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Brandeis IBS Professor Robert Reitano’s new book teaches students to "think in mathematics" rather than simply apply formulas by rote.

May 17, 2010

A new textbook by Brandeis International Business School Professor Robert Reitano prepares students entering the fast-paced world of quantitative finance to “think in mathematics” and learn how to apply mathematical frameworks to solve real world problems in finance.

Introduction to Quantitative Finance: A Math Tool Kit (MIT Press)

Most finance texts take a cookbook approach to financial math, implicitly encouraging students to apply formulas by rote. But Reitano’s book, Introduction to Quantitative Finance: A Math Tool Kit (MIT Press) provides a deep understanding of fundamental mathematical theory. With chapters on mathematical logic, probability theory, and calculus, Reitano’s book gives students an appreciation of where a given formula comes from, how and why it works, and its dependence on underlying assumptions. 

“My book’s goal is to connect the thought processes in math to applications in finance,” said Reitano, who is a Professor of the Practice in Finance at IBS. “Finance is such a dynamic field that yesterday’s formulas may work, or they may not. I am trying to teach students to go deeper than just blindly applying a formula. I want them to ask: are yesterday’s assumptions for this formula still true today? If so, the formula applies; if not, either the formula needs a modification or a complete overhaul. Because in the real world, you have to come up with a formula for a number whether it’s for a measure of risk, a price, or a trade.”

Reitano was inspired to write the book based on his experience as Executive Vice President and Chief Investment Strategist at John Hancock/Manulife, the financial services company, where he managed 50 investment strategy officers and financial analysts. “Over the years I interviewed and hired a lot of people who had very different facilities in math,” he said. “My goal was to sensitize staff to the fact that you can get into a whole lot of trouble when you don’t use math properly.”

Reitano points out that the financial markets are constantly evolving and technology can now execute much of the rote quantitative processing. “A lot of the finance problems that lend themselves to a mindless application of formulas are being solved by computers 24 hours a day. ‘Program trading’ is a good example. But sophisticated quant jobs are not rote. If you want a meaningful career in this field, you have to go beyond that,” he said. “You have to understand the math behind the formulas – you have to be quantitatively competent, but also able to adapt what you’ve learned to evolving situations.”

Reitano said this inability to adjust to changing financial circumstances played a role in the global economic crisis. “One of the issues that lead to the crisis involved how quants modeled risk – people applied quantitative techniques and formulas and didn’t pay enough attention to the assumptions. There is no question that better quantitative work would have decreased the appetite for risky securities, and that would have significantly lessened the crisis. That said, the crisis had many other facilitators than just the quants.”

The purpose of his book is to instill a “thoughtful, skeptical approach to finance.” “I want my readers to come away with an elevated understanding of how to evaluate problems. I want them to be mindful of the fact that no formula is absolutely true: every formula has conditions and assumptions. They will need to address future finance problems in a more thoughtful, careful way.”
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