With the majority of large UK and many US banks collapsing or being forced to raise capital over the 2007–9 period, blaming bankers may be satisfying but is patently insufficient; Basel II and Federal oversight frameworks also deserve criticism. We propose that the current methodological void at the heart of Basel II, Pillar 2 is filled with the recommendation that banks develop fully-integrated models for economic capital that relate asset values to fundamental drivers of risk in the economy to capture systematic effects and inter-asset dependencies in a way that crude correlation assumptions do not. We implement a fully-integrated risk analysis based on the balance sheet of a composite European bank using an economic-scenario generation model calibrated to conditions at the end of 2007. Our results suggest that the more modular, correlation-based approaches to economic capital that currently dominate practice could have led to an undercapitalisation of banks, a result that is clearly of interest given subsequent events. The introduction of integrated economic-scenario-based models in future can improve capital adequacy, enhance Pillar 2’s application and rejuvenate the relevance of the Basel regulatory framework.

In the first part of this paper we address the non-coherence of value-at-risk (VaR) as a risk measure in the context of portfolio credit risk, and highlight some problems which follow from this theoretical deficiency. In particular, a realistic demonstration of the non-subadditivity of VaR is given and the possibly nonsensical consequences of VaR-based portfolio optimisation are shown. The second part of the paper discusses VaR and expected shortfall estimation for large balanced credit portfolios. All standard industry models (Creditmetrics, KMV, CreditRisk+) are presented as Bernoulli mixture models to facilitate their direct comparison. For homogeneous groups it is shown that measures of tail risk for the loss distribution may be approximated in large portfolios by analysing the tail of the mixture distribution in the Bernoulli representation. An example is given showing that, for portfolios of lower quality, choice of model has some impact on measures of extreme risk.

We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a kernel measure which makes explicit the user’s priorities for model performance. The class of spectral backtests includes tests of unconditional coverage and tests of conditional coverage. We show how the class embeds a wide variety of backtests in the existing literature, and further propose novel variants which are easily implemented, well-sized and have good power. In an empirical application, we backtest forecast distributions for the overnight P&L of ten bank trading portfolios. For some portfolios, test results depend materially on the choice of kernel.

Under the Fundamental Review of the Trading Book, capital charges are based on the coherent Expected Shortfall (ES) risk measure, which is sensitive to tail risk. We argue that backtesting of the forecasting models used to derive ES can be based on a multinomial test of Value-at-Risk (VaR) exceptions at several levels. Using simulation experiments with heavy-tailed distributions and GARCH volatility models, we design a statistical procedure to show that at least four VaR levels are required to obtain tests for misspecified trading book models that are more powerful than single-level (or even two-level) binomial exception tests. A traffic-light system for model approval is proposed and illustrated with three real-data examples spanning the 2008 financial crisis.