Skip to content
All library documents

Why Cointegration Pairs Trading Often Uses Log Prices

Article Quant Q&A · Author: Rkl4397qa
Read the original

Summary

The document explains why cointegration-based pairs trading research often regresses log prices instead of raw prices. In an Engle–Granger approach, cointegration is assessed through the regression residuals; logging prices may make their relationship more nearly linear and improve the fit and residual distribution. Better-behaved residuals can support later standardization, such as forming z-scores for a trading signal.

The answers present this as a modeling choice rather than a universal rule. The appropriate transformation depends on the data and the intended model, and alternative transformations may improve fit in some settings. Because a pairs strategy often uses the regression hedge ratio to set position sizes, changing the transformation can also affect the interpretation and scaling of positions. The document offers qualitative reasoning but no empirical comparison, formal selection test, or evidence that log prices improve every pair.

Key ideas

  • Log prices may make relationships between asset prices more linear for cointegration regression.
  • The Engle–Granger procedure evaluates whether regression residuals are stationary.
  • Residual fit and distribution can affect subsequent signal standardization, including z-scoring.
  • The transformation can affect hedge-ratio interpretation and position sizing, so it should fit the strategy and data.

Tags

Pairs tradingStatisticsEquitiesMean reversion
Full text
# What is the reason for using log prices in Pairs Trading (Cointegration)?


# What is the reason for using log prices in Pairs Trading (Cointegration)?












I was wondering, why some of the research papers on pairs trading (using the cointegration approach) are using log prices to determine the spread of a pair? Why are they not simply using regular prices?

Thanks a lot in advance for any answers!

## Answer by databento (score 8, accepted)

https://quant.stackexchange.com/a/64184

I'm assuming that the paper you're referring to uses the Engle-Granger test for cointegration. The standard test procedure checks for unit roots in the residuals of a linear regression. It is a "stylized fact" to econometricians, who tend to be the ones publishing papers on pairs trading, that log prices better linearize the features and hence produce a better model fit for the linear regression (i.e. make the residuals look most normal).

Outside of pairs trading, there's many similar situations where we use other transformations to improve the model fit. As appropriate, you can apply Box-Cox transformations to the data or more specifically, the Yeo-Johnson extension. However, there is one practical issue to keep in mind here: In the typical construction of a pairs trading strategy, position sizing is determined by the "hedge ratio" from the same regression. There's no scaling issue for using log prices for small values of returns, but this may not be the case for other transformations.

## Answer by Katie (score 5)

https://quant.stackexchange.com/a/64197

This is for better linearity/normality in the QQ plot at the tails, which as both @noob2 and @rkr allude to, give a better fit and hence better properties for normalizing the residuals with z-scoring later on.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.