MPT Efficient Frontier for Portfolio Optimization

Modern Portfolio Theory (MPT) recognizes that investment returns also carry risks. When assembling a portfolio of risky assets, it is necessary to account for these two components as well as the correlation among the assets.

When risky assets are combined in a portfolio, the expected return of the portfolio, E(Rp) is the weighted average of the returns for each asset. If the asset returns are not perfectly correlated, the expected risk of the portfolio is somewhat more complicated. By convention, standard deviation, the square root of the variance, is a proxy for asset risk.

The Efficient Frontier plots in risk-expected return space every possible combination of assets A, B, and C. The upper edge of the curve represents each outcome for which the portfolio return is maximized for a given level of portfolio risk.

The ‘blue star’ shows the return along the efficient frontier at the risk level selected by the slider. Additionally, the shares of assets A, B, and C for the portfolio that produced this point are displayed to the right of the graph.


change in version 2.3
  • Updated for newer versions of iOS and iPhones
changes in version 2.2
  • Changes to accommodate iOS 9, mostly font changes
  • GUI modifications
  • Added links to Facebook and Twitter
change in version 2.0
  • Major rewrite and redesign for iOS 7
change in version 1.6
  • Minor GUI enhancements
changes in version 1.4
  • Expanded screens to accommodate size of iPhone 5
  • Data entry bug fix

revised: December 21, 2018