Modern Portfolio Theory and the CAPM

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 optimizer 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.

What does beta measure?

The capital asset pricing model, developed in the early 1960s by William Sharpe, John Lintner and Jan Mossin, says that investors are paid for bearing market risk and nothing else. It gave finance the idea of beta, and it remains the starting point for almost every later model of expected returns.

Beta measures how much a stock’s return moves with the return of the market as a whole. A beta of 1.5 means the stock has tended to rise or fall one and a half times as much as the market. In the CAPM, only this market-related risk earns a premium, because other risk can be removed by holding many stocks.

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.

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 optimization.
• State the CAPM, its assumptions and the meaning of beta.

Syllabus, module by module

1. Return and risk

   Expected return, variance and covariance for single assets and portfolios.

2. Diversification

   How correlation reduces portfolio risk, and the limit set by common risk.

3. The efficient frontier

   Mean-variance optimization, the minimum variance portfolio and the frontier.

4. Risk and return

   Expected return, variance, diversification and the risk that cannot be diversified away.

What every course contains

Every paid course comes with the first seven and the certificate, whichever level it sits at. The proctored exam and the credential come when the course is taken as part of a Certificate, Diploma or Fellowship. Everything is self-paced: the material is yours to study in any order, at any hour, for the whole of the license.

1. Workbooks. Written to train the thinking patterns and the important concepts of the course, with worked problems and the reasoning behind each answer, so that you learn to think the way the subject is thought.
2. Audio edition. Focused, well-presented recordings with explainers and examples of the material, made to be interesting, relevant and entertaining, so that the general subject can be learned away from the desk.
3. Notes. Pre-produced notes with every fact the course relies on, written out in full, so that nothing has to be transcribed from the films or the audio.
4. Cheat sheet. One sheet with every important learning concept of the course on it, to keep beside you during the work and to revise from before the exam.
5. Named sources. Every fact in the notes names its source, the paper, the book or the dataset, for anyone who wants to dig in further.
6. Explainer films. Focused films, in the style of the sample films on the catalog page, that walk through the most difficult concepts of the course with visual explanations of a high standard.
7. Transcript. A full transcript of every film and every audio recording, searchable and quotable.
8. Proctored exam. Taken as part of a Certificate, Diploma or Fellowship, the course ends in a proctored multiple-choice questionnaire, with a pass mark of 60% and three retakes included. A course taken on its own is assessed by its coursework and has no exam.
9. Verifiable certificate. A certificate of completion that a third party can verify: an employer sends the code on it to the credentials office and receives written confirmation of the course, the date and the result.
10. Credential of the program. The Certificate, Diploma or Fellowship of the program, track or path the course belongs to, awarded when every course in it is passed. Which one depends on the program you choose.

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 and the CAPM, issued by the Institute with a verification code. A course taken as part of a Certificate, Diploma or Fellowship ends in a proctored online exam with a pass mark of 60%. The fee includes three retakes; each attempt after that carries a reduced proctored exam fee. A course taken on its own is assessed by its coursework and has no exam. Read how certification works.

Before you start

This course assumes the material of the courses below, or the same knowledge gained elsewhere.

• Probability for Quantitative Finance, with Statistics