VaR: The number that killed us

November 30, 2010 06:00 PM

Invented by Wall Street in the late 1980s, VaR quickly became the accepted de rigour market risk measurement tool inside dealing floors around the globe. Trading decisions and traders’ compensation began to depend on what VaR said; if the number churned by the model was deemed unacceptably large, a trader would be asked to cut down his positions, if the number was deemed comfortably tame the trader would be assigned more capital. If he made good money while enjoying a low VaR, he would be considered a hero by his bosses, someone capable of bringing in big bucks in a (purportedly) risk-lite manner. Clearly, traders had every incentive to own portfolios endowed with low VaRs, and thus began a long-honored tradition to try and game the system into delivering subdued mathematical risk estimates. The pernicious effects of such gaming may have come fully home to roost during the credit crisis, two decades after the quantitative prodigal son was first allowed to infiltrate us.

VaR´s reputation as a risk measurement tool certainly has taken a big hit during the recent malaise. During the nightmarish days that saw the eruption of the worst financial meltdown in eight decades, the device insultingly misbehaved as a warning signal when it came to the fallen financial giants. The real losses witnessed were way above the predicted theoretical losses, and VaR numbers were breached far more abundantly than what the model would dictate.

Take Swiss giant UBS, a very prominent victim of the crash. It reported 50 VaR exceptions for 2008 and 29 for 2007. At the 99% confidence level chosen by UBS, there should have only been about 2.5 exceptions (trading days when actual losses exceeded VaR´s predictions) per year. Or take local rival Credit Suisse. The Zurich powerhouse experienced 25 and nine VaR exceptions in 2008 and 2007, respectively; also at 99% confidence, this implies above six times more real losses than theoretically forewarned. It seems unnecessary to state that VaR did not properly warn the Helvetians during the unfolding of the bloodbath.

And you didn´t need to be based in a neutral country with magnificent ski slopes and exquisite private bankers in order to experience your own dose of VaR disillusionment. Perhaps it shouldn´t be exceedingly surprising that Lehman Brothers and Bear Stearns witnessed less-than-glorious VaR behavior, particularly in the latter case (in excess of 20 exceptions during its last three quarters as a living independent entity, more than twice the predicted number for the adopted 95% confidence level, which allows for only twelve yearly exceptions); but they were not alone by any means, with Morgan Stanley, JP Morgan and Bank of America (BoA), for example, similarly witnessing the breakdown of the theoretical dogma (BoA had 14 violations in 2007 at 99%, JP Morgan had eight in 2007 at 99% and Morgan Stanley had 18 violations in 2008 at 95%). And other Europeans can boast plenty of misguiding too. Mighty Deutsche Bank, for one, was surprised to observe 35 VaR violations in 2008 and 12 the year before, in all around ten times higher than theory would dictate.

Dangerous limitations

Twenty years after it was first brought into the fold of finance, should VaR still be used as risk radar following such a disappointing track record? So far, the thing continues to be employed by banks, hedge funds and other firms. It´s true that it´s not the only risk reference consulted, typically complemented with additional analysis such as stress testing. And yet, it appears hard to understanding why a device that can malfunction so gravely (especially at crunch time) should be given so much credence and respectability. When a bank reports its market exposures to investors, journalists, regulators and other outsiders through its quarterly filings, it continues to do so through the VaR lens. To this day, VaR continues to be openly equated with market risk. It´s almost as if the crisis had not happened at all.

Even more important than becoming the in-house method for calculating and managing risk and for informing the rest of the world as to a firm´s riskiness, VaR was adopted by policymakers as the tool to be used for the crucial purpose of determining the mandatory capital charges that financial institutions should face for their trading activities. Trading, you see, is not free. A while back, international regulators decided to impose a capital levy on market punting: for every trading position that a bank took on, a certain amount of capital had to be set aside so as to act as protective cushion for possible future setbacks. Naturally, the size of said capital requirement can play a huge role in the amount (and type) of trading assets that a bank would hold. If the charges are too exacting, accumulating tons of assets will be excruciatingly capital-intensive (i.e., excruciatingly expensive). Expressed differently, the size of the requirements will determine how much trading-related leverage a bank can enjoy. If the capital charge is modest, then traders need only to put up a small upfront deposit to own a whole lot of assets, being allowed to finance their portfolio mostly via borrowing. That is, by crowning VaR as the king of capital requirements, regulators essentially left the determination of banks leverage in the hands of a mathematical construct of dubious reliability. As the recent meltdown clearly shows, few things can be as impacting as the amount of gearing undertaken by financial institutions.

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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).