Value At Risk Underestimates Extreme Scenarios

by: CERF

Value at Risk is like an air bag that works well all the time, except when you have an accident.
--David Einhorn

Value at Risk (VaR) is a well-accepted measure of market risk. It is defined as the minimum loss that could be expected to occur over a specified (short) horizon with a specified (low) probability. For example, the 99% one day VaR would be the amount of daily loss that should be expected to be exceeded one day in a hundred. The VaR measure is ubiquitous today; part of the risk measurement or risk management process of nearly all commercial banks, investment banks and insurance companies, and many if not most money management firms and hedge funds. Regulated companies typically have minimum capital standards that are tied to a VaR calculation.

A nice thing about one day VaR is that you get a lot of feedback on the quality of the measure. Each day you compute your actual gain or loss and then compare that to the VaR calculated at the prior day’s market close. If the calculation is reasonably accurate, you should expect to observe actual losses in excess of the calculated 99% VaR 2 to 3 times per year. If you cannot produce a VaR calculation that meets this criterion, then your risk management process needs some work. By observing the trend in VaR over time, you can get a sense of the trend in the amount of risk that is being taken. That is, unless the nature of the risk changes a lot.

But having a successful daily VaR calculation does not mean that you are prepared for an extreme scenario. In an extreme scenario, you might easily see losses many times the VaR. This is partly because the typical VaR calculation is based on recent data, and most of the time recent data does not include extreme scenarios. It is also partly because the VaR focuses on the minimum loss that could be expected every hundred days or so. The VaR does not estimate how serious the loss could get in the extreme event. Nor does it capture the effects of a series of successive VaR violations. It is generally assumed that each day’s market move is independent of the prior day’s move. In a severely negative scenario this is not likely to be the case.


As indicated by the above quote, VaR has come in for its share of criticism. Some critics argue that VaR is worse than useless because it gives a false sense of security. Others claim that it amplifies cycles. Are these criticisms deserved? I think the answer is that VaR is highly useful for its intended purpose as a risk measurement and monitoring device. But, it is not the proper tool for estimating potential losses in an extreme scenario.

Many people associate VaR with the worst case outcome. This interpretation can lead to problems. If the calculated VaR is small relative to capital, naïve senior executives might incorrectly conclude that the firm’s risk profile is too low, and that they should take on heightened risk. This is an understandable but unfortunate misreading of the meaning of VaR, which is that it is reliable only for normal times.

If you are trying to assess tail risk, VaR should be supplemented by a methodology that aims at estimating the magnitude of loss that could be expected to occur in an extreme event. This is the province of stress testing. Stress scenarios should be based on the worst case that we have seen or believe to be plausible. It seems to me that capital levels for a company that intends to be a going concern should be based on such a calculation. What happens in extreme scenarios for the major risk factors that impact your performance? Does your profit/loss profile look like a smile or a frown?

My view is not shared by all. Many commentators argue that hold capital against extreme scenarios is overkill. Under this approach, they say, many useful investment projects would not be undertaken.

But, I think we have learned at least two things over the recent past. First, worst case outcomes occur rather frequently, certainly more frequently than we expect. Second, it is not good for long-term returns when investments are periodically wiped out. I think it is reasonable for equity investors to expect that management maintains a sufficient capital cushion to handle extreme scenarios.