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Pairs Trading Strategy

In this study we explore a trading strategy that isolates pairs of instruments within a sector that are highly correlated. We enter a trade if the price paths of these instruments diverge, going long one instrument and short the other, with the assumption that their price paths will converge.

We construct our strategy in four parts: (1) isolate the target set of tradable instruments, (2) choose a rule for finding correlated pairs within that set, (3) pick criteria for entering trades, and (4) test the trading strategy.

Choosing the Target Set

We begin by selecting the sector to explore. In this example we choose the stocks in the S&P 500 that belong to the Financial sector.

Finding the Pairs in Our Group

For this study we want to isolate pairs of instruments whose correlation is above a certain threshold. At the beginning of each quarter, we restrict our target stocks to the top 5 in the sector by 252-day correlation to the S&P 500. Then our Strategy uses a metric that, for a given group of stocks, outputs a list of pairs with a correlation above our target threshold of .60 over the same time period.

Selecting and Testing the Criteria

Across every day and every pair in our trading list, we check the 21-day z-score (number of standard deviations from the mean) of the difference between the two series. We classify the stocks as diverging when the absolute value of the z-score is between 1.5 and 3.0. When this condition is met we short the stock that is rising and long the stock that is falling, sizing our position relative to the z-score and the number of pairs currently trading.

The results of our Strategy are shown below. We started with $1,000 NAV on May 19, 2008 and ended with $2,537 on May 18, 2009. Notably, of the 739 trades made in the past year there were 10 more winners than losers. We also achieved a Sharpe ratio of 2.69.

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We can test the Strategy’s sensitivity to different parameter values. In the image below, we vary the minimum correlation from .5 to .8, the z-score window from 10 to 22 days, and the minimum z-score from 1 to 2. The Strategy is successful throughout, producing Sharpe ratios ranging from 1.85 to 3.2.

The next step is to repeat the analysis for all the sectors in the S&P 500.  Using Chart, the breakdown of all the sectors is below:

Over the past year, the Financials (dark green) have performed the best, followed by Telecom (dark orange) and Industrials (light blue). The Materials sector (orange) recorded losses in excess of 40%. Aggregating the sectors together (bold green) shows an overall net profit of 30% over the past year. The statistics for the all sector portfolio are promising, with a Sharpe ratio of 3.25 and a maximum drawdown of 3.78% over 5,858 trades.

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From here there we could take our analysis in a number of directions, building on our initial work. We could specify additional criteria for entering trades; for example, we could require that volatility be within some range or average dispersion of the group be above a certain level.

Updated May 25, 2009

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