VaR: The number that killed us

November 30, 2010 06:00 PM

On Sept. 10, 2009 former trader and bestselling author Nassim Taleb did something that he very seldom does: he wore a tie. Taleb has oftentimes publicly expressed his distaste for the blood-constraining artifacts, as well as for those who tend to don them, so the Lebanese-American let the world know that was a very special day for him by betraying a sacred personal disposition.

So what prompted the composer of “The Black Swan” to button his shirt all the way up on that fall date? He had been invited to a very solemn venue by very distinguished hosts. And that was an invitation that Taleb had every intention of accepting. In fact, he had been waiting and expecting it for more than a decade. The raison d’etre of the event for which his company was now being required had been close to Taleb´s heart for most of his professional and intellectual life. It represented a central theme in his actions and ideas, close to an obsession. He had through the years incessantly warned as to the havoc that might be wreaked should others massively act in a manner counter to his convictions. Such concerns typically went unheeded (to the detriment, it turned out, of society), but now he was being offered a pulpit that seemed irresistible. This time, the world would have no option but to listen attentively.

As Taleb entered the Rayburn Building of the U.S. House of Representatives on Capitol Hill that September morning, he must have felt vindication. As he approached the sober room where several men and women awaited the start of the House Committee on Science and Technology´s hearing on the responsibility of mathematical model Value at Risk (VaR) for the terrible economic and financial crisis that had caused so much misery, Taleb probably reflected proudly on all those times when, indefatigably and in the face of harsh opposition, he alerted us of the lethal threat to the system posed by the widespread use of VaR in finance. Now that the damage wrought by VaR seemed so inescapably obvious that lawmakers had been motivated into investigating the device, Taleb no longer seemed like a lone wolf howling at the moon.

What is so wrong about VaR, and why was Taleb so concerned about its impact? More importantly, why should VaR be held responsible for the crisis? VaR is a number that purports to estimate future losses derived from a portfolio of financial assets, and presents two major problems: 1) it is doomed to being a very wrong estimate, because of its analytical foundations and the realities of real-life markets; 2) in spite of such (well-known) deficiencies, it has for the past two decades become an ubiquitously influential force in the financial world, capable of directing decision-making inside the most important banks. In other words, by letting trading activity be guided by VaR, we have essentially exposed our economic fate to a deeply flawed mechanism. Such flawedness, as was the case not only in this crisis but also before, can yield untold malaise.

One dimension in a 3D world

VaR is an untrustworthy measure of future market risk for one main reason: it is calculated by looking at the past. The upcoming risk of a trading asset (a stock, bond or derivative) is essentially assumed to mirror its behavior over the historical time period arbitrarily selected for the calculation (one year, five years, etc). If such past happened to be placid (no big setbacks, no undue turbulence) then VaR would conclude that we should rest easy, safe in the statistical knowledge that no nasty surprises await. For instance, in the months prior to the kick-start of the crisis in mid-2007, the VaR of the big Wall Street firms was relatively quite low, reflecting the fact that the immediate past had been dominated by uninterrupted good times and negligible volatility, particularly when it came to the convoluted, eventually lethal, mortgage-related securities that investment banks had been enthusiastically accumulating on their balance sheets. A one-day 95% VaR of $50 million was typical, and typically modest in its estimation of losses: at that level, a firm would be expected to lose no more than $50 million from its trading positions 95% of the time (in other words, it would be expected to lose more than $50 million only 12 days out of a year´s 250 trading days). Once we keep in mind that those Wall Street entities owned trading assets worth several hundred billion dollars and that the eventual setbacks amounted to several dozen billion dollars, we can appreciate that VaR´s predictions were excruciatingly off-base. The soulless data rearview mirror may have detected no risk, but that certainly did not mean that the system was not flooded with the worst kind of risk, ready to explode at any time. In finance, the past is simply not prologue, but someone forgot to tell VaR that.

Beware of the fat tails

The fact that the mathematical engineering behind VaR tends to assume that markets follow a normal probability distribution (thus assuming extreme moves to have negligible chance of happening, something obviously quite contrary to empirical evidence) can also contribute to the model churning unrealistically low numbers as big losses are ruled out, as can VaR´s reliance on the statistical concept of correlation, which calculates the future expected co-movement of different asset classes, based on how such co-dependence worked out in the past. If several assets in the portfolio happened to be uncorrelated or, better yet, “negatively correlated” in the past, VaR will take for granted that those exposures should cancel each other out, yielding lower overall portfolio risk estimates. However, as any seasoned trader would tell you, just because several assets were negatively correlated last year, we can´t imply that they won´t move in tandem (positively correlated, implying that chances are that they can all tumble concurrently, thus painting a much worse overall risk picture) next month. Market history is flooded with cases when assets that were supposed to move independent of each other all tanked at the same time. Correlation in finance simply can´t be captured mathematically.

As the alert reader may have by now noticed, the main problem with VaR is not so much that its forecasts won´t be accurate, but that it can be quite easy to get a VaR that´s very low. You just need a portfolio of assets that happened to have recently enjoyed benevolent calm and/or little correlation with each other. If you manage to compose such grouping, the model will yell to the world that you run a sound, riskless operation. That´s exactly what was taking place on Wall Street all those years prior to late 2007. According to VaR, the situation could not have been rosier and less worrisome, risk-wise.

Such misplaced generosity would not be a big concern if VaR did not play a relevant role in the markets. But, rather unfortunately, the tool could not have played a more decisive part. Simply put, VaR may have been the single most influential metric in the history of finance. No other single number ever impacted, shaped and disturbed market (and thus economic) activity as profoundly as it did. VaR´s perilously inexact estimations of risk mattered because the model mattered so much.

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About the Author
Pablo Triana is the author of "Lecturing Birds On Flying: Can Mathematical Theories Destroy The Financial Markets?" (John Wiley & Sons).