Tuesday, January 6, 2009

VaR - a "fraud"?


Joe Nocera
has triggered off an interesting debate about risk management practices and models extensively applied in recent years, especially Value at Risk (VaR) - the likelihood that a portfolio will suffer a large loss in some period of time or the maximum amount that you are likely to lose with some probability (say, 99%). Regulatory institutions like the SEC and the Basel Committee on Banking Supervision had unwittingly laid the ground for adoption of fanciful risk quantification parameters like Value at Risk (VaR), developed in JP Morgan in the mid-nineties, by validating it as acceptable risk quantification measures for disclosure and setting capital requirements. If the VaR number increased from year to year in a company’s annual report, it meant the firm was taking more risk.

Nassim Nicholas Taleb, one of the fiercest opponents of all risk models, had been continuously calling VaR a "fraud", since it did not factor in the "black swan" events (that appear to be so remote based on standard stochastic models as to be irrelevant for consideration, but do occur much more frequently). But despite its assumed utility only under normal distribution market conditions (not available in the real world) and for smaller periods of time, VaR came to become the gold standard among risk models. It became the most widely accepted measure of risk, being used in uncertain and volatile market conditions and for longer time durations.

Managers and executives loved it for its utility in easily comparing performances of different claases of assets and different trading desks, besides indicating the risk exposures of various trading positions. To top it all, VaR came to be used as a conveniently customizable parameter, with no uniform standard, interpreted differently by firms, instruments, and even trading desks within the same institution. This set the stage for ingenious gaming of VaR data to suit the specific requirements. With all the incentives — profits, compensation, glory, even job security — institutionalized in the direction of taking on more and more risk, VaR came to be viewed as a convenient number that could be used to promote increased risk taking.

Nocera also briefly documents the numerous other flaws of VaR - it didn't measure liquidity risk (the relative value of ones position in relation to the normal trading volumes), relied on a two-year data history, failed to distinguish between different sources of leverage (long term bonds and short term loans), did not properly account for leverage that was employed through the use of options etc.

However, Nocera's final judgement appears to be that though VaR may have been a flawed number, it was the best number anyone had come up with, atleast for measuring the short term risks. But the problem was that instead of using it as a signal to make judgements about such risks, risk managers started using it as direct measure of risk itself.

Yves Simth elaborates that VaR modelling assumes that asset prices follow a "normal" (or Gaussian) distribution, or the classical bell curve, despite the fact that financial assets do not exhibit such distributions. In fact, apart from the fact that equities and bonds exhibit negative and commodities positive skewness in their respective probability distributions, the probability distribution of financial asset prices also shows kurtosis or "fat tails", an indicator of the greater probability of "black swan" events. Like Nocera, he too argues that though models based on normal distributions are good at managing day-to-day market movements (which are more likely to be smaller), the "tails risk" becomes significant over longer periods of time.

James Kwak draws attention to another shortcoming of VaR - by relying on a probability distribution curve constructed from historical data to calculate the likelihood of future events, it fails to account for the fact that the original distribution itself was an accident of history and can be subjected to random shocks that can completely distort the distribution - the world can change! In other words, while your future calculation sample, which reflects your population of interest as closely as possible, is drawn from the past, your population of interest is the future! Given this, even going ever farther back in history and constructing probability distribution may not be of much help, since there is no way of ascertaining whether and when the world will change and if so by how much.

Kwak also makes a very pertinent point about why executives may have looked the other way despite the strong possibility that they knew they were in a bubble which could burst any time - "the enormity of the short-term compensation to be made outweighed the relatively paltry financial risk of being fired in a bust (given severance packages, and the fact that in a downturn all CEO compensation would plummet); and bucking the trend incurs resume risk in a way that playing along doesn’t."

Jon Danielsson in Vox highlights the folly of measuring financial risk. He writes that endogenous risks, those arising from the interaction of the behaviours of intelligent human agents, are almost impossible to predict. And worryingly, the article also points to the importance the Basle II Accord gives to the failed risks management tools like VaR. He writes, "In the absence of accurate risk measurements, risk-sensitive bank capital is at best meaningless and at worst dangerous."

The final word goes to John Dizard, who writes about a more fundamental problem that drives risk managers and executives to the indiscriminate use of unreal risk management models like VaR, "A once-in-10-years-comet-wiping-out-the-dinosaurs disaster is a problem for the investor, not the manager-mammal who collects his compensation annually, in cash, thank you. He has what they call a "résumé put", not a term you will find in offering memoranda, and nine years of bonuses."

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"The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on quantification and numbers, determined by the patterns of the past, and those who base their decisions on more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved." - Peter L Bernstein, from the introduction to "Against Gods: The remarkable story of risk".

Update 1
Mostly Economics weighs in, a primer on VaR from IMF, and Dean Foster and Peyton Young detects a lemon problem in identfying alpha managers among hedge funds (through Mostly Economics)

Update 2
Chris Dillow and The Economist on VaR and excessive reliance on mathematical models.

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