Pairs trading: basic concepts and examples

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Identify 1SD moves in pairs trading.
Identify 1SD moves in pairs trading.

What is pairs trading

Pairs trading is a trading strategy that aims to minimize risk by buying one instrument and simultaneously selling another instrument.

Forex (FX) traders know this concept all too well, or at least they apply the concept of pairs trading without knowing it. In FX trading, one currency is always bought or sold against another. The currency that was bought is expected to gain more or lose less than the second currency that it is held against.

Pairs trading can also be performed with equities, wherein one stock is bought (longed) and another one is sold (shorted) with the expectation that the bought stock will appreciate faster in value or that the bought stock will depreciate slower in value as compared to the stock held in short.

Correlation Tool for Pairs Trading
Correlation Tool for Pairs Trading

Basic approaches in pairs trading

  • The initial and absolute monetary value of both the members of the pairs should be the same

This allows for a clean baseline. Each instrument should be bought/sold with the same absolute monetary value so that the net amount to be paid is zero or very close to it.

To give an example: A stock with a value of $50 is to be long. The pair to be shorted has a value of $100. Depending on the trade size, the minimum shares to be bought is 2 (2 shares x $50 = $100 long) for instrument one, and 1 share to be sold for instrument two (1 share x $100 = $100 short).

  • A strong positive correlation exists

This will simply remove the noises that can be caused by economic or industry factors.  Instruments within the same industry are usually affected the same way, with the difference of: the stronger company will benefit more or lose less, depending on the factors.

We express correlation using correlation coefficient (r, rho).

  • Same industry

See explanation above. In addition: equities can be compared to their index. In the case of currency trading, we compare an entire economy with another.

  • Existing correlation deviation

Pairs moving in a positive correlation sometimes move outside of their relationship to each other. This can happen if one of the equities experiences sudden price fluctuations due to factors specific to that instrument only. However, instruments with existing strong correlation tend to normalize again. Such a condition is correlation deviation and if it is strong enough, let’s say a standard one deviation move, is often used by pairs traders to enter or exit a pairs trading position. The deviation analysis can be applied on the price quotient (price of instrument one divided by the price of instrument two).

Correlation Tool for Pairs Trading
Correlation Tool for Pairs Trading

How to understand correlation coefficient

The following correlation values can be interpreted as follows.

  • Exactly –1. A perfect negative linear relationship
  • 70. A strong negative linear relationship
  • 50. A moderate negative relationship
  • 30. A weak negative linear relationship
  • No linear relationship
  • +0.30. A weak positive linear relationship
  • +0.50. A moderate positive relationship
  • +0.70. A strong positive linear relationship
  • Exactly +1. A perfect positive linear relationship

Thus, a correlation coefficient of 0.70 and above is a good starting point to look for pairs trading and breakouts (deviations). I personally go for 0.80 and above.

How to compute for correlation coefficient and standard deviation

For one, excel has a great feature for this. Lastly, for those wh0 would want to integrate this within a program or algorithmic trading robot, here are the important formulas.

  1. Using Pearson’s correlation coefficient formula:

2. Compute for standard deviation

Some personal thoughts

We never open a position without it being hedged in some form or another. Pairs trading, Credit Spreads and Delta Hedges have become one of the few tools we use to always be engaged yet minimize risk.

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