Portfolio Optimization From Scratch

A technical guide to understanding modern portfolio optimization theory

Photo by Patrick Weissenberger on Unsplash

Summary

• The main purpose of portfolio optimization is to maximize returns and minimize the risk of a portfolio of assets according to modern portfolio theory (Markowitz, 1952)
• For investors and asset managers, knowing how much capital needs to be allocated to a particular asset or a basket of assets can statistically make or break a portfolio
• Modern portfolio theory (Markowitz, 1952) simply formalizes and extends the concept of portfolio diversification

Underlying Theory Behind Portfolio Optimization

Portfolio optimization is the process of selecting proportions of various assets to include in a portfolio, in such a way as to make the portfolio better than any other according to specific constraints.

Modern Portfolio Theory (Markowitz, 1952), presumes that in general, investors and/or asset managers seek to strategically maximize a portfolio’s rate of return for a well-defined level of risk. Risk is in this particular set up is simply defined as the standard deviation of the portfolio’s return. Furthermore, the concept of optimal or efficient portfolios was introduced to describe portfolios that maximize returns given a…