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Measuring market risk: the Fundamental Review of the Trading Book

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John Hull

Transcript of the video:

The first of the two aspects that I particularly want to focus on are that the regulators are to some extent throwing out value at risk and saying they want to replace it with expected short form and, you know, we’ll make things a bit more precise in a moment, but what they’re saying is that instead of using value at risk with a 99 per cent confidence level they’re actually going to use expected shortfall with a 97.5 per cent confidence level. And it turns out that if you have a normal distribution those two are almost exactly the same.

In other words, you’re going to be at the same, for those of you who don’t know what expected shortfall is it’s on my next slide, but it turns that, you know, VaR, value at risk with 99 per cent is equivalent to expected shortfall with 97.5 per cent if we’re talking about normal distributions. If we go on distributions with fatter tails than the normal distribution then you’ll find the expected shortfall measures higher.

So perhaps it’s about time we defined what we mean by these measures. Value at risk, the abbreviated VaR is the last level that will not be exceeded with specified probability. One way of thinking about that is you’re just asking the simple question how bad can things get? You know, what’s the worst that can happen? Well, we know it’s all sorts of horrible things could happen. We could have, you know, third World War, half the planet being destroyed and that sort of thing.

But say you sort of had to sort of define some confidence level and you have to define some time horizon, but you’re saying just how bad, you know, what’s the percentile of the distribution that corresponds to that confidence level that I am interested in, which as we said was 99 per cent for the original Basel capital requirements.

Now, expected shortfall is the expected loss given that the loss is greater than the VaR level. It’s also called CVaR and tail loss. So what you’re saying is, you know, express crudely if things do get bad just how bad will it get? In other words, if we’re in that tail of the distribution what is our expected loss, just how bad might the loss be?

So here’s a picture of why two distributions or two lost distributions can give the same value at risk but actually different expected shortfalls. If we look at the top distribution it’s a sort of fairly bell-shaped normalish kind of looking distribution and, you know, we’ve got, can’t see very well here, but got the VaR level there, the two distributions have got the same VaR levels, so they got the same probability mass in the tails there, okay, it’s the same probability of the loss exceeding the VaR level in both cases. These distributions are constructed so the positive access is a gain, the negative access is a loss.

So, you know, we’re talking when we’re in the tail of the distribution about losses, but you can see that if we wind up in the tail of the distribution you can see that the loss is going to be a lot worse for the lower distribution than the upper distribution.

[4.16 minutes]

This video was filmed as part of the Rotman Master of Finance Speaker Series on May 25, 2015.

John Hull is university professor, Maple Financial Group chair in derivatives and risk management and academic director of FinHub, the financial innovation lab at the Rotman School. His is the author of Machine Learning in Business: An Introduction to the World of Data Science and three best-selling books in the derivatives and risk management area.