Practitioner course in portfolio management
Portfolio Optimization, Risk Parity and Black-Litterman
Portfolio construction that survives real data: estimating covariance with shrinkage, constrained and robust optimization, risk budgeting and risk parity, hierarchical risk parity, and the costs of rebalancing. It also teaches asset allocation and risk parity and the Black-Litterman model.
Portfolio optimization in textbooks takes expected returns and covariances as given. In practice they are estimated from noisy data, and an optimizer fed noisy inputs produces confident, extreme and unstable portfolios. This course is about building portfolios that hold up when the inputs are wrong, which they always are.
How do you make portfolio optimization more robust?
By improving the inputs and constraining the outputs. Shrinkage pulls an unstable covariance estimate towards a simpler structure. Constraints and penalties stop the optimizer from betting heavily on small differences. Methods such as risk parity avoid expected-return estimates altogether. You will implement each and compare them out of sample.
What is risk parity?
A way of setting weights so that each asset or asset class contributes the same share of portfolio risk, rather than the same share of capital. Because bonds are usually less volatile than equities, a risk parity portfolio holds more of them than a traditional mix does, and is often leveraged to reach a target return.
Why budget risk instead of capital?
Asset allocation decides most of what a portfolio earns and how far it falls. The choice between shares, bonds, commodities and cash, and how much risk each is allowed to carry, matters more than the pick of any single security. This course teaches the methods pension funds, endowments and multi-asset desks use, including risk parity.
Because a portfolio that is 60% shares by money is close to 90% shares by risk. Budgeting risk shows where losses will come from before they happen, and lets an investor spread them deliberately. Risk parity is the simplest form of that idea, and the course builds it from first principles.
How does Black-Litterman combine views with the market?
Fischer Black and Robert Litterman developed the Black-Litterman model at Goldman Sachs because mean-variance optimization, 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.
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.
Who is this course for?
Portfolio managers, quant analysts and allocators who build or review portfolios.
What you will be able to do
- Estimate covariance matrices with shrinkage and factor models.
- Solve constrained portfolio problems with a convex optimizer.
- Build risk parity and risk budget portfolios.
- Implement hierarchical risk parity and compare it with mean-variance.
- Build a strategic asset allocation from long-run return, risk and correlation assumptions.
- Derive implied equilibrium returns by reverse optimization.
Syllabus, module by module
The estimation problem
Why sample means and covariances make poor inputs, with numerical examples.
Covariance estimation
Ledoit-Wolf shrinkage, factor models and exponential weighting.
Constrained optimization
Convex problems, cvxpy, budgets, bounds, sector and tracking error limits.
Robust approaches
Resampling, uncertainty sets and regularized weights.
The strategic mix
Capital market assumptions, the policy portfolio and why allocation drives most of the return.
The problem it solves
Extreme mean-variance weights and the need for a neutral starting point.
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Transcript. A full transcript of every film and every audio recording, searchable and quotable.
- 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.
- 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.
- 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
An assessed project: you build three portfolio construction methods, compare them out of sample with costs on a multi-asset universe, and submit the code with a report. On a pass you receive the Course certificate in Portfolio Optimization, Risk Parity and Black-Litterman, 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.
This course counts toward
- Certificate in Systematic InvestingSeven courses and a capstone on rule-based investing over months and years: asset pricing, trend, factors, carry, allocation and the portfolio construction and risk control that hold them together.
- Certificate in Quantitative Portfolio ManagementSeven courses and a capstone on building portfolios with numbers: mean-variance and its failures, robust optimization, Black-Litterman views, factors, asset allocation, bonds, attribution and risk.
- Professional Diploma in Algorithmic TradingThe top credential on the practitioner path. Twenty-one courses and an 80-hour capstone covering everything between the mathematics and a book you could defend to a risk committee.
Questions applicants ask
Which portfolio optimization method is best?
No method wins in all conditions. Out-of-sample studies often find that simple methods, including equal weights, are hard to beat once estimation error is counted. The course compares methods on the same data so you can see when each helps.
What software does the course use?
Python with numpy, pandas and cvxpy for convex optimization. All code is written in the course rather than taken from a black-box library.
What is risk parity?
Risk parity sets the weights so that each asset class contributes the same share of the portfolio’s risk. Because bonds are less volatile than shares, it holds more bonds, and it often uses leverage to reach a target return.
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.