Managing financial risk and the limitations of quantitative modeling

John Kay in a 2011 column says that the management of risk is “almost entirely a matter of management competence, well-crafted incentives, robust structures and systems, and simplicity and transparency of design.” (“Don’t blame luck when your models misfire” Wednesday 2 March 2011). Mr. Kay is absolutely correct. This idea needs to be spread far and wide. Formal modeling is limited.

But focusing on management competence, etc., hardly means rejecting quantitative techniques, as the balance of Mr. Kay’s column seems to imply. In today’s complex financial markets management competence requires quantitative techniques, not as a substitute for managing but as a set of tools that enhance true management competence. Managers need to upgrade their quantitative skills and understanding, making a concerted effort to learn and use such techniques rather than turning their back on them.

For example, what is the chance that we would observe a run or streak of 10 heads in a row? Intuitively we would think very low, because the chance of flipping 10 straight heads with a fair coin is less than one in a thousand. Seeing such a streak our intuition tells us that the coin is probably biased or the person flipping the coin is cheating. It turns out, however, that our intuition can mislead and we must supplement intuition with formal modeling. Consider flipping a coin once a day for a year, roughly 255 working days. The probability of getting a streak of 10 or more heads sometime during the year is about 11%. Surprising but true.

Now let us turn to a real-life situation. Say we were considering a mutual fund and compared the fund’s day-by-day returns for the past year with the S&P index. What if the fund beat the S&P for 10 days running at some point in the year? Is that strong evidence for a “biased coin,” that our fund beats the S&P more often than just flipping a coin? No. The formal modeling tells us that such a streak is not so unlikely after all.

Or take the case of William Miller, manager for the Legg Mason Value Trust Fund. Through 2005 the fund beat the S&P 500 index for 15 years straight. (Leonard Mlodinow, in his delightful 2008 book The Drunkard’s Walk, discusses Miller’s streak, and I have studied that streak and more recent, shall we say, less stellar performance.) A 15 year streak seems extraordinary. One analyst was quoted as putting the chance of such a streak at lower than one in 372,000 or 0.003%. But in reality such a streak is not unlikely. When we look back over many years, and when we consider the pool of many thousand mutual funds that might by chance outperform, such a streak becomes pretty likely. The chance we would see some fund during the last 40 years with such a streak is something like 30%, not 0.003%. Another example where formal modeling tutors our intuition.

Formal modeling does not have all the answers by any means. Extreme events are a prime example. By their nature they are rare and so hard to quantify. But an understanding and appreciation of quantitative modeling can prove invaluable.

What does it mean when David Viniar, chief financial officer of Goldman Sachs, says “We were seeing things that were 25-standard deviation moves, several days in a row” (August 2007). Maybe he meant “Don’t blame us, we couldn’t foresee events, bad things have happened and it’s not our fault.” If so it was a silly, even disingenuous, statement, and he would deserve the opprobrium he has received. But I suspect he meant: “We have seen a number of days with large profit and loss, much larger than expected given the history that we used to build our risk models, and much larger than would be predicted if markets behaved according to a normal distribution. This is a warning sign – a sign that our models are wrong and that something is happening that we do not understand.” This is a sign of a robust organization that responds to new evidence. And we know that Goldman did cut their exposure to mortgage-backed securities during 2007 because their risk models showed something was awry, and that as a consequence Goldman did not suffer the same scale of losses during that summer. (See Joe Nocera’s useful story in the New York Times, 4 January 2009.)

Quantitative tools have a role throughout the finance industry. They apply to insurance companies as well as investment banks or hedge funds. Insurance companies do fail, and they fail for the very reasons described in quantitative risk models.

Reflect on the case of the Equitable Life Assurance Company, the world’s oldest mutual insurance company. Equitable closed to new business in December 2000 following an unexpected adverse ruling in the House of Lords in July 2000. The closure, however, was not the result of an unanticipated event; the ruling was the proximate but not the underlying cause. The foundations for the closure were laid over 40 years earlier, with insurance policies that included an embedded interest rate option. The situation gets a little complicated (which is why careful thought and attention to detail is important for managing risk) but in essence many policyholders had the option to choose an annuity that would pay out either a pre-set fixed rate or a market-determined rate. During the inflationary 1970s that option was worth virtually nothing, but as rates fell the contingent liability grew. When the market rate fell below the fixed rate (which happened in 1993) many policyholders started to exercise their option to receive the higher rate.

This was a classic interest rate option, with the Equitable’s liability rising as interest rates fell. Quantitative risk models are well-designed to capture the risk of such options. In practice the Equitable did not hedge against, reinsure, or adequately plan for such risk. This risk, a risk that we can see could have been quantified and managed, is what ultimately brought the Equitable to its knees. It was not an unforeseen event, but poor management allied with sloppy risk measurement. It was a failure of management to apply the appropriate quantitative models rather than a failure of the models to adequately capture reality.

In conclusion, Mr. Kay is absolutely right that managing risk is a matter of management competence, but management competence requires using and understanding quantitative models and tools. Too often senior managers in financial firms sidestep their responsibility to understand the businesses they manage. Finance is a complex business and cannot be run simply by hunch and instinct. Intuition too often misleads. Intuition needs to be married with hard analysis and concrete facts. Running a financial firm cannot be reduced to a mathematical model but it does require careful use of quantitative tools.

About Thomas Coleman

Thomas S. Coleman is Senior Advisor at the Becker Friedman Institute for Research in Economics and Adjunct Professor of Finance at the Booth School of Business at the University of Chicago. Prior to returning to academia, Mr. Coleman worked in the finance industry for more than twenty years with considerable experience in trading, risk management, and quantitative modeling. Mr. Coleman earned a PhD in economics from the University of Chicago and a BA in physics from Harvard College.
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