Researcher course in portfolio management
The Black-Litterman Model
The Black-Litterman model in full: reverse optimisation to implied equilibrium returns, expressing views, the Bayesian combination and its derivation, the choice of tau and the view uncertainty matrix, and extensions to views on factors.
Fischer Black and Robert Litterman developed the Black-Litterman model at Goldman Sachs because mean-variance optimisation, fed with an analyst’s return forecasts, produced portfolios no one would hold. Their answer was to start from the returns that the market’s own weights imply, then move away from them only as far as the investor’s views justify.
How does Black-Litterman combine views with the market?
It treats the market-implied returns as a prior and each view as a noisy observation. Bayes’ rule combines them, weighting each by its precision. A confident view moves the expected returns a lot; a vague one barely moves them. Assets without views keep returns close to equilibrium, so the portfolio stays close to market weights except where the views say otherwise.
Why is this a researcher-level course?
The assessment requires you to derive the posterior, not only to apply a formula, and to justify the choice of parameters that published papers set in different ways. That needs the linear algebra and Bayesian statistics, written up as a paper.
Who is this course for?
Portfolio managers, strategists and researchers who combine forecasts with portfolio construction. It counts toward the Certificate in Quantitative Portfolio Management and the Fellowship in Computational Finance.
What you will be able to do
- Derive implied equilibrium returns by reverse optimisation.
- Express absolute and relative views in matrix form.
- Derive the Black-Litterman posterior from Bayes' rule.
- Choose and justify tau and the view uncertainty matrix.
- Implement the model and test how views change the portfolio.
Syllabus, module by module
The problem it solves
Extreme mean-variance weights and the need for a neutral starting point.
Equilibrium returns
Reverse optimisation from market weights, risk aversion and the CAPM link.
Views
The pick matrix, absolute and relative views, and confidence.
The posterior
The Bayesian derivation, the mixed estimation interpretation and the master formula.
Parameters
Tau, omega, Idzorek's confidence method and their effect on weights.
Extensions
Views on factors, non-normal views and Meucci's generalisations in outline.
Assessment preparation
Supervised work on the written assessment.
How the certificate is earned
A written paper-style assessment: you derive the model, implement it on a multi-asset universe with views of your own, and write up the derivation, choices and results. On a pass you receive the Course certificate in the Black-Litterman Model, issued by the Institute with a verification code. Read how certification works.
Before you start
Linear algebra, Bayesian statistics to the level of normal-normal updating, and the material of Portfolio Optimization.
This course counts toward
- 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.
- Fellowship in Computational FinanceThe top credential on the researcher path. Nine courses, eight of them at researcher level, and a supervised dissertation, examined by two faculty members.
Questions applicants ask
What is the Black-Litterman model?
A method developed by Fischer Black and Robert Litterman at Goldman Sachs around 1990 for combining the returns implied by market weights with an investor’s own views, producing expected returns that give sensible, diversified portfolios.
What are tau and omega?
Tau scales the uncertainty in the equilibrium returns, and omega sets the uncertainty of each view. Together they decide how far the views move the portfolio away from market weights. Their choice is the most debated part of the model, and the course covers the main approaches.