Value-at-risk models can be misunderstood

I learned recently that I have an incorrect understanding of value-at-risk models, which many banks and Wall Street firms use to measure how much risk they are taking.

And I suspect my misunderstanding was shared by E. Stanley O’Neal, the former chief executive of New York-based Merrill Lynch & Co. Inc., and Charles Prince, former chairman and CEO of Citigroup Inc. of New York, and many other senior executives like them at financial firms.

Perhaps because of the way value at risk was explained to me years ago when it was first popularized, or perhaps because I have confused the explanation over the years, I believed VAR specified the maximum amount of possible loss in a one-day period at a 95% confidence level. That is, if someone told me my one-day 95% VAR was $1 million, I assumed that on any, day there was a 5% chance I could lose as much as $1 million.

I was wrong. A one-day 95% VAR of $1 million implies there is a 5% chance of losing at least $1 million on any single day. That’s a big difference.

I learned of my mistake from an essay by Brent C. Skilton, an analyst with Lotsoff Capital Management, a fine bond and equity management firm in Chicago. The essay was published in the February issue of the LCM Perspective, the firm’s monthly client letter.

Of course, that was a far less painful way of discovering my mistake than that experienced by Mr. O’Neal and Mr. Prince, if they suffered from the same misunderstanding. They’ve lost their jobs and no doubt have taken painful blows to their egos.

“In certain ways, VAR is like flipping a coin, but with a catch. The coin is so heavily weighted that 95% of the time, it comes up heads and you are above your VAR level. But 5% of the time, it comes up tails and Mount Vesuvius erupts in your portfolio,” Mr. Skilton wrote.

He noted that Goldman Sachs’ average one-day 95% VAR in the last quarter of 2007 was $151 million, according to a recent report. That means that on 5% of a year’s 252 trading days — or on 13 days — Goldman could lose at least $151 million each day.

“Clearly,” Mr. Skilton wrote, on other days, “Goldman expects to make enough on average to overcome this risk.”

But what if “tails” comes up several days in a row? The losses would mount quickly and possibly even overwhelm a firm with insufficient capital.

“Having a low one-day VAR doesn’t mean that someone can’t have a very bad year. This explains why we seem to have these financial disasters once every decade,” Mr. Skilton wrote.

The situation could be even worse, he noted, because the true probabilities of events that have never, or rarely, occurred in the past are “ridiculously hard to measure accurately.”

Even a small error in estimating the probabilities can have enormous costs, greatly increasing the chance of exceeding the VAR on multiple days in the year.

No doubt, the risk managers at Wall Street firms and banks understood this when they were making bets on mortgage-backed securities, but did senior management? They had to approve the positions and ultimately had to answer to shareholders. Did board members understand the information when it was presented to them?

My guess is, many did not. My guess is, many thought of VAR the way I did and that this misunderstanding meant they were not able to recognize the potential for disaster.

Michael Clowes is the editor at large of InvestmentNews.