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# P1.T1 Factor Portfolios - (Bodie)

#### chiaaugu

##### New Member
Hi all

1) Can you help me understand what is the factor portfolio used for?

Based on the notes, since the factor portfolio only has a beta of 1 and beta = 0 for all other factors, it looks like the factor portfolios are being used as a tool to measure the impact of the common factors in the multi-factor APT (i.e based on the impact of the common factor on such factor portfolios, we estimate the risk premiums for each of the common factors)

For example in page 12:
factor portfolio 1 - measures risk premium of common factor 1 = 6%
factor portfolio 2 - measures risk premium of common factor 2 = 8%

Since portfolio A is impacted by both common factor 1 and 2 based on the multiple factor APT Formula
The expected returns of portfolio A is = R(F) + Beta1CommonFactor1 + Beta2CommonFactor2 = 0.4 + 0.5(0.06) + 0.75(0.08)

2) Also what does it mean that "overall risk premium on this portfolio must equal the sum of the risk premiums require as compensation for each source of systematic risk" (In bold)

3) Is the Multiple Factor APT formula: E(R) = R(F) + B1RP1 + B2RP2 + B3RP3 .... ?

Appreiciate your help as i am quite struggling with this chapter

#### ShaktiRathore

##### Well-Known Member
Subscriber
hi,
factor portfolio isolates a factor X such that its exposed to that factor X only so that beta=1 for the factor X and 0 for other factors so that factor portfolio excess return=1*risk premium of factor X=risk premium of factor X.Thus factor portfolio measures risk premium of factor X.
Thus factor portfolio 1 - measures risk premium of common factor 1 = 6%
factor portfolio 2 - measures risk premium of common factor 2 = 8%
2)Since A is exposed to factor 1 and factor 2 therefore it should be compensated for bearing this risk exposure as sum of risk premiums 0.5(0.06) + 0.75(0.08).(qty of exposure*risk premium).
thanks