I don’t know why i’m so confused by this but I saw a hedge fund’s marketing book with a 20 year track record that broke out the below formula for the past 20 years.

Gross % Return = Rf + (Beta x Rmrkt) + Alpha Given this formula if I reversed it to break out Alpha I would get: Alpha = Gross % Return - [Rf + B(Rmrkt)] Everything seems to work. However the formula in CFA would have you subtract the Rf at the end. Alpha = Rp - [Rf + B(Rm - Rf )] So how can they ignore this. I originally thought maybe since the 1 month is like 0.1% it doesn’t matter, but they go back to 1996 when it was 5.2%. Any ideas?

The hedge fund could be using a market model, which shows returns as a function of the market return with a slope of beta. The CFAI formula is for SML (CAPM), which models returns as a function of beta with a slope of the MRP.

I guess to simplify my whole question the hedge fund is just using the return of the market (S&P 500) rather than the market risk premium (S&P - risk free rate). Does that make any sense?

It does. They are using a market model, and the formula in CFAI is the CAPM. The market model is not supported by theory, whereas CAPM is based on the capital asset pricing theory. Both can be used to estimate alpha (residual return).