Say you think your positive pairs trade returns are due to pairs trades you made on small stocks (measured by market capitalization).
Describe how would you test this hypothesis?
What regression equations would you use, and what would your null and alternative hypotheses be on the coefficients?
If your positive pair trade returns are indeed from trades on small stocks, would you expect to accept or reject the null hypotheses for your coefficients?
A pairs trade is one where we find two stocks and short one and go long the other. In this case we are looking at trying to distinguish whether our positive pairs trades on small capitalization stocks outperformed those of mid cap and large cap stocks.
In order to test this hypothesis, we would want to set up a regression equation which had a dummy variable for small cap stocks. The small cap dummy variable would have a value of 1 if the pairs trade was on small cap stocks and a value of 0 if not. It would also be informative to have a dummy variable for mid-cap stocks included as well. The mid cap would have a value of 1 if the pair trade stocks were considered mid cap ...
The pairs trading hypothesis tests are examined. The positive pair trade returns are discussed.