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
Introduction to Portfolio Analysis in R

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
Introduction to Portfolio Analysis in R

The H. Markowitz approach

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Introduction to Portfolio Analysis in R

The H. Markowitz approach

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Introduction to Portfolio Analysis in R

The H. Markowitz approach

ch_4_video_1.003.png

Introduction to Portfolio Analysis in R

The H. Markowitz approach

ch_4_video_1.004.png

Introduction to Portfolio Analysis in R

The H. Markowitz approach

ch_4_video_1.005.png

Introduction to Portfolio Analysis in R

Let's practice!

Introduction to Portfolio Analysis in R

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