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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!

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  • $\begingroup$ If two stocks' prices increase by the same percentage, the logs of their prices increase by the same amount, which is nice graphically. The dots on an x,y chart line up on a diagonal line (a line with slope 1) through $(x_0,y_0)$. This type of chart makes it easy to visualize the behavior of two stocks in relation to each other, without any fancy maths. $\endgroup$
    – noob2
    May 24 '21 at 19:14
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    $\begingroup$ The actual value of a stock price in dollars is an arbitrary historical accident depending on the number of shares created and the size of the company. There is no economic difference between a company with 1bn shares which change value from \$1 to \$2 each, or the same company with 1m shares which change value from \$1,000 to \$2000 each. Log prices eliminate the arbitrary price scale for different stocks. (For example, US markets seem to "like" stocks to have much higher prices than in the UK. You won't find many large companies with stocks trading at \$10 in the USA, or at £1000 in the UK. $\endgroup$
    – alephzero
    May 25 '21 at 17:27
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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.

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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.

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