If you’re a homeowner, and you want to be well-diversified against the risk of nowhere to live, you might buy a house in another state, based on the assumption that what may happen in New York is unlikely to reach Colorado and vice versa. However, as we caveated in our original post on this topic, what if the threat isn’t a localized disaster but a global threat to the entire human race, like a fast-moving zombie apocalypse? All preconceptions have to be thrown out the window because you’re now operating in a never-before-experienced scenario.

Now, let’s switch out zombies for a sudden economic crisis in Germany. Markets are shaky, stocks are diving, clients are calling you panicked. “Don’t worry; this is why we have risk models,” you tell them. “We modeled this scenario and diversified investments accordingly. There will be write-downs, but nothing life threatening.” But the correlations on which this model is built, aren’t reflective of the current environment. That is, the assumptions underpinning the model were calculated when everything was ticking along nicely, not when financial turmoil was spreading across Europe, sending shockwaves through the global financial system. At this point, the realization hits that the expected benefits of your diversification strategy will be much smaller than anticipated, as it is based on assumptions that no longer fit the current market reality. Regarding our analogy, the zombie contagion outbreak is going to reach New York and Colorado.

A lot of smart people spend a lot of time thinking about the correct modeling approach for risk. But, because of the scenario outlined, I think a little more time needs to be spent on the correlation assumptions.

Most bankers can calculate a historical correlation matrix; Excel’s analysis toolkit make them pretty easy to build. But, because they are easy to build, it has also become easy to overlook data nuances, and as such, historical correlation matrices are often naively applied.

Some market pundits would even argue that the inappropriate use of correlation matrices in subprime CDO rating models were a driver of the 2008 recession—a big statement for sure, but not untrue. In fact, I would list overly simplistic correlation matrices as one of the top ten things that could cause an economic Armageddon.

So how uncertain are correlations? Let’s look at an example using EUR and GBP. The trailing two-year correlations have ranged from +0.43 to +0.82, with a standard deviation of 0.09.

So what should risk managers do?

There are three approaches I like:

1. Perform a confidence interval calculation around the correlation and use the more "dangerous" number (this can vary in each situation) in your risk management modeling.
2. Stress test your correlation matrix.
3. Use a Bayesian approach and augment point-estimates with distributions. Trust me, it’s not as scary as it sounds1.

Given the technical concerns of each, I prefer the Bayesian approach as it includes all the information about how correlations might be realized rather than forcing the choice of a confidence or stress level.

Learn More

If you’re reading this thinking you need more detail on the approaches; you’re right, each requires further construction and calculation explanations, as such we’re working on a white paper covering Bayesian correlation and covariance matrices with details on implementation. If you want to be added to the distribution list or just can’t wait and want to chat about these approaches sooner, email me at adrian.s.crockett@gmail.com.

In the meantime, next time you see a correlation matrix as an assumption, ask the hard questions, such as how were the numbers calculated? What was the time period? What assumptions were made? It can lead to a stronger model—something you’ll be glad of when things go wrong.

1. This has deficiencies but is the closest thing you will get to a win concerning trade-off between applicability and analytical robustness. My former team at Credit Suisse received the Alexander Hamilton Award from Treasury & Risk magazine for a model using this approach, so it doesn’t necessarily require a team of PhDs to get it right. ↩