Cutting Edge introduction: Creative stress testing

Quants and decision-makers are often different people – which is all the more obvious in stress testing, where a decision maker’s subjective views on the market have to be able to endure the mathematical rigour of the exercise. Thanks to a new technique, neither party has to compromise.

Despite the growing importance of stress-testing exercises, such as those applied by regulators to European and US banks, or those used to set clearing house default fund sizes, stress-testing methodology in itself has not changed much in the last 20 years.

"Scenario analysis and stress testing, from a purely statistical point of view, is predicated on the assumption that in some funky, complicated way the future looks like the past. But say Greece defaults or leaves the EU tomorrow – we do not have one such instance in the historical past. So how do we say something meaningful about something extremely relevant without having to rely in a slavish manner on what is happening in the past?" says the head of research at a large asset management firm in London.

This month's first technical, Stress testing in non-normal markets via entropy pooling, by Attilio Meucci, chief risk officer at investment management firm KKR in New York, and David Ardia, an assistant professor of finance in Laval University in Québec, offers one answer.

"Typically, risk managers specify one scenario – or joint scenarios – for a couple of risk factors, then run their models and look at the impact on expected profit and loss under simple assumptions like the normal distribution," says Meucci.

The process is tedious and mechanical and churns out one output number per scenario. In addition, the types of market views that can be incorporated are limited to expectations on measures such as return and price.

The authors believe it is possible to do better than that. The two quants develop a stress-testing method that is able to not only include flexible views on the market – on rankings, inequalities, correlations, tail risk and skewness, for example, while working with non-normal distributions - but that can also output whole distributions instead of a single profit-or-loss value like in traditional methods.

What allows this is a technique Meucci developed in 2008 called entropy pooling, the latest version of which can incorporate non-normal distributions and flexible investor views in both portfolio and risk management.

Entropy pooling, like the more popular Bayesian techniques, takes in an arbitrary market distribution, called the prior, and investors' views on the market, and generates a posterior distribution by minimising the relative entropy – a measure of the difference between two distributions. The result is a posterior distribution consistent with both market data and investors' views.

"Typically, the views are based on expectations, but here you can have views on any feature like value-at-risk, for example – you can really get creative with your views," says Meucci.

Applying this to stress testing, the prior becomes the assumed distribution of a measure the risk manager is interested in – such as the profit and loss (P&L) – and the scenarios form the views. The posterior, in this case, is the stressed P&L distribution.

With flexible views, using the brute force method for the stress test is computationally demanding, but the authors apply a copula marginal decomposition – representing dependence between distributions of different variables – to decompose the relative entropy so it is easier to compute in the presence of flexible views.

The advantage to all this is being able to link intuitive views to a mathematically rigorous stress test.

"Very often, the users of stress testing will not be well-versed in quantitative methods, so they want something that is intuitive. They want something akin to what the decision-maker understands and can make a call about, not something like ‘what if we had doubled the frequency in the Fourier expansion? '. So it is very much a matter of language. And it is very important that the vocabulary used by different approaches is the vocabulary understood by the decision-makers," says the head of research at the asset management firm.

While entropy pooling may not be widely used in stress testing today, it is understood one regulator is actively looking at the benefits of Bayesian approaches – which may be the start of a wider move away from purely historical and statistical methods.

In our second technical, Scaling operational loss data and its systemic risk implications, Roberto Torresetti and Claudio Nordio, both senior quantitative risk analysts in the risk management division of Banca Carige in Genova, show how external operational risk data – required by regulators to capture tail risk – needs to be adequately scaled to ensure the accuracy of a bank's own capital charge.