Foundation course in portfolio management
Modern Portfolio Theory
Markowitz's framework from first principles: expected return and covariance, the benefit of diversification, the efficient frontier, the minimum variance and tangency portfolios, and the capital market line, all computed in Python.
Harry Markowitz’s 1952 paper “Portfolio Selection” founded modern portfolio theory and turned investing from picking good assets into building good portfolios. Its central point is that what matters is how assets move together. The ideas it introduced, diversification measured by covariance and the efficient frontier, are still the foundation of portfolio management.
What is the efficient frontier?
The set of portfolios that give the highest expected return for each level of risk. Any portfolio below it could be improved by holding a different mix of the same assets. You will compute the frontier for a set of real assets in Python and see how its shape changes with correlations.
Why do mean-variance portfolios look strange in practice?
Because the optimiser treats estimated returns and covariances as exact. Small errors in expected returns produce large, unstable swings in weights, often concentrated in a few assets. The course shows the problem directly and points to the methods, such as shrinkage and Black-Litterman, that address it.
Who is this course for?
Anyone starting portfolio management or systematic investing, and investment professionals who want the quantitative basis of what they already use. It counts toward the Certificate in Quantitative Portfolio Management and the Certificate in Systematic Investing.
What you will be able to do
- Compute portfolio expected return and variance from asset statistics.
- Explain diversification in terms of correlation and covariance.
- Trace the efficient frontier and find the minimum variance and tangency portfolios.
- Explain the capital market line and the role of the risk-free asset.
- Describe the practical weaknesses of mean-variance optimisation.
Syllabus, module by module
Return and risk
Expected return, variance and covariance for single assets and portfolios.
Diversification
How correlation reduces portfolio risk, and the limit set by common risk.
The efficient frontier
Mean-variance optimisation, the minimum variance portfolio and the frontier.
Adding a risk-free asset
The tangency portfolio, the capital market line and the Sharpe ratio.
Constraints
Long-only, position limits and their effect on the frontier.
Limits of the theory
Estimation error, unstable weights and the bridge to robust portfolio optimisation.
How the certificate is earned
Quizzes at the end of each unit and one graded problem set in which you build an efficient frontier for a set of assets and interpret it. On a pass you receive the Course certificate in Modern Portfolio Theory, issued by the Institute with a verification code. Read how certification works.
Before you start
Basic statistics and matrix notation. Working Python is helpful.
This course counts toward
- Certificate in Systematic InvestingSix courses and a capstone on rule-based investing over months and years: asset pricing, trend following, factors and the portfolio construction that holds them together.
- Certificate in Quantitative Portfolio ManagementSix courses and a capstone on building portfolios with numbers: mean-variance and its failures, robust optimisation, Black-Litterman views, factors, attribution and risk.
Questions applicants ask
What is modern portfolio theory?
The framework Harry Markowitz published in 1952 for choosing portfolios by their expected return and variance. Its central result is that combining assets that are not perfectly correlated reduces risk, so portfolios should be judged as a whole, not asset by asset.
Is modern portfolio theory still used?
Its concepts, diversification, the efficient frontier and the Sharpe ratio, are used throughout the industry. Its direct use for setting weights is limited by estimation error, which the course explains and which Portfolio Optimization addresses.