Pair Trading: a two-horse bet

Pair trading is a very popular strategy in quant finance. This is a simple form of statistical arbitrage that relies on there being some link, on average, between the prices of certain stocks. Of course, this assumes that markets are not efficient.

The basic idea

Pair trading involves buying one stock and selling (going short) another stock. Essentially this is a bet on one stock vs another stock. For simplicity, suppose we buy one share of X and sell one share of Y at the same price, so we have a net position of zero. At any point in time our profit is X – Y. So we are hoping that the gap between X and Y share prices will increase. Note that it does not actually matter if the market falls or goes up. Both X and Y can go down and we will still make money if Y goes down more. Conversely both X and Y can go up and we can lose money if Y goes up more. We need some means of deciding on two stocks to trade, a means of predicting in what direction they will move relative to each other and also some means of deciding when to exit the trade.

Pair traders often search for pairs of stocks that tend to move together. Say we find that when stock X goes up, stock Y tends to go up as well. That is they are positively correlated. The basic assumption behind pair trading is that if this relationship should break down temporarily, say stock Y tumbles a bit and X is not affected, the market will move in such a way as to restore the relationship. This is one form of mean reversion. If there is some long-term average spread between the prices of stocks X any Y we would expect any deviation from it to be only temporary. That is, we would expect stock Y to go up (relative to X) in order to restore the balance. So we would go long (that is, buy) Y and short (that is, sell) X. When the spread has returned to its average level we can end the trade.

The two companies traded are often in the same sector, say they are both widget makers. Companies in the same sector tend to experience the same risk factors and react to the same news and so their shares are correlated. Of course we do not only need to look for some average spread. If one has reason to believe that, say, Ford will outperform General Motors (because it more innovative, perhaps), one can short General Motors and go long Ford.

Market neutral

Pair trading is one of a class of strategies called market neutral. This means that it (should) make profits (or losses) that are uncorrelated with the market. This means it should be able to make profits (or losses) whether the market goes up or down. In the Ford/GM example, it does not matter how the car industry performs (both shares can do terribly or extremely well) or even the market as a whole. All that matters is whether you were right that Ford would outperform GM.
This can be contrasted with another common, non-quant strategy, of buying an index fund, which mimics the market. This strategy is 100% correlated with the market. Whatever the market return, that is what you get.

Pros

• Risk is reduced by reducing dependence on market movements. Profit can be made in any market conditions, even where the market or the sector you are looking at crashes.
• The strategy is self-funding. In principle, the short trade can be used to finance the long trade.
• There is lots of data available for finding pairs to trade and this can (and is) done algorithmically.

Cons

• Of course, there is a risk that your bet is wrong. Essentially, you have exchanged market or sector risk for a new risk. If the securities move in the opposite direction (relative to each other) to that you assumed you will lose money.
• In a trending market you will always lose money on one half of your trade. If you trade two technology stocks, say, and technology has a good period, both stocks may go up substantially, whereas the spread between them may remain small. You could have made more money by buying both stocks, or just one. However, now you lose money on the stock that you shorted.
• In the above cases and where deviations from long-term spreads are not very large, the strategy will only result in moderate profits (if any).
• If you analyse enough data, you WILL find a pair of correlated stocks. This correlation may be spurious (that is, illusory). Correlations and spreads between stocks change. Using the past to predict the future is always a risky business.
• In a small market, there may not be enough truly correlated stocks for pair trading to be a strategy worth pouring much capital into. Notably, in South Africa only the top 40 stocks are usually considered by large funds.

Pair trading that went wrong

A notable pair trader was the fund LTCM, back in the 90’s. The petrol company Royal Dutch Shell had shares listed on two exchanges. One set of shares was for Shell, the other for Royal Dutch. However, Royal Dutch traded at a nearly ten percent premium to Shell. This is strange because these represent identical claims on the same company – common sense dictates they should have the same price. LTCM assumed the premium would disappear: they sold Royal Dutch and bought Shell.

All LTCM had to do was wait for the prices to converge. Unfortunately, that is exactly what it could not do. The premium widened to 22% in a short period. LTCM was forced to close its positions because of lack of liquidity in its other operations. It lost more than $100 million dollars on this trade alone.

Some references

Pair trading

• Goodby, D. (2008). A Basic Introduction to Pairs Trading. TradingMarkets.com. Retrieved from http://www.tradingmarkets.com/.site/stocks/how_to/articles/-76543.cfm
• Investopedia. (2011). Pairs trade. Investopedia. Retrieved from http://www.investopedia.com/terms/p/pairstrade.asp#axzz1Zkm97SeJ
• Junge, C. (2011). A simple pair trading example. www.christoph-junge.de. Retrieved from http://www.christoph-junge.de/pairstrading.php
• Preston, T. (2005, November). Pairs Trading. Traders Mag, 40 - 44. Retrieved from http://www.google.nl/url?sa=t&source=web&cd=1&ved=0CBwQFjAA&url=http%3A%2F%2Fmediaserver.thinkorswim.com%2Farticles%2FTPPairsTradingArticle.pdf&ei=ZMqSTsj_Ds3sOf6mzKgO&usg=AFQjCNET8DDNLyk7rI_RTsymC5opuBvbng&sig2=OsjJCEKVGDyDJEgAdj2QUQ
• Skiena, S. (2008). Lecture 23: Pairs Trading. Retrieved from http://www.cs.sunysb.edu/~skiena/691/lectures/lecture23.pdf
• Stone, C. (2011). The Secret to Finding Profit in Pairs Trading. Investopedia. Retrieved from http://www.investopedia.com/articles/trading/04/090804.asp#axzz1Zkm97SeJ
• The Hedge Fund Guide. (2011). Pair trading. www.thehedgefundguide.com. Retrieved from http://www.thehedgefundguide.com/pairstrading.html
• Wikipedia. (2011). Pairs trade. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Pairs_trade

LTCM

• Wikipedia. (2011). Dual-listed company. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Dual-listed_company
• Wikipedia. (2011). Long-Term Capital Management. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/LTCM