It makes a wonderful (and possibly apocryphal) story. French mathematical wunderkind and father of fractal geometry Benoit Mandelbrot wandered into a colleague’s office in the early 1960s before giving a lecture on mathematical uncertainty, and there, on his friend’s chalk-board, was exactly the graph he planned to use. When queried, Mr. Mandelbrot’s friend said the chart tracked cotton prices back to 1880—one of the longest price data sets on record. When it, and other long-term time series, were sliced and diced into longer and shorter time-frames they consistently and clearly showed that asset prices are not characterized by the Gaussian, or normal, distribution. Mr. Mandelbrot published his findings in 1962.
That should have fatally undermined the then-unheralded but soon-to-be-blockbuster Modern Portfolio Theory of Harry Markowitz, positing the “efficient frontier,” which would be tweaked further in the theoretically elegant, realistically irrelevant and more insidiously entrenched capital asset pricing model by the equally brilliant Bill Sharpe, who, to his great credit, later disavowed his creation.
BIRTH OF A SUMMATION
Despite Mr. Mandelbrot’s observation, 30 years later the mice in JPMorgan’s skunkworks, seeking to give their chief Sir Dennis Weatherstone something concrete in his vaunted “4.15” risk report (so-called because he wanted to know his whole bank’s risk position, in one number, every day at 4.15 pm), came up with Value-at-Risk.
To be fair, the so-called parabolic (Guassian) VaR that Sir Dennis and his equally brilliant, but again often wrong, derivatives factotum Peter Hancock based their decisions upon was soon supplanted by VaR based on Monte-Carlo stochastic models (the name of which engenders no end of confidence), which rely on a branch of statistics that seeks to model random outcomes. But setting the parameters of such models (so they didn’t simply turn into computer versions of severe autism) required assumptions and—you guessed it—Herr Carl Friedrich Gauss slipped in through that side door.
Fast forward to 2010 and you’ll find a lot of corporates starting to use VaR, or further embedding it into their decision criteria, despite the fact that the exposures they are managing have been proven beyond a doubt by the financial crisis to be leptokurtic—fat tailed—or worse. How much of a problem is this?
Well, VaR, when you get down to it, isn’t a complete waste. Banks using it to determine firm-wide risk might as well throw darts, because it is impossible to stretch VaR across trading desks and business lines and aggregate it into any sort of meaningful number.
A USEFUL TOOL
But corporates that use VaR just for, say, FX risk, might find it a useful arrow in their quivers. In fact, a handful of the deepest FX cross-rates are among the only assets that historically demonstrate Gaussian pricing behavior, so using VaR for FX might not be entirely misleading. That’s a far cry from an endorsement, however, since many cross rates, even the biggest, behaved in unexpected ways during the crisis, and it is an entity’s potential loss in a crisis that VaR is meant to ascertain.
After all, it’s the losses in that last five percent or one percent—in the 95 or 99 percent confidence models—that kills you dead in a crisis like the one we’ve just endured. Indeed, it’s hard to see how a model with even a 99 percent confidence interval lets anyone sleep better, since it posits that losses outside its estimate can occur in 2.8 trading days per year. And since those model-exogenous losses are outside the model’s ken, a corporate using VaR may be in no better position than a blackjack player who reflexively stands pat on 16.
Just as your resting heart rate may give clues to your health but not predict whether you’ll suffer a heart attack if chased by a hungry lion, treasury needs to be cognizant of VaR’s limitations under situations of market stress. And for anyone using it, Mr. Mandelbrot’s work on markets and risk should be required reading.