The Geometry of Investing


The Problem

When choosing between investment opportunities, each has its own expected return and risk. Generally, the greater return you wish to receive, the more risk you have to take. You have a sum of money that you would like to invest, and you are trying to decide between two investments. What is the percentage of your money that should be invested in each to maximize return and minimize risk? Using mathematical formulas and interactive Geometer’s Sketchpad tools, your goal is to develop an efficient portfolio mathematically.

Background Information

When comparing between two securities in which an investor could put his/her money, there are two concerns an investor will have: risk of the investment and the possible return. Graphing this in the 1st quadrant of the coordinate plane could look like this:

risk-return graph

Obviously, the best place for an investment to be is in the top left quadrant of this graph. It represents the greatest return with the least amount of risk.

Materials Included

  • Suggested problems and sample solutions
  • Student worksheets (“Worksheets.doc”) introducing the topic
  • Article: The Mathematics of Finance, by Al Cuoco and Marvin Freedman
  • Two Geometer’s Sketchpad worksheets