VaR at risk

July 31, 2009 in Finance,Risk

In a piece called "The Risk Mirage," BusinessWeek assails its peers for falling for VaR-based evaluations of Goldman's risk levels:

[A] VaR-based analysis of any firm's riskiness is useless. VaR lies. Big time. As a predictor of risk, it's an impostor. It should be consigned to the dustbin. Firms should stop reporting it. Analysts and regulators should stop using it.

Some, including regulators who base capital reserve requirements on this metric, may call VaR a "measure of market risk" and "predictor of future losses." But it is neither of those things. Its forecast of how much an investor can lose from a trading position is entirely calculated from historical data. It's a mathematical tool that simply reflects what happened to a portfolio of assets during a certain past period. (The person supplying the data to the model can essentially select any dates.)

I'm certainly not one to stick up for VaR as a risk measure by any means, but sometimes you have to stand up for the underdog (or, in this case, the recently toppled dictator). In truth, VaR has a very concrete, well defined use: it measures the edge of a distribution's tail. How one makes use of that information is another story.

How one calculates it is up for even more debate. VaR is not "entirely calculated from historical data," though it is quite informed by it. A proper risk model of any sort will involve some form of forward-looking simulation (absent closed form expressions) and account for the firm's best intuition about the future. So let's not discount the measure on an incorrect assumption regarding it's origin.

A well-specified VaR model can do a surprisingly good job of defining the distribution's tail. From a risk managment perspective, I believe this is insufficient information on which to act. However, I will make this generalization: as VaR increases, the edge of the tail moves farther into negative territory, and "risk" (however you define that measure) has increased as well. Note there is no absolute statement here - I don't care if VaR is $1 or $1mm. But if that number doubles, you would be wise to conclude that the portfolio's risk has increased as well.

Another thought - as long as we only care about relative moves in VaR, and not absolute levels, the distinction between a normal and fat tailed distribution becomes less important - yes, a high-kurtosis distribution could conceivably have a lower VaR but longer tail, but if I don't think the distribution changes significantly over time then my relative-moves insight should hold true.

Caveat: I'm merely suggesting that VaR has a well-defined meaning and a plausible use for that measure; I'm not arguing in favor of it over any other analytic. VaR is but one tool among many.

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