risk aggregation methodologies, we find significant variation amongst these, and conclude that simple aggregation or the variance-covariance approximation over-states risk relative to standard copula formulations (Gaussian,  t-copula, empirical and Archimadean), on the order of about 30% and 20% across all banks, respectively.  Diversification benefits, as measured by the relative VaR reduction vis a vis the assumption of perfect correlation across all frameworks considered, range in 20% to 30% across all banks.  We also demonstrate, through a resampling exercise, that the variability of VaR itself varies significantly across copula formulations; in the process we make a contribution to the practice of sensitivity analysis.