Michael Magill and Jaksa Cvitanic

Tracking Market Trends
At the intersection of math and money lies a fortune of opportunity

By Nicole St.Pierre

As the number of people who invest in stocks, bonds and hedge funds climbs, there is a growing desire to understand—and in a perfect world predict—the ups and downs of Wall Street. While there is no sure-fire way to take advantage of fickle markets, USC mathematics professor Jaksa Cvitanic and economics professor Michael Magill say mathematical models are key to putting portfolios in the black.

At USC College, Cvitanic and Magill direct a relatively new field of academic study: computational finance, also referred to as mathematical finance. The program takes a fresh look at how mathematics and economics can be merged to better understand financial markets.

The College has offered the unique master of science degree in mathematical finance since 1999. The program gives students insight into how financial markets work and fit into the overall economy. More particularly, it shows how business people can learn to hedge their risks in a real-time environment, teaching graduate students how to price options, improve asset-liability management and analyze stock returns.

In their research, Cvitanic and Magill develop complex economic models to study relatively new investment vehicles like hedge funds while using data from the U.S. Census to explain what influences market volatility over the long term. Not surprisingly, graduates of the program are in steady demand even in the current bear market.

Converting Numbers Into Dollars
Cvitanic, who joined USC in 1999, has become one of the world’s leading experts on the computational techniques of tracking financial markets. He currently is developing a model to help investors determine the optimal percentage of their portfolio to invest in hedge funds—actively managed funds where returns are often extremely difficult to predict.

“There are many formulas that estimate the percentage of stocks and bonds an investor should hold in a diversified portfolio depending on their financial goals. But modeling hedge funds is a relatively new field of research, since they have only recently entered the mainstream,” says Cvitanic.

In his next book, “Introduction to Economics and Mathematics of Financial Markets,” Cvitanic develops the basic mathematical machinery and models needed to understand financial markets. The book is co-authored by professor Fernando Zapatero of the USC Marshall School of Business, who also holds a joint appointment with the economics department in the College.

Cvitanic’s inspiration for the research was work done by 1997 Nobel Laureates Myron Scholes and Robert Merton. They showed that in a perfect, frictionless market, money managers could insulate themselves from risk using sophisticated hedging strategies. In proving this, they developed the tools that are now critical in the field of computational finance.

“When I was writing my thesis at Columbia [University], I became mesmerized by the sophisticated way you could use math to really understand money, make money and protect money,” he recalls. “Who knows, maybe the next Scholes and Merton are sitting in our classrooms.”

Cvitanic also is developing a formula to answer a question often asked in the boardroom: Is it optimal to compensate top executives with stock options or stock?

“Companies first have to understand their own corporate risk tolerance at a given time and the individual risk tolerance of the executive at a given time,” he says. Using sophisticated mathematical models, Cvitanic has produced research indicating that if both entities have similar risk tolerance, then compensation is best given in stock. But if risk aversion differs, stock options are the ideal incentive.

Predicting the Next Tidal Wave
Down the corridor, Magill is equally passionate about crunching numbers on computers to understand financial markets. But unlike most in his field, his research injects a human factor into hard-core financial analysis. Specifically, Magill analyzes data from the U.S. Census to show how demographics quietly influence the stock market. By analyzing the general population’s proportion of middle-aged people to young people, he has developed a mathematical model that predicts the market’s consistent peaks and valleys that occur about every 20 years.

“People tend to look at the stock market with the short view on a day-to-day basis. In the long view, demographics are a tidal wave that push the market up and down over time,” says Magill, who collaborates with economists at Yale University and UC Davis to study demographic trends.

His paper “Demography and the Long-Run Predictability of the Stock Market” studies five periods of alternately high and low birth rates—the 1910s, 1930s, 1950s, 1970s and 1990s—and analyzes their impact on security prices. His research shows that prices, although random, have a strong predictable component that is in line with shifts in population size.

The idea that demographics influences security prices had circulated among economists for a number of years, but Magill was the first to develop a mathematical formula to prove the correlation.

Magill’s findings indicate that changes in the number of births over time leads to changes in the age pyramid, which then alters the relative demands for different types of securities on financial markets. “It’s impossible to predict every shock to the market, but it’s not hard to imagine that when the remarkable number of baby boomers withdraw their retirement savings from 401(k)s and IRAs, this will have an effect on the market’s overall performance and security prices,” he says. His model supports the view that a substantial fall in price-earnings ratios is likely to occur in the next 20 years.

The same mathematical model shows that the size of a generation to which people belong crucially influences the prices that they will encounter in the bond and equity markets over their lifetime. Specifically, people in small age groups face favorable terms of market trade, whereas those in larger groups face unfavorable market prices.

Achieving Solid Returns
As for predicting the future of the College’s mathematical finance program, Cvitanic and Magill say they are insulated from market forces to a large extent. “We’re not subject to market volatility,” Cvitanic laughs. “When the economy is hot, everyone wants to understand it to make money. When the economy isn’t so hot, people realize, ‘Hey, I need to really understand the complexities of the market in order to get ahead.’”

Magill agrees. “The economics and mathematics that are taught in this program can be applied every day in the real world,” he adds. “No math is needed to understand that this is a solid investment.”