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Lessons from Questrom’s Toughest Class

Mathematical finance—that esoteric land of quants and derivatives—will give your brain a workout and could boost your business (and your retirement fund)

The welcome page for the Questrom MS in Mathematical Finance greets would-be students with a stark warning: the 17-month program is “not for the faint of heart.”

On their journey to becoming traders, risk analysts, financial software developers, industry regulators, or quants—the in-demand financial analysts specializing in math and statistics—students will have to crack some of finance’s most complex, often arcane, theories: stochastic mathematics, algorithmic trading, derivatives modeling.

But first, they have to get in. The average quantitative GRE of the latest class is around 168 (the maximum possible score is 170) and the only “basic” thing in the prerequisites list is basic computer programming skills; from there, things spiral through the fundamental theorem of integral calculus to multivariate optimization. Although 1,335 mathematicians, engineers, physicists, economists, computer scientists, and others applied to join the Questrom MS in Mathematical Finance Class of 2019, just 30 percent were accepted, making it the School’s most competitive master’s program.

Despite the welcome page admonition and the dauntingly high bar for entry, the program is increasingly popular. Founded in 1999 with just three students, it now has more than 200, including 15 doctoral candidates, and 9 full-time faculty.

“It’s the right program at the right time,” says Allen Questrom Professor and Dean Kenneth W. Freeman, who notes that the faculty is the highest rated of any at Questrom. “The need for sophisticated mathematical modeling has never been higher. Our graduates have the tools to make an immediate impact.”

The theories might seem inscrutable, but the applications aren’t. Mathematical finance underpins your pension and mortgage, helps banks figure out the risks of big deals, and could save us from another stock market crash. You might never need to know an eigenvalue from an eigenvector, but your business might not function without someone who does.

Why You Should Pay Attention

For the majority of students joining Questrom’s math finance program, the goal is to land a job in the financial services sector, working on the complex models that underpin much of modern finance. The models are encoded in computer programs that banks use to calculate the pricing and structure of things like derivatives, the contracts that allow businesses to hedge against future changes in prices or speculate on shares with an option to snap them up at an agreed price and date. Quants help banks to figure out a fair price for those deals—and to understand the risks involved.

They’re also building and managing the programs making the majority of stock market trades. Today, 70 percent of all US stock trades are made by computers—not people. Automated trading—where sophisticated computer programs make thousands of deals per minute using intricate mathematical algorithms—accounts for anywhere from 50 to 85 percent of the daily volume of share dealing in the United States. In 2005, that figure stood at around 30 percent.

“That’s really relevant to anyone who has a mutual fund and wants to save for retirement,” says Marcel Rindisbacher, the faculty director of the math finance program.

When mutual funds—what Rindisbacher calls “slow traders”—try to place bulk orders, they’re spotted in advance by the high-frequency traders, algorithm-based competitors that cash in and force the share price up. Rindisbacher says that’s why it’s important to train and hire people “who know the risk exposure of these strategies; in order to do that, you need to know how these algorithms work.”

Enter the quants. All students in Questrom’s program have to learn the fundamentals of finance and computer programming, then pick from electives focusing on asset management, quantitative analytics, risk management, or analytics and research. According to the Wall Street Journal, it pays to have them on your side. “In the past five years,” the paper reported in May 2017, “quant-focused hedge funds gained about 5.1% a year on average. The average hedge fund rose 4.3% a year in the same period.”

Even smaller banks are beginning to see the importance of having someone on staff who can do complex number crunching.

the class of 2019


“This perceived need was probably initiated by increased regulations and the associated complications, but in the process, these smaller financial institutions may have appreciated the value of quants’ rigorous risk modeling,” says Eric Jacquier, clinical professor of finance and a specialist in volatility forecasting and financial econometrics.

As well as helping companies comply with oversight rules like those in the 2010 Dodd-Frank Wall Street Reform and Consumer Protection Act, quants can also stop businesses, not just banks, from getting ripped off.

Pretend you’re an oil refiner who wants to hedge the cost of your primary ingredient: crude. You call your banker in New York to ask about using a crude oil swap to lock in the price for your next 10,000 barrels. Your banker will quote you a series of prices at which you’ll be able to buy crude out into the future—at prices guaranteed today. How do you know if the price is right? “Your quant might be able to tell you that,” says Jacquier.

Increasingly, he adds, the boundary between commodities traders and asset producers has begun to break down; the bankers are also becoming refiners.

“Commodities trading firms have started buying real assets; they’ve started buying refineries, and they’re buying refineries because they want information about market pricing for the spot price of those underlying commodities.”

Causing a Crash; Preventing Another

Not everyone holds mathematical finance in such high esteem, however. Some blame it for the subprime mortgage crisis that sparked the 2007 global recession.

In a 2009 Wired article, “Recipe for Disaster: The Formula that Killed Wall Street,” financial journalist Felix Salmon charted the rise and fall of the Gaussian copula function, a formula for calculating risk. Wall Street bosses loved the formula because it allowed them to bundle “just about anything…into a triple-A bond—corporate bonds, bank loans, mortgage-backed securities, whatever you liked,” wrote Salmon. At the time, plenty said the formula was flawed—it assumed unpredictable, once-in-a-lifetime events would never happen—but, with money to be made, plenty were prepared to use it.

And then the unpredictable started happening: house prices began tumbling.

“In the world of finance,” wrote Salmon, “too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years' worth of data and come up with probabilities for things that may happen only once every 10,000 years.”

“There’s a perception that mathematical sophistication has contributed to evil things, not prevented the evil things. But sometimes people use the models very blindly, without understanding the deeper consequences.”
—Marcel Rindisbacher, faculty director of the math finance program

The end of the housing boom turned out to be a concrete dose of reality. Homeowners began to default on their loans and suddenly those supposedly triple-A securities—packed to the brim with mortgage debt—didn’t look so risk-free. Wall Street institutions, stuck with junk securities, were out of pocket in a big way.

“There’s a perception that mathematical sophistication has contributed to evil things, not prevented the evil things,” says Rindisbacher. “But sometimes people use the models very blindly, without understanding the deeper consequences.” Decision makers choose to ignore risks; mathematicians churn out complex models—mathematical formulas—without understanding the real world they operate in.

“The crisis exposed the problems that many of these mathematical models have—they are approximations that do not take into account possibly rare events and other market complications,” says Jacquier. “While they may work decently most of the time, they might be completely useless in some situations. The fundamental problem is complacency: people become comfortable with approximations. It takes a well-trained quant to understand the dangers.”

Rindisbacher calls the financial crisis a “motivation to do better next time” and to work harder at informing people about “the limitations and the dangers” of these complex financial instruments. “It’s really important to educate people because the application of these instruments in the industry has not been reduced, they’re still there.”

Most banks now see the benefit of having someone on staff with a mathematical finance background, but those at the top haven’t always been great at listening to quants’ advice. And quants haven’t always been adept at giving it. Both need to change to help prevent future crashes. Rindisbacher hopes graduates of the Questrom program are equipped to argue their case, translating complex math into useful briefings that anyone can grasp.

“A lot of quants have disappeared into back offices and might not be influential in decision-making processes,” says Rindisbacher. “It was very visible during the financial crisis that a lot of the CEOs would continue to play games in the markets where things were very fragile and not based on good models. We want to elevate our students to the level where they become influential in the decision-making process. Some of the things that we have can be very dangerous, as the financial crisis showed, but it would be good to put that in the hands of financial engineers who are very conscious of the limitations of their models, but nevertheless help the decision makers.”

Many of Questrom’s risk management students are increasingly policing those who can’t exercise restraint, joining regulatory bodies like the Federal Reserve, the Securities and Exchange Commission, and the Comptroller of the Currency.

Rindisbacher wants the lessons he and his colleagues impart in the classroom and test in research papers to filter through the industry, changing it for the better. The Class of 2016—the latest to be surveyed—is already doing its part, landing jobs at companies like Goldman Sachs, Moody’s Analytics, Fannie Mae, and State Street Corporation, and pulling in an average starting salary of $84,000.

Once his students have finished their classes, Rindisbacher has one final lesson to impart. He might be talking about financial models, but there’s wisdom in it for the rest of us.

“What you’re doing in terms of model building, don’t believe that because it works at some moment in time, it will always work,” he says. “Always try to question what is missing, what are the potential factors you didn’t take into account? If you ever find something that looks good, don’t believe that this is the final answer.

“You have to have a lifelong learning approach. Just because you’re now relatively state of the art because you have been through a very rigorous program, doesn’t mean this is sufficient for your career. Things will change—you have to be alert and place all that you have learned in a broader context.”