Macroeconomic vs Fundamental Factor Models

[cleverCFA]

I’m a bit confused about what the material is talking about when they talk about the difference between these models.
Ri = ai + b2F2 + b3F3 + ….
In the macroecon model they say that we solve via regression to get the ai, b2, b3, etc. and then we use the Fs (i.e the surprises) to calc the Ri
But for the fundamental factor model, they say that we are doing the opposite. The b2, b3, are attributes data (i.e. P/E, etc), not sensitivies. I don’t get this, what are the Fs in that case?
The CFAI material gives an example with div yield but it’s not making much sense.
Can someone help explain what they mean? Thanks.

 

[S2000magician]

In a fundamental factor model, each term deals with a specific factor that is thought to influence returns. To make the discussion easier, let’s focus on a specific factor, say, P/E ratio. In a fundamental factor model that includes a P/E ratio term. the factor F(P/E) is the additional return that is expected for a firm whose P/E ratio is 1 σ above the mean P/E ratio for all stocks. A firm with a P/E ratio 2 σ above the mean P/E ratio for all stocks would get an additional return of 2 × F(P/E), a firm with a P/E ratio 1.5 σ below the mean P/E ratio for all stocks would get an additional return of -1.5 × F(P/E), and so on. The coefficient on F(P/E) for security i is calculated as:
bi = ((P/E)i – Avg(P/E)) / σ(P/E);
think of it like a critical Z-value.
The factor F(P/E) is estimated using cross-sectional multiple regression. For each stock, the b-values for each factor are standardized (the Z-value thing, above), and the Fs are the unknowns in a multiple regression; the resulting estimated value for each F is the additional return associated with a 1 σ increase in the corresponding b-value.
Continuing the example, suppose that for the P/E factor, we estimate F(P/E) as 0.5%. Then, a stock whose P/E ratio is 1 σ above the mean P/E ratio for all stocks will get an additional 0.5% added into its expected return. A sotck whose P/E ratio is 3 σ below the average P/E ratio for all stocks will get 1.5% subtracted from its expected return, and so on. Such adjustments are made for all of the factors in the model.
Hope that this helps.

 

[cleverCFA]

Hey S2000, thanks for that. Its definitely clearer.
This may sound like a stupid question, but what makes it different to a macroeconomic model in that case apart from the Bs and the Fs being switched around. What’s the difference between the 2 (i.e. why aren’t the Bs just called Fs). In your decription, the Fs have now become the sensitivity (i.e. F(P/E)= 0.5%) and the Bs are the “what’s going on” (i.e. company has +1 stddev P/E) whereas in the macroeconomic it just the opposite, the Bs are the sensitivity to surprises (i.e. to inflation), and the F are the what’s going on (1% surprise inflation).
In both cases, we’re using regression analysis to solve for the Bs or the Fs.

 

[shrubaks123]

Can i add one more question to this .CFA problem says return has negative senstivity to Inflation in macro factor model.I was thinking that when inflation surprise is positive then it’s sensitivity to it should also be positive because you demand a highter return in that case ( when inflation is high),instead the problem has mentioned nagetive sensitivity to highter inflation surprise.