L1.1.6 Factor models and Arbitrage Pricing Theory (Old question)

[Ludwma]

Hi David,

I'm not able to understand the solution of the archived question that you can find here:

http://forum.bionicturtle.com/threa...nd-arbitrage-pricing-theory-foundations.4104/

First, I do not understand why R(A) and R(B) are defined as you have written.

Applying APT, R(A) should be equal to: Alfa(A) + 0.75 * F(E) + 0.20 * F(B) + Epsilon(A).

Where am I wrong?

Thanks,

FS

 

[David Harper CFA FRM]

Hi Ludwma, I answered where you posted ... I don't think you are technically wrong, not at all, but GARP's practice question simply omits the intercept (alpha) and the error (epsilon). And note the alpha would not impact the variance, anyhow, as it is a constant it drops out; the error, on the other hand, would complicate the variance. Otherwise, we have the same return, yes? Thanks,

 

[Ludwma]

Hi David,

Thanks for the quick answer. Are there any reason why they have obmitted Alpha and Epsilon? It's quite strange for me.

Thanks,

FS

 

[David Harper CFA FRM]

Hi FS, Sure, to be frank because they are not always precise, and GARP has never been sufficiently precise with respect to APT (every year I submit requested clarification wrt APT; for years, alpha was variously defined). So, I will add your observation to the errata that I submit to GARP (see http://forum.bionicturtle.com/threa...i-question-1-three-issues-with-question.5355/).

However, I would not characterize this as an error (you might disagree with me?) but rather an imprecision ... Thanks,

 

[David Harper CFA FRM]

FS,

Although, since you seem to know this topic, can you let me know if you disagree with?

• The lack of alpha (intercept) is inconsequential: it disappears in the variance/covariance (by definition has zero correlation to variables; and zero variance itself)
• The imprecision is specifically the error term, and only this "specific" or "idiosyncratic" component (that will be i.i.d. by definition, but therefore would add a term to the Variance[R(A)])

Thanks,