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.

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    $\begingroup$ I would like to see the performance of that strategy between 2007 and 2008. It seems like the dataset stops at the right time for the strategy to show some decent results. Pairs trading is the basic buy cheap sell expensive strategy. That kind of strategy, just did not work the next year. In fact, the opposite was true. Buy expensive stock... and hold it. $\endgroup$ Dec 14, 2013 at 3:27

1 Answer 1


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.

  • $\begingroup$ thanks for the explanation, as far as you mentioned Ornstein-Uhlenbeck process, are you aware of some sites or other resources that could explain physical meaning and purpose of Ornstein-Uhlenbeck process for non-mathematicians? $\endgroup$
    – Anonymous
    Aug 16, 2014 at 9:38
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    $\begingroup$ @Art Ornstein-Uhlenbeck is a stochastic model for mean reversion: the drift term depends on the deviation from a long term mean value. There is a review by Attilio Meucci on the subject: papers.ssrn.com/sol3/papers.cfm?abstract_id=1404905 Another example is the Vasicek model for short term rates. $\endgroup$
    – Felix
    Aug 18, 2014 at 13:25

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