Researcher course in risk management
Expected Shortfall and CVaR
The risk measure that replaced VaR in bank trading-book rules: coherence and subadditivity, estimating expected shortfall with historical, parametric and extreme value methods, the elicitability debate and backtesting, and minimising CVaR in portfolios.
Value at risk tells you the loss you should exceed only rarely, but not how much you lose when you do. Expected shortfall, also called conditional value at risk or CVaR, answers that question: the average loss beyond the VaR level. It has better mathematical properties, and bank regulators adopted it for market risk capital under the Fundamental Review of the Trading Book.
Why is expected shortfall a better risk measure than VaR?
Because it is coherent. In particular, it is subadditive: the risk of a combined portfolio is never greater than the sum of the parts, so it never penalises diversification. VaR can break that rule, and it can be lowered by hiding risk in the tail. The course proves both properties and shows examples where they matter.
Is expected shortfall harder to backtest?
Yes. Expected shortfall lacks a property called elicitability, which makes direct comparison of forecasts with outcomes harder than for VaR. Researchers have since developed workable tests, including the methods of Acerbi and Szekely and joint tests with VaR. You will apply one of them to your own estimates.
Who is this course for?
Risk researchers, quants and senior risk analysts who need the theory behind current market risk measures. It counts toward the Certificate in Quantitative Risk Management.
What you will be able to do
- State the axioms of coherent risk measures and show where VaR fails them.
- Estimate expected shortfall with historical, parametric and EVT methods.
- Fit a generalised Pareto distribution to tail losses.
- Explain the elicitability problem and apply an ES backtest.
- Formulate and solve CVaR minimisation as a linear program.
Syllabus, module by module
Coherent risk measures
The Artzner, Delbaen, Eber and Heath axioms, subadditivity and VaR's failure of it.
Expected shortfall
Definitions, CVaR and tail conditional expectation, and their properties.
Estimation
Historical, parametric and filtered methods, and estimation error in the tail.
Extreme value theory
Peaks over threshold, the generalised Pareto distribution and threshold choice.
Backtesting expected shortfall
Elicitability, joint VaR and ES tests, and the Acerbi-Szekely approach.
CVaR optimisation
The Rockafellar-Uryasev linear program and portfolio applications.
Assessment preparation
Supervised work on the written assessment.
How the certificate is earned
A written paper-style assessment: you estimate and backtest expected shortfall for a portfolio with at least two methods, solve a CVaR-optimal allocation, and write up the derivations and results. On a pass you receive the Course certificate in Expected Shortfall and CVaR, issued by the Institute with a verification code. Read how certification works.
Before you start
Probability to the level of distributions and quantiles, optimisation to the level of linear programs, and the material of Value at Risk.
This course counts toward
Questions applicants ask
What is the difference between VaR and expected shortfall?
VaR is the loss level exceeded with a given probability. Expected shortfall is the average loss in the cases where that level is exceeded. Expected shortfall therefore reflects how bad the tail is, which VaR ignores.
Is CVaR the same as expected shortfall?
For continuous loss distributions they coincide, and the names are often used interchangeably. They can differ for discrete distributions, and the course shows the definitions that keep the measure coherent in all cases.
Why did regulators move from VaR to expected shortfall?
The Basel Committee’s Fundamental Review of the Trading Book replaced 99% VaR with 97.5% expected shortfall for market risk capital, mainly because expected shortfall captures tail risk that VaR does not.