Comparing Cointegration and Statistical Arbitrage for Pairs Trading
Summary
The discussion compares a price-based pairs trading framework with the statistical arbitrage approach described by Avellaneda and Lee. In the former, log prices are related through a fitted spread, cointegration tests such as Johansen's can identify candidate pairs, and an error correction model can inform entry and exit decisions. In the latter, returns are regressed on risk factors or security baskets, and cumulative residuals are modeled as mean reverting with an Ornstein–Uhlenbeck process.
The answer emphasizes that the approaches differ in scope: a conventional pair uses two price series, whereas the statistical arbitrage approach can use factors or baskets. It also notes that the latter does not explicitly test cointegration strength, since mean reversion is imposed through the residual process. The account is a conceptual comparison rather than an empirical evaluation; it offers no evidence that either method is more stable or effective intraday, which was the questioner's concern.
Key ideas
- Traditional pairs trading often relates log prices and uses cointegration to identify candidate spreads.
- Error correction models can help define entry and exit behavior for cointegrated pairs.
- The Avellaneda–Lee approach regresses returns on factors or baskets and models cumulative residuals as mean reverting.
- Statistical arbitrage can extend beyond pairs, while its mean-reversion assumption is built into the model rather than tested as cointegration strength.
- The discussion provides no comparative performance or intraday stability evidence.
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# How do different methods and techniques used in pairs trading compare?
# How do different methods and techniques used in pairs trading compare?
I was going through the paper of Avellaneda (2008) on stat arb and I found it interesting that he uses asset returns vs. their respective ETFs to compute the s-score.
I am wondering if anyone has tried this approach to pairs trading. How does it compare to Johansen's method, where the actual price series is used?
I can't imagine this approach being stable if trying to trade intraday, due to all these return computations.
I haven't tried either method so I would appreciate some feedback on your experience.
## Answer by Felix (score 4)
https://quant.stackexchange.com/a/9800
Both models are based on a spread, which has to be as stationary / mean reverting as possible.
$ y_t = \beta_0 + \beta_1 x_t + \epsilon_t $
In pairs trading, $y_t$ and $x_t$ are log prices, and (e.g.) the Johansen cointegration test is used to identify candidates for a pairs trade. For entry and exit points an error correction model is used. In the Avellaneda & Lee (AL) paper the $y_t$ and $x_t$ are indeed the returns. Mean reversion is modeled as an Ornstein-Uhlenbeck process on the cumulated residuals
$ X_k = \sum_{t=1}^k \epsilon_t,\ \ k = 1,2,...,T$
which are stationary (mean zero) by construction. Since the residuals are cumulated or 'integrated' they are stable and may display mean reversion, much like in traditional pairs trading.
I see two important differences: the AL method is (as the title says) a statistical arbitrage approach where $x_t$ are risk factors or baskets of securities, such as the PCA and ETF examples in the paper: it is not limited to pairs. Also, in AL there is no explicit test of the cointegration strength, as the mean reversion is built into the model.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.