Practitioner course in portfolio management
Portfolio Optimization
Portfolio construction that survives real data: estimating covariance with shrinkage, constrained and robust optimisation, risk budgeting and risk parity, hierarchical risk parity, and the costs of rebalancing.
Portfolio optimization in textbooks takes expected returns and covariances as given. In practice they are estimated from noisy data, and an optimiser 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 optimisation 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 optimiser 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.
Who is this course for?
Portfolio managers, quant analysts and allocators who build or review portfolios. It counts toward the Certificate in Quantitative Portfolio Management.
What you will be able to do
- Estimate covariance matrices with shrinkage and factor models.
- Solve constrained portfolio problems with a convex optimiser.
- Build risk parity and risk budget portfolios.
- Implement hierarchical risk parity and compare it with mean-variance.
- Include transaction costs and turnover limits in rebalancing.
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 optimisation
Convex problems, cvxpy, budgets, bounds, sector and tracking error limits.
Robust approaches
Resampling, uncertainty sets and regularised weights.
Risk budgeting
Risk contributions, equal risk contribution and risk parity.
Hierarchical risk parity
Clustering, quasi-diagonalisation and recursive bisection.
Rebalancing
Costs, turnover penalties and no-trade bands.
Project lab
Supervised work on the assessed portfolio project.
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, issued by the Institute with a verification code. Read how certification works.
Before you start
Working Python, linear algebra to matrix level, and the material of Modern Portfolio Theory.
This course counts toward
Questions applicants ask
Which portfolio optimisation 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 optimisation. All code is written in the course rather than taken from a black-box library.