Let's say I want to run a series of regressions for zero-cost portfolio Y that goes long on stocks based on high variable x and short stocks with a low variable of x. How do I run the regression, for example, for CAPM? Is it:
$$Y - r_f = a + b(market-r_f) + e$$
$$Y = a + b(market-r_f) + e$$
Is it the first one only if we assume that the portfolio actually has zero beta/systematic risk?