Pairs Trading Issues

A few words for those of you who are not familiar with the “pairs trading” concept. First you should understand that the movement of every stock is dominated not by the companies performance but by the general market movement. This is the origin of many “factor models”, the factor that drives the every stock is the market factor, which is approximated by the S&P index in most cases.


OLS beta VS. Robust beta

In financial context,  \beta is suppose to reflect the relation between a stock and the general market. A broad based index such as the S&P 500 is often taken as proxy for the general market. The  \beta , without getting into too much detail, is estimated using the regression:

    \[stock_i = \beta_0+\beta_1market_i+e_i\]

A  \widehat{\beta_1} of say, 1.5 means that when the market goes up 1% the specific stock goes up 1.5%. (Ignoring all the biases at the moment!)