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As far as I am aware:
CAPM = Long-term Govt Yield
BYPRP = Long-term firm yield
Fama French = Short-term Yield
Pastor Stanbaugh= Short-term yield
Ibbotson Chen = Supply Side = Not specified in the CFAI curriculum
BIRR = Short-term yield
GGM = Long-term yield
To answer your second question I THINK it is as follows:
1) This is the output of a linear regression model using historic data to quantify the stock’s relationship to market returns – with “alpha” being the stock specific return expected when the market return is zero, and “beta” being the slope coefficient between the market returns and stock returns
2) This is a forward looking “ex ante” model of expected returns based on the specific CAPM theory. It doesn’t include an “alpha” as there is no historical regression.