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, former chief executive officer of Merrill Lynch & Co., and Charles Prince, former chairman and CEO of Citigroup Inc., and many other senior executives at financial companies.
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 it 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% value at risk was $1 million, I would assume that on any day, there was a 5% chance I could lose as much as $1 million.
This is wrong. In fact, 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 money 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 Messrs. O'Neal and 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. Mr. Skilton wrote. 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.
He noted that a recent report put Goldman Sachs Group Inc.'s average one-day 95% VAR in the last quarter of 2007 at $151 million. That is, on 5% of the 252 trading days of the year Goldman could lose at least $151 million. That is, Goldman could lose at least that much on each of 13 days in a trading year. 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 might 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, Mr. Skilton wrote. This explains why we seem to have these financial disasters once every decade.
The situation could be even worse, Mr. Skilton 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 value at risk on multiple days in the year.
No doubt risk managers at Wall Street firms and banks understood this when they were making bets on mortgage-backed securities. But did senior management, those who had to approve the positions and risk exposure, and who ultimately had to answer to the shareholders? Did the members of the boards understand when they were presented with information on the positions at their quarterly meetings?
My guess is many did not. My guess is many thought of value at risk the way I did, and that this misunderstanding meant they were not able to recognize the potential for disaster.