Page 24 – How to Play the Spread Using Unilateral Pairs Trading

Pairs trading usually means employing a  market neutral strategy on two highly correlated assets where you long one asset and short another, profiting as the spread between the two assets converge.  Although this strategy is market neutral, it is a very biased bet on the direction of the spread between those two assets.  For example, say GM and F are highly correlated and usually move together in lockstep, but then suddenly, GM moves down sharply without F moving down sharply.  A pairs trader would go long GM and short F, with the viewpoint that spread between the two stocks would converge to its historical norm.

Unilateral pairs trading is a slight variation in that we only trade the more volatile side of the pair.  The strategy assumes the more volatile side is most often the reason the correlation has temporarily broken down.  For example, the QQQ and SPY are highly correlated, but QQQ is obviously more volatile.

1. Calculate the ratio of the QQQ price over the SPY price.  For example, on May 1, 2003, QQQ was 27.42 and SPY was 91.92.  The ratio is 27.42/91.92 = 0.298
2. Calculate the 20-day moving average of the ratio.
3. Calculate the difference between the ratio and the ratio’s moving average.
4. Calculate the 20 day moving average of those differences.
5. For each day, calculate the standard deviation of the difference in ratios for that day and its moving average.  Calculate the standard deviation for each day using its prior 20 days.
6. For each day, if the standard deviation calculated is greater than 1.5 and QQQ is 2 percent greater than the prior day, then short QQQ.  i.e. QQQ has broken out irrationally and due to volatility.
7. For each day, if the standard deviation calculated is less than -1.5 and QQQ is 2 percent lower than the prior day, then buy QQQ.  i.e. QQQ has broken down irrationally and due to volatility.
8. Sell / Cover when the standard deviation of the difference in the ratios is less than 0.5 (in the case of a short) or greater than -0.5 (in the case of a long).

Example:
On May 19, 2003, QQQ fell 3.6 percent and SPY fell 2.3 percent.  This was more than 2 standard deviations away from the average difference between the ratio between the two assets and the 20-day moving average of that ratio.  Since on May 19, QQQ had fallen over 2 percent, we bought at the open the next day at 27.76 and held until the number of standard deviations between the ratio and its moving average went back above -0.5 standard deviations, which occurred on May 28, when we sold at 29.16 for a 5.04 percent profit.  We could apply this strategy not only to the QQQ and SPY, but to any two highly correlated stocks.

SPY - QQQ 05-19-2003

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