# Multufactor (a & e??)

I have two questions about multifactor models.

On page 27 of the Economic and Asset Allocation CFAI book (vol 3), there is a formula smack in the middle of the page for the “return on market i, M”…

M = a + bF + bF + bF … e (where bF is the series of coefficients times related factors)…

What exactly is “a” if making a forward looking return forecast???

I know it is the intercept term but it isn’t in the table above. Is it the constant derived from the regression equation for each market? Is it the risk free rate?

And my second question is…

Should e be = 0 when making a expected return calculation?

Thanks

GG

a is the market return when all of the factors equal zero: _F_1 = _F_2 = ∙ ∙ ∙ = Fn = 0.

As a practical matter, a by itself is generally pretty meaningless, as it’s generally impossible for all of the factors to be zero simultaneously. (Note: this is the reason that many macroeconomic models use as factors changes in fundamental variables (e.g., change in inflation, change in GDP, and so on); in such a model having all factors equal zero simultaneously is meaningful, so the constant is meaningful.)

Yes, when making an expected return calculation you set e = 0: the expected value of the error term is zero.

S2000 - so would a = E® [expected return] for the asset??

I believe I read this in some APT model presentations, but not sure if it applied here as well.

It would be if the expected value of each factor is zero.

That doesn’t have to be the case. For example, if one of the factors is GDP, it certainly isn’t zero.