Researcher course in statistical arbitrage
Cointegration Models for Spread Trading
The econometrics behind spread trading: unit roots, Engle-Granger and Johansen cointegration tests, vector error correction models, baskets of more than two assets, and optimal entry and exit for an Ornstein-Uhlenbeck spread.
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.
How do you test whether assets are cointegrated?
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.
How should you trade a cointegrated spread?
If the spread behaves like an Ornstein-Uhlenbeck process, you can work out the expected time for it to return to its mean and choose entry and exit levels that maximise expected profit after costs. You will derive those levels, compare them with the common two-standard-deviation rule, and test both.
Who is this course for?
Researchers and quant traders who want the econometric foundations of relative-value trading. It counts toward the Certificate in Statistical Arbitrage and the Fellowship in Computational Finance.
What you will be able to do
- Test for unit roots and cointegration and interpret the results correctly.
- Apply the Johansen procedure to find cointegrating vectors among several assets.
- Estimate and interpret a vector error correction model.
- Derive trading thresholds for an Ornstein-Uhlenbeck spread.
- Assess the stability of a cointegrating relationship over time.
Syllabus, module by module
Unit roots
Random walks, spurious regression and the Dickey-Fuller and KPSS tests.
Engle-Granger
The two-step method, its critical values and its weaknesses.
Johansen
Trace and maximum eigenvalue tests, cointegrating rank and normalisation.
Error correction
Vector error correction models, adjustment speeds and which asset does the correcting.
Baskets and portfolios
Spreads of more than two assets, sparse cointegrating portfolios and stability.
Optimal spread trading
The Ornstein-Uhlenbeck spread, first-passage times and optimal entry and exit with costs.
Assessment preparation
Supervised work on the written assessment.
How the certificate is earned
A written paper-style assessment: you test a set of assets for cointegration, build and trade a spread, and write up the method, the derivation of your trading rule and the results. On a pass you receive the Course certificate in Cointegration Models, issued by the Institute with a verification code. Read how certification works.
Before you start
Time series to the level of ARMA models and unit roots, linear algebra, and the material of Pairs Trading and Mean Reversion.
This course counts toward
- Certificate in Statistical ArbitrageFive courses and a capstone on market-neutral trading: time series foundations, pairs and baskets, cointegration and the validation that keeps spread strategies honest.
- Fellowship in Computational FinanceThe top credential on the researcher path. Nine courses, eight of them at researcher level, and a supervised dissertation, examined by two faculty members.
Questions applicants ask
What is cointegration in simple terms?
Two or more prices are cointegrated when each wanders like a random walk but some combination of them stays stable. That stable combination is the spread a trader can bet will return to its average.
What is the difference between the Engle-Granger and Johansen tests?
Engle-Granger tests one relationship between two series using a regression and a unit-root test on its residuals. Johansen tests a system of several series at once and can find more than one cointegrating relationship.
Why is this a researcher-level course?
The assessment asks you to derive and justify a trading rule, not only to run tests. That needs the econometrics and the stochastic process material, written up as a paper.