STEM Program

Applied Mathematics in Finance: Portfolio Optimization with Modern Portfolio Theory

Faculty Advisor: Professor and Director of Undergraduate Studies, Mathematics, Georgia Institute of Technology

Research Program Introduction

Applied Mathematics is the use of mathematics as a tool to solve and/or better understand problems from different disciplines.

This use of mathematics generally involves two steps:

  • The first one, known as mathematical modeling, is the abstraction of the real-world problem into mathematical variables and the equations they satisfy.

  • The second step is solving these equations.

Stocks, bonds, real estate and precious metals are examples of assets. To grow wealth, an investor buys assets that he or she believes will go up in price. The percentage of this increase during a period of time is known as the return on the asset. To maximize gains, the investor may select the asset whose return is expected to be the largest.

If the price of the asset the investor buys goes down, the investor loses money. This possibility of loss is known as risk. Investors are not only interested in maximizing the returns of their investments, but they are also interested in minimizing their risk.

To mitigate risk, investors buy several assets, not just one. This group of assets forms what is known as the portfolio of the investor.

For example, Apple stock tends to go up in price in times of economic growth and down during recessions. Gold, on the other hand, tends to go down during periods of economic growth but up during recessions.

By allocating 50% of a portfolio to Apple stocks and 50% to gold, the investor will likely see 50% of the portfolio go up in value, regardless of whether the economy enters a growth or recession period. Modern Portfolio Theory is a mathematical model for constructing portfolios that are expected to have large returns and also involve lower risk.

Possible Topics For Final Project: 

During the first half of this program, students will learn probability, optimization methods, the computer language Python, as well as aspects of the economy and finance through Modern Portfolio Theory. Students will be provided with material in the form of videos, notes and computer code so they can study and learn outside the meetings.

During the second half of this program, students will carry out their projects from the following list of topic options:

  • Research historical data on the returns of assets and apply Modern Portfolio Theory to construct an optimal portfolio

  • Use historical data to test the accuracy of the predictions of the theory

  • Research a complementary finance theory known as Factor Model. This theory can be used as a preliminary step of Modern Portfolio Theory leading to more powerful results.

  • Research optimization methods 

  • Research other methods and/or theories in finance

Program Detail

  • Cohort size: 6 students maximum

  • Duration: 12 weeks

  • Workload: At least 5 hours per week (not including meeting time)

  • Target students: 9 to 12th graders interested in Mathematics, Artificial Intelligence, Machine Learning, and/or Interdisciplinary STEM studies.

  • Prerequisites: Basic programming skills are preferred but not mandatory. The students will be provided with materials to supplement their learning.

  • Schedule: TBD (meetings will take place for around one hour per week, with a weekly meeting day and time to be determined a few weeks prior to the class start date)