Proceed with Caution: The Pitfalls of Value at Risk

Value at Risk, or VaR, continues to garner a great deal of attention from the investment community, the media, and academia. While it is commonly used at banks, in trading depart-ments, and by many asset managers, we must ask how reliable it is. In Lecturing Birds on Flying (2009), Pablo Triana criticizes it amply; however, there may be more objective ways to grasp its shortcomings.

VaR is a rather unique risk measure in that it indicates the potential loss a portfolio might encounter and thus aligns with a prevailing view about what risk actually is: the possibility of loss. Unlike many risk measures that are backward looking (ex post), VaR is forward looking (ex ante). Perhaps best of all, it measures risk in dollars.

When reporting VaR, we specify three key attributes: amount of possible loss, time frame over which VaR is measured, and confidence level. For example, we might say that a portfolio’s VaR is $10 million, over the next day, at a 95% confidence level.

VaR makes several questionable assumptions:

• That the return distribution is normal (that is, that returns take the shape of a bell curve) under the variance covariance (VCV) method. However, much evidence suggests that, typically, returns are not normally distributed.
• That market conditions are normal. Today it seems that the only “normal ” factor today is that the market is behaving abnormally. Though volatility may be considered normal, it still raises questions about VaR’s accuracy.
• That we can easily liquidate our portfolio. VaR fails to take into consideration the portfolio’s liquidity risk, which might otherwise alter its estimates. It is often used over a single day, but the likelihood that we can liquidate our entire portfolio without incurring huge transaction costs is poor, reflecting the market impact that may result.
• That the portfolio will not change over the time period. Modifications to the portfolio’s makeup result in changes to its VaR.

When presented with VaR’s level of precision—for example, the prediction that the most we can lose is $9,487,512, at a 95% confidence level, for the next day—we might conclude that the information must be highly accurate. This method of reporting implies that the dollar figure is closer to reality than it actually is. When Long-Term Capital Management reported VaR in such a manner, it gave clients false confidence that the firm had great control on risk (Lowenstein 2001). Rounding up to the next hundred thousand or even million can help avoid this misunderstanding.

Even when we round up the VaR number (for example, to $10 million), however, the confidence level only covers a portion of the possible losses.. It does not take extreme events into account. When these occur, losses can be much greater than what is stated in VaR reports. A 95% confidence level used on a daily VaR means that on one of 20 days we may experience an extreme event. Even at the 99% confidence level, VaR will be incorrect, on average, one out of 100 days.

VaR assumes that the past can be used to predict the future and allows you to decide how far back to go to make your predictions. Consequently, we could get different results depending on how much history we bring to bear. Many challenge the assumptions that past market behavior is a valid predictor of future behavior and that past prices are a sound predictor of future prices.

In general, how good are we at foreseeing the future? While many prophets and soothsayers pontificate about coming times, most are right, if ever, only some of the time. In The Production of Knowledge (2006), William H. Starbuck deftly challenges any such predictions.

Yet interest in predictions is as strong as ever. Many investors prefer knowing, at least to some degree, what the future holds from a risk perspective rather than what risk was taken to obtain their historical results. However, we need to recognize the limitations of any forward-looking risk measure; when it comes to VaR, we must be cautious about how much confidence we place in the reported information.

The calculation of VaR requires numerous assumptions and thus VaR should not be viewed as a precise measure of risk. Rather, it should be evaluated in the context of known limitations. These limitations include but are not limited to the following: VaR measures do not convey the magnitude of extreme events; historical data that forms the basis of VaR may fail to predict current and future market volatility; and VaR does not fully reflect the effects of market illiquidity (the inability to sell or hedge a position over a relatively long period). (Merrill Lynch disclaimer, quoted in Triana 2009)

VaR users should be mindful of such caveats when they read reports and include them in their own reporting.

VaR is a useful statistic in risk reporting, but it should not be the only measure, nor should it be seen as more than it is: an estimate of potential loss. Managers should also take into consideration their liquidity risk as well as an analysis of their extreme events: that is, a worst-case-scenario analysis. Risk needs to be “ganged up on, ” and the more measures we employ—the more facets from which we view risk—the better.

REFERENCES

Lowenstein, Roger. 2001. When Genius Failed: The Rise and Fall of Long-Term Capital Management. New York, NY. Random House.

Starbuck, William H. 2006. The Production of Knowledge . New York, NY. Oxford University Press.

Triana, Pablo. 2009. Lecturing Birds on Flying: Can Mathematical Theories Destroy the Financial Markets? Hoboken, NJ. John Wiley & Sons.

–David Spaulding, CIPM, is an internationally recognized authority on investment performance measurement and president of the Spaulding Group Inc. Based in Somerset, New Jersey, the Spaulding Group is a provider of investment performance products and services, including the Journal of Performance Measurement. Spaulding is the author, contributing author, and coeditor of several books on performance measurement.