What is the point of Value-at-Risk?
Yesterday, in a mildly
confused post, I said that if a bank loses more than its VaR six days in
one quarter, that’s "a sign of utter cluelessness". In fact, it’s
not quite as bad as all that, since I assumed erroneously that Morgan Stanley
was using 99% VaR when in fact it was using 95% VaR. But it’s still pretty bad.
At 95%, one expects to exceed VaR three times a quarter – but wouldn’t
that be three days on both the upside and the downside? Morgan Stanley,
it seems, exceeded its VaR, on that basis, not six times but 29 times
in the past quarter.
I do understand it’s not quite as simple as that. You’re not going to stop
out of a position which is soaring in value, so you should have more big up
days than big down days. But even so, the number of big up days does give some
indication of the magnitude and volatility of your trading returns, which should
in turn be reflected in your VaR.
But the bigger question is what the VaR is there to tell us in the first place.
Helen Thomas today quotes one John
Kemp:
Kemp added that standard VaR calculations tend to understate the likelihood
of large gains or losses and say nothing about the size of these gaiins or
losses in the tails of the distribution. Plus diversification effects firm-wide
become less significant in a crisis, where correlations tend to one – as the
summer so aptly demonstrated.
He estimates that given these effects, assuming that extreme day profits and
losses are a multiple of 99 per cent VaR, that the risk on Goldman’s
books could be more than $500m. Which helps to explain how Morgan Stanley
arrived at a $390m one-day loss in what was an exceptional quarter.
In other words, Morgan Stanley’s VaR model isn’t necessarily broken, even if
it manages to lose $390 million in one day with a VaR of $85 million. But in
that case, one clearly can’t use Value-at-Risk as a measure of the amount of,
um, value that’s at risk. Is it just there to make regulators happy?