Statistical Arbitrage, Pairs Trading and Cointegration

Statistical arbitrage trades relationships rather than direction. When two or more instruments that usually move together drift apart, a stat arb strategy sells the expensive side, buys the cheap side, and waits for the gap to close. The method is old, crowded and still widely used, and the difference between a strategy that works and one that does not usually lies in the details this course covers.

How does a statistical arbitrage strategy make money?

It takes many small, market-neutral bets that a spread will revert towards its usual level. Each bet has a modest edge. The return comes from running many of them at once, so that the noise in individual spreads averages out while the edge adds up. Market and sector exposure are hedged away, so the result should depend little on whether the market rises or falls.

Why do so many stat arb backtests fail live?

Three reasons recur. Costs, including borrowing fees for the short side, are larger than assumed. Relationships that held in the sample break when regimes change. And the universe used in the test often contains only the stocks that survived. The course builds a test that addresses all three before any result is trusted.

How do you choose a pair to trade?

Pairs trading is the simplest market-neutral strategy and the usual starting point for statistical arbitrage. Two related instruments, a long position in one and a short position in the other, and a rule for when the gap between them is wide enough to trade. The idea fits in a sentence; doing it carefully takes a course.

Start from an economic reason the two prices should move together, such as two companies in the same business or two share classes of one firm. Then test whether the spread between them is stable. Searching thousands of pairs for the best statistical fit finds pairs that fitted the past by chance, so the course treats pair selection as a multiple-testing problem.

How do you test whether assets are cointegrated?

Cointegration is the statistical idea that makes spread trading possible. Prices on their own drift without a fixed level, but some combinations of them do not, and a combination that returns to its average is something you can trade. The course covers the econometrics properly and connects it to the trading decisions it supports.

For two assets, the Engle-Granger method regresses one price on the other and tests whether the residual is stationary. For several assets, the Johansen procedure estimates how many independent stable combinations exist and what they are. Both have known weaknesses, including sensitivity to the sample and to which variable is put first, and the course covers them.

Who is this course for?

Quant traders and researchers who want a working method for relative-value strategies.

What you will be able to do

• Explain what makes a spread mean-revert and how to test for it.
• Build residual signals from a factor model and trade them market-neutral.
• Design entry, exit and sizing rules for a portfolio of spreads.
• Estimate the effect of costs, borrowing and capacity on a stat arb strategy.
• Screen a universe for candidate pairs and explain the risk of data snooping.
• Test for unit roots and cointegration and interpret the results correctly.

Syllabus, module by module

1. What statistical arbitrage is

   Relative value, market neutrality and the difference between statistical and pure arbitrage.

2. Mean reversion

   Stationarity, the Ornstein-Uhlenbeck process and estimating the speed of reversion.

3. From pairs to portfolios

   Distance, correlation and cointegration approaches, and why single pairs are fragile.

4. Residual signals

   Removing market, sector and factor exposure, and trading what is left.

5. The pairs trade

   Origins, the logic of relative value, and what a pair has to have in common.

6. Unit roots

   Random walks, spurious regression and the Dickey-Fuller and KPSS tests.

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.

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. Transcript. A full transcript of every film and every audio recording, searchable and quotable.
8. 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.
9. 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.
10. 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 a market-neutral statistical arbitrage strategy on a universe of your choice, test it out of sample with costs, and submit the code with a report. On a pass you receive the Course certificate in Statistical Arbitrage, Pairs Trading and Cointegration, 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

Working Python with pandas, regression, and the material of Time Series Analysis and Financial Econometrics and Backtesting: Methods, Pitfalls and Validation.

• Time Series Analysis and Financial Econometrics
• Backtesting: Methods, Pitfalls and Validation