Lewis Honors College Capstone Collection

Year of Publication

2021

College

Arts and Sciences

Department/School/Program

Mathematics

Degree Name

Bachelor of Science in Mathematics; Bachelor of Science in Economics

First Capstone/Thesis Advisor

Dr. Yuan Zhou

Abstract

One classic problem in quantitative finance is portfolio optimization, which consists of assigning weights to assets in a portfolio to maximize one’s expected return while keeping the level of risk at a desired level. This problem can be modeled as a linear program (LP), using a risk aversion parameter mu. For a given single value of mu, the LP can be solved using any standard LP solver. In this work, however, the problem is considered parametrically: the optimal solution is sought for every possible value of mu. This describes how weights to the portfolio assets would be assigned from the timid investor to the bold. This is accomplished by applying the novel technique of semi-algebraic parametric analysis by metaprogramming (SPAM). Demonstrated in this talk is the method of applying SPAM to a textbook example of portfolio optimization. Generated in this way are numerical and symbolic representations of the solution set as well as a graphical representation of these results.

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