## Reducing Economic Risk: Everything to gain -- Engineer takes on financial world

In the financial world, two plus two doesn’t always equal four.

Within a given financial portfolio, each investment is typically assigned a number to indicate its level of riskiness, or how likely it is to lose money. Determining the risk of the entire portfolio, however, goes far beyond simply adding the risk measures of individual investments. Often, the investments are dependent on one another, meaning that the failure of one can trigger a chain reaction and have an effect on the entire portfolio far greater than expected.

Patrick Cheridito, an assistant professor of operations research and financial engineering, is developing better ways to quantify risk that take these complexities into account. His work may one day allow individuals, regulating agencies, pension plans, insurance companies and banks to make more informed decisions.

“There are so many different reasons and methods for quantifying risk,” Cheridito said. “Will there be profits or losses in a given week? How much is at stake? Risk is so complex, and it often needs to be reduced to just one number. Then, someone has to decide whether it is an acceptable financial position or not and act accordingly.”

Of course, quantifying risk is nothing new: For over a century, people have been attempting to pin it down using a variety of mathematical and statistical tools.

But existing techniques have tremendous disadvantages. For example, one common technique called “variance” measures how far the performance of an investment deviates from an expected outcome, but it treats being above and below the anticipated result in the same way. Essentially, it views gains and losses equally—a position that, for obvious reasons, is not shared by investors.

Additionally, these measures were developed on the assumption that the financial world follows a normal, bell-shaped curve, so that the likelihoods of major returns and major losses are the same, with most outcomes falling somewhere in between.

“Traditional risk measures work well with a normal distribution,” Cheridito said. “But in recent years, people have noticed that the financial world is not well-modeled by this distribution. Crises occur more often than you would expect, and losses are more severe than would be expected.”

Finally, traditional risk measures are static, providing information about risk at only one moment in time, whereas real financial decisions are based on dynamic models that analyze data and make predictions over time. These models often rely on static measures to assign value to risk, which limits their forecasting capabilities.

“Tomorrow you’ll have new information. If risk measures aren’t dynamic, they may result in people and institutions acting in such a way that they contradict themselves over time,” he said. “There can still be surprises, and people will still have to react to new events, but not in ways that will contradict what they did before.”

To address the many drawbacks of existing tools, Cheridito is developing metrics that more accurately represent risk, work within non-normal probability distributions and change over time. In one case, his method measures asymmetries between the upper and lower ends of a distribution and also looks at the steepness of the peak in the middle of the graph. Such measures are more risk averse to extremely bad events, and thereby lessen the likelihood of financial disaster.

“Patrick Cheridito has made important contributions to a better structural understanding of risk and introduced new classes of risk measures that are able to detect risk exposures in situations where traditional methods do not perform well,” said Nizar Touzi, a professor of mathematical finance at the École Polytechnique in Paris. “This has applications in risk management, the determination of insurance premiums and the pricing and regulation of complex financial products.”

In May, Cheridito was awarded a prestigious CAREER award from the National Science Foundation, which provides $400,000 over five years to support his work on risk quantification. He joined the Princeton faculty in 2003, after a year as a visiting research fellow at the University, and holds bachelors and doctoral degrees from the Swiss Federal Institute of Technology in Zurich.

“While many of us in operations research and financial engineering call ourselves financial engineers, what we really do is study risk with an eye toward reducing or otherwise mitigating its effects,” said Robert Vanderbei, chair of operations research and financial engineering. “Risk lurks everywhere and having a deep mathematical understanding of it is critical. Patrick’s work provides important new ways in which we can assess risk, not only in financial markets, but in all aspects of modern life.”

Cheridito’s current focus on risk stemmed from a long-time interest in mathematics and probability theory. Realizing that risk is an important concept in many areas, including finance and engineering, he saw an opportunity to apply his expertise to real-world problems. Now, he can often be seen at the tables in EQuad Café, developing new measures with nothing more than a pencil and paper.

“In the broader context, lots of problems require us to make decisions under uncertainty,” he said. “Sooner or later, you have to think about risk.”

Asked whether his research emphasis has perhaps made him more risk-averse, Cheridito took a minute to ponder the question.

“Maybe it creeps in unconsciously,” he said. “Everyone faces uncertain situations and risk. We all cross streets, ride on airplanes and invest money and I think about it like everybody else—just maybe a little bit more concretely.”