# 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?

• 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. May 24 '21 at 19:14
• 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. May 25 '21 at 17:27