Correlation and Pair Trading

TL;DR: Correlation shows how two investments move relative to each other. You use it to spread your risk. Pair trading uses the same idea to bet that two related stocks will return to each other after an outlier. It is a difficult strategy with its own risks and is not for beginners.

Step-by-step guide

1. Collect the daily closing prices of two investments over at least 60 days.
2. Convert the prices into daily percentage changes.
3. Calculate the correlation with the spreadsheet function CORREL.
4. Read the result: close to +1 means they move almost together, close to 0 means little link and close to -1 means opposite moves.
5. Calculate the correlation again over a different period to see whether the link is stable.
6. Use the result when spreading your portfolio.
7. To understand pair trading, follow the price ratio of two related stocks and work out its average and standard deviation.
8. Practise on a demo account only, and decide in advance when you will close the trade, even if the link breaks.

What is correlation?

Correlation is a number between -1 and +1 that shows how two things move together.

• +1: they always move in the same direction
• Around +0.8: they usually move in the same direction
• 0: there is no clear link
• Around -0.8: they usually move in opposite directions
• -1: they always move in opposite directions

Two caveats. Correlation describes the past, not the future. And a high correlation does not mean one stock causes the other.

Worked example

Suppose you track the daily price change (in %) of two stocks over 6 trading days:

• Stock A: +1.0 / -0.5 / +2.0 / -1.0 / +1.5 / +0.5
• Stock B: +0.8 / -0.2 / +1.6 / -1.2 / +1.0 / +0.6

Work out the correlation and it comes to about 0.97. On these days the two stocks move almost together. Six days is of course too few to conclude anything. In practice use many more observations and see how the number changes when you shift the period.

Correlation changes over time

The number is not a fixed property. In calm times two investments can have little to do with each other, while in a crisis they often fall together. A portfolio that looks diversified on paper can then be much less protected than you thought. So recalculate correlations regularly, for example over the last 60 days, and do not count on a fixed result.

Using correlation to spread risk

Choosing investments that do not all fall at the same time gives a smoother ride. This is called diversification. A few examples of the thinking behind it:

• Two stocks from the same sector often have a high correlation. Buying both spreads the risk very little.
• Stocks and bonds had little or negative correlation in some periods. In other periods they fell together. So there is no fixed rule.
• Investments in different regions and sectors can reduce risk, but never remove it completely.

Do you want to actively protect against price falls (hedging)? That often involves derivatives such as options, which are complex. First read Options: the Basics and the guide to hedging.

Pair trading: an explanation

Pair trading looks at two related stocks that usually move together, for example two companies in the same sector. The idea: when the ratio between their prices becomes unusually large, it may return to its average. You are then not betting on the direction of the market, but on the ratio between the two stocks.

Worked example in euros

Suppose stock X costs €60 and stock Y costs €51. The ratio Y/X is then 51 / 60 = 0.85. Recent prices show this ratio averaged 0.75, with a standard deviation of 0.05. The z-score is then (0.85 - 0.75) / 0.05 = 2.0. The ratio is unusually high: Y is expensive relative to X.

A pair trader might now reason: sell Y (go short) and buy X, expecting the ratio to return to 0.75. But that does not always happen:

• If the ratio keeps rising to 0.95, your loss keeps growing.
• If something has really changed, for example poor results at X or a takeover at Y, the ratio stays high or rises further.
• Going short brings extra costs and extra risk. In theory the loss on a short position is unlimited.

Where pair trading can go wrong

• The link breaks: the reason the two stocks moved together has gone.
• Costs and interest: two positions mean two sets of costs, plus possible interest on the short position.
• Hard to carry out: not every broker offers short selling, and it often costs extra. Brokers may ask whether you have enough knowledge and experience for these products.
• Too much trust in the past: a ratio that often returned does not always do so.

So pair trading is not a guaranteed or ‘risk-free’ strategy. Test your rules first with a backtest and decide in advance, using the position size calculator, how much you are willing to lose at most.

Calculating and tracking correlation

1. Download daily closing prices from a free source or from your broker.
2. Put them in a spreadsheet and calculate the daily changes in percent.
3. Use CORREL over the last 60 days and watch how the number changes over time.
4. Some charting platforms also have a correlation indicator. Check what is available in yours.

Trading involves risk: you can lose all or part of your money, and with short positions even more than your deposit. Past performance is no guarantee of future results. This tutorial is information, not investment advice.