On Goldman’s fat tail risk

Financial blog Zero Hedge points us in the direction of a risk management presentation from Goldman Sachs.

The majority of slides are typical management-type stuff. There are some impressive Venn diagrams and graphics of interlocked puzzle pieces, as well as a few intriguing comments on mark-to-market accounting, but the most interesting thing, we think, is the slide on fat tails and Value at Risk, or VaR.

VaR is a way of measuring the expected risk of loss on a portfolio, using observations of historical market movements. The VaR model used by Goldman Sachs looks at 95 per cent and 99 per cent tail risk. Tail risk is the the ‘unexpected’ losses or gains that happen to the portfolio, assuming normal distributions.

In the three months to March 27, 2009 Goldman’s VaR value was $240m at the 95th percentile. That means there was a 5 per cent probability Goldman’s portfolio would fall in value by more than $240m over a one day period. That compares with a VaR value of $197m in the three months to November 28th, 2008, and a VaR of $157m in the three months to February 29th, 2008 (Goldman Sachs, we all remember, changed its reporting period last year).

In any case, here’s the fat tail slide from Goldman’s risk presentation:

And here’s Zero Hedge’s commentary:

. . . the fat tail analysis is also somewhat non-self explanatory. As the chart [above] indicates that Goldman is dead set on analyzing the 99 percentile (in addition to the 95%) non-fat tail distribution. Does this explain the meteoric rise in VaR in recent reporting periods? Also – what happens on that rare 100th day, week, month? Especially if there is nobody left to bail you out.

The rise in VaR, we think, is explained by the below slide from the same presentation, which shows the illiquidity in recent market environments and an example of a crowded trade — when investors rush to unwind their positions simultaneously; something akin to the notorious Volkswagen short squeeze of death.

VaR’s been rising in recent reporting periods because the illiquidity of markets has been destroying the functionality of VaR models, which assume the ability to liquidate positions at any given time. In illiquid or crowded trading environments, like the Volkswagen situation recounted above, assets get stuck or become unsellable — rendering VaR pretty useless.

In 2008 and early 2009, normal was not normal anymore. Thus we heard talk of 6.2 sigma events — things which should be happening once every 6,800 years — occurring 10 times in a single month. Quantitative models like VaR failed to predict or account for the new normality.

On Zero Hedge’s final point– what happens to Goldman on that rare 100th day, week, month? — we think we can help.

This slide is from a Dresdner analysis produced back in February, 2009:

Dresdner chart of GS VaR in 2008

The short answer is they tend to make money.

Related links:
VaRy complex — FT Alphaville
Lord Turner, VaR and the FSA – FT Alphaville
Goldman Sachs risk management presentation – The Long Room

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