P1.T1.20.8. Modern portfolio theory (MPT)

[Elizabeth_Babalola]

This does not relate to this thread. Unfortunately, i could not find a suitable one. Taking a look at the second bullet point under the relationship between Sharpe and Jensen; are we dividing by \[ \sigma p\; \] or \[ \sigma m\; \]

 

[David Harper CFA FRM]

Hi @Elizabeth_Babalola dividing by σ(P) because Jensen's alpha says E(Rp) - Rf = α(P) + β*E(Rm - Rf) and dividing by α(P) gives [E(Rp) - Rf]/α(P) = α(P)/α(P) + β/α(P)*E(Rm - Rf), but if B ~ σ(P)/σ(M) then β/α(P) = σ(P)/σ(M) * 1/σ(P) = 1/σ(M) and α(P) = α(P)/α(P) + 1/σ(M)*E(Rm - Rf).

Append, mistake(s) above, I meant:
dividing by σ(P) because Jensen's alpha says E(Rp) - Rf = α(P) + β*E(Rm - Rf) and dividing by σ(P) gives [E(Rp) - Rf]/σ(P) = α(P)/σ(P) + β/σ(P)*E(Rm - Rf), but if B ~ σ(P)/σ(M) then β/σ(P) = σ(P)/σ(M) * 1/σ(P) = 1/σ(M) and [E(Rp) - Rf]/σ(P) = α(P)/σ(P) + 1/σ(M)*E(Rm - Rf).

 

[Elizabeth_Babalola]

Thanks @David.

The last equation is not clear though

 

[David Harper CFA FRM]

@Elizabeth_Babalola sorry, in haste i wrote α(P) instead of σ(P). Fixed above. Should be as follows:

E(Rp) - Rf = α(P) + β*E(Rm - Rf); divide by sides by σ(P):
[E(Rp) - Rf]/σ(P) = [α(P) + β*E(Rm - Rf)] / σ(P) = α(P)/σ(P) + β*E(Rm - Rf)/σ(P). But β ~= σ(P)/σ(M), so
[E(Rp) - Rf]/σ(P) = α(P)/σ(P) + [σ(P)/σ(M)]*E(Rm - Rf)/σ(P); and we can cancel σ(P)/σ(P):
[E(Rp) - Rf]/σ(P) = α(P)/σ(P) + [σ(P)/σ(M)]*E(Rm - Rf)/σ(P) = α(P)/σ(P) + *E(Rm - Rf)/σ(M)

 

[Elizabeth_Babalola]

Duly noted. Thanks