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Phi Beta Kappa members Katharine Wolchik ’05 (Randolph, N.J.) and Usman Khan ’05 (Karachi, Pakistan) presented their senior honors research on investing this semester at the 19th annual National Conference on Undergraduate Research and the Moravian College Student Mathematics Conference. The adviser for their thesis projects is Qin Lu, assistant professor of mathematics.

Wolchik, a Trustee Scholar pursuing a B.S. in mathematics and an A.B. with a major in economics & business, has been accepted into the Ph.D. program in finance at New York University. Khan will begin a full-time job at Merrill Lynch in New York this summer, where he will work in the convertible bonds group as an investment banking analyst.

At the conferences, Wolchik presented her analysis of different trading strategies for maximizing the expected value of an investment portfolio. She selected a portfolio of three diverse, widely held stocks — Yahoo, General Electric, and Proctor & Gamble – and used a method called Monte Carlo simulation to compare “wealth evolution” for a non-optimal trading strategy and an optimal trading strategy. She also analyzed the results for a ten-stock portfolio using stocks in the Dow Jones Industrial Average.

“An investor’s wealth is comprised of shares of various stocks and a sum of cash in an interest-bearing cash account,” she explains. “The goal of portfolio optimization is to maximize the expected value of the utility of wealth (stocks and cash) by appropriate selection of a continuous stock trading strategy. Since trading is ‘continuous,’ shares of stock can be bought and sold as often as every day using the cash account balance to finance stock purchases and collect revenues from stock sales. Transaction costs associated with buying and selling shares of stock are ignored [in her study]. Shorting is allowed, so that within certain limits depending on the investor’s risk tolerance, funds can be borrowed to purchase stock shares.”

In addition to Lu, Wolchik received guidance from Thomas Bruggink, professor of economics and business, and Art Gorman, associate professor of mathematics. Previously, she used game theory, which is rooted in evolutionary economics, to help predict when people might cooperate with one another or act independently in an effort to achieve success. She conducted the EXCEL Scholars research with Christopher Ruebeck, assistant professor of economics and business. She also did EXCEL research with Susan Averett, professor of economics and business, studying abstinence education in the United States over a 10-year period.

Wolchik says her Lafayette education has opened the door to a wide variety of future opportunities.

“I always knew that I wanted to find a career that combined both the theory of economics and the logic of math,” she says. “After having my first taste of financial math from Dr. Qin Lu, I realized that this was exactly what I was looking for. Professor Lu worked with me for the first semester of my senior year and taught me a lot of the basic theory of mathematical finance. After some discussion with Qin of where my interests were, we decided on the topic of continuous stock portfolios for my senior thesis, which I have worked on my whole second semester at Lafayette College. I have grown to appreciate this field and have also grown to learn that the stock market is not just random.”

Khan, who is pursuing a B.S. in electrical & computer engineering and an A.B. with a mathematics- economics major, also has been assisted by Donald Chambers, Walter E. Hanson/KPMG Professor of Business and Finance; Michael Kelly, visiting assistant professor of economics and business; and Thomas Hill, professor of mathematics. He presented “A Binomial Tree Approach to Pricing Callable Convertible Bonds,” which discusses the issues surrounding convertible bonds. Because convertible bonds are considered a combination of debt and equity, a variety of complex factors are involved.

“A convertible bond (CB) is a corporate debt security that can be converted into the issuer’s equity,” he explains. “Basically what that means is that CB’s are bonds that can be converted into stock. Therefore CB’s are a hybrid between debt and equity. They provide the investor with downside risk protection in the sense that he/she can redeem the bond for face value (principal). But since there is an option to convert embedded within the bond, CB’s also provide the investor the opportunity to participate in gains from stock price increases.”

As a hybrid security, the value of a convertible bond depends on many factors, including interest rates, stock price, coupon rates, credit, and the default risk of the issuer.

“In addition, most CB’s have complex features like call provisions, put provisions, and re-fix clauses incorporated in them,” adds Khan. “As part of my honors project I have implemented a binomial tree model for valuing callable convertible bonds using spreadsheets and used this model to price a real issued CB and calculate its price sensitivity to the input variables.”

His classes prepared him well for undertaking the research project and for his job at Merrill Lynch, he says.

“I have found the experience to be very useful, especially since this project has enabled me to bring together skills from most of my previous finance courses at Lafayette,” he says. “Dr. Chambers’ course on Options and Futures and the higher-level Probability and Statistics sequence are a couple of courses that have definitely been required to even understand any of the literature on the subject.”

He gained related experience through a summer internship at InteCap Inc. hosted by Alan Friedman ’68, the New York firm’s managing director, which involved financial consulting, litigation services, securities, and valuations, including valuation of a real estate holding company. He also interned for a semester as an international financial analyst for Siemens Corp. in Iselin, N.J.

Khan completed an externship during his sophomore year with James Flowers ’69, project manager for the power and transmission department of the Omaha (Neb.) Public Power District. During his junior year, he conducted research on fuel-cell technology with William A. Hornfeck, professor of electrical and computer engineering, and an independent study on a portfolio analysis method called the Markowitz Frontier with Qin Lu, assistant professor of mathematics.

“The academic environment at Lafayette is probably one of the best in the nation,” he says. “I feel that the College affords one so many opportunities; it is just up to the individual to find them. I have found all the professors and administrative staff very helpful in helping me achieve all my goals. What sets Lafayette apart from other schools is that even though it is a small school, the best resources and opportunities are available to the students.”

Khan says the NCUR trip was “absolutely great.”

“Everything from the travel arrangements to the accommodations and the conference proceedings themselves were great,” he says. “Even though most of the presentations at the conference were of the highest quality, I felt that all Lafayette students definitely excelled in their sessions and the credit for that must go to all the faculty and administrators here. Overall, NCUR was a thoroughly enjoyable and refreshing academic experience, and I would definitely recommend all students doing any research at Lafayette to present in the following years.”

Categorized in: Academic News