Modern portfolio theory of Harry Markowitz

Introduction to Portfolio Analysis in R

Kris Boudt

Professor, Free University Brussels & Amsterdam

Portfolio weights are optimal

...when they optimize an objective function while satisfying the constraints.

Possible Objectives	Possible Constraints
Maximize expected return	Only positive weights
Minimize the variance	Weights sum to 1 (all capital needs to be invested)
Maximize the Sharpe ratio	Portfolio expected return equals a target value

Harry Markowitz

• Nobel Prize Winner
• Recommends finding optimal portfolios by
  • Objective: Minimize portfolio variance
  • Constraints:
    • Full investment
    • Expected return should be equal to a pre-specified target return

The H. Markowitz approach

The H. Markowitz approach

The H. Markowitz approach

The H. Markowitz approach

The H. Markowitz approach

Let's practice!

Introduction to Portfolio Analysis in R