Date of Award

12-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Yu-Ju Kuo, Ph.D.

Second Advisor

H. Edward Donley, Ph.D.

Third Advisor

John J. Lattanzio, Ph.D.

Fourth Advisor

Greg Wisloski, Ph.D.

Abstract

Two-thirds of professional money managers cannot earn a return on investment greater than the rate provided by the S&P 500 index. Portfolio selection in the face of an uncertain future requires the use of subjective probabilities about that future and the impact those events may have on the market. These subjective probabilities about unknown future events and unknown future impacts are difficult, if not impossible, to estimate. This problem can be circumvented. The profit from a trade is modeled as a Bernoulli random variable with a stop-loss parameter. Using the historical behavior of an exchange traded fund called the DIA and describing the relationship between the DIA and its underlying call options through regression, the mathematical expectation of the expression is empirically determined. By making only one key assumption about the market--that it will react to future events in a similar manner to its history- a system of trading call options is developed whereby the mathematical expectation of the return on investment is greater than the return provided by the S&P 500 index. The result is confirmed via simulation.

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