Practitioner course in risk management
Value at Risk, Expected Shortfall and Stress Testing
How value at risk is calculated, tested and misused: historical simulation, variance-covariance and Monte Carlo methods, volatility-weighted variants, time scaling, regulatory backtesting, and what VaR does not tell you. It also teaches expected shortfall, also called CVaR and stress testing and scenario design.
Value at risk compresses the risk of a portfolio into one number: a loss that should be exceeded only on a small share of days. Since the 1990s it has been used by banks, regulators and asset managers to set limits and capital. It is useful, easy to misread, and the subject of this course.
How is value at risk calculated?
There are three standard methods. Historical simulation applies past changes in market prices to today’s portfolio and reads off the loss at the chosen percentile. The parametric method assumes a distribution, usually normal, and uses volatilities and correlations. Monte Carlo simulates many possible scenarios from a model. You will implement all three on one portfolio and compare them.
How do you know if a VaR model is working?
By backtesting: counting how often actual losses exceeded VaR and testing whether the count, and the timing of those exceptions, is consistent with the model. Too many exceptions, or exceptions that cluster, mean the model is failing. The course covers the statistical tests and the regulatory traffic-light approach.
Why is expected shortfall a better risk measure than VaR?
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.
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 penalizes 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.
How do you design a good stress scenario?
Stress testing asks a direct question: what would this portfolio lose if a particular bad thing happened? Unlike value at risk, it does not depend on a model of how likely the event is. That makes it the main tool for thinking about losses beyond what recent data shows.
Start from a story with a cause, such as a sharp rise in rates or a credit event, and translate it into shocks to every relevant risk factor in a way that is internally consistent. Historical episodes give realistic patterns of co-movement; hypothetical scenarios cover events that have not happened yet. The course covers both and how to judge whether a scenario is severe enough.
Who is this course for?
Risk analysts, portfolio managers and traders who use or report VaR.
What you will be able to do
- Calculate VaR by historical simulation, the parametric method and Monte Carlo.
- Use volatility-weighted and filtered historical simulation.
- Backtest a VaR model with the Kupiec and Christoffersen tests.
- Aggregate VaR across positions and explain diversification effects.
- State the axioms of coherent risk measures and show where VaR fails them.
- Design historical and hypothetical stress scenarios for a portfolio.
Syllabus, module by module
What VaR measures
Definition, confidence level, horizon and the quantile of the loss distribution.
Parametric VaR
The variance-covariance method, delta-normal VaR and its assumptions.
Historical simulation
Plain, age-weighted and volatility-filtered historical VaR.
Coherent risk measures
The Artzner, Delbaen, Eber and Heath axioms, subadditivity and VaR's failure of it.
Why stress test
What VaR misses, and the role of stress tests in risk management and regulation.
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 and backtest three VaR models for a multi-asset portfolio over a period that includes a crisis, and submit the code with a report. On a pass you receive the Course certificate in Value at Risk, Expected Shortfall and Stress Testing, 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.
- Certificate in Quantitative Risk ManagementA financial risk management certification in six courses and a capstone on measuring and governing market and credit risk: VaR and expected shortfall, volatility models, stress tests, credit and counterparty risk, bank capital and the validation of the models themselves.
- 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.
- Fellowship in Computational FinanceThe top credential on the researcher path. Twenty-one courses and a dissertation supervised in writing and examined by two faculty members.
Questions applicants ask
What does a VaR figure mean?
A one-day 99% VaR of 1 million means that, if the model is right, losses should exceed 1 million on about one day in a hundred. It says nothing about how large losses are on those days.
Which VaR method is best?
Each method trades off assumptions against data needs. Historical simulation avoids a distribution assumption but depends on the window; parametric methods are fast but understate fat tails; Monte Carlo handles options but is costly. The course tests all three on the same portfolio.
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.
What is the difference between stress testing and VaR?
VaR estimates a loss level from a statistical model of normal variation. A stress test asks what happens under a specific severe scenario, whether or not the model thinks it likely. The two answer different questions and are used together.