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Errors Found in Study Materials P1.T1. Foundations


R9.P1.T1 Page 8:
In the Notes of the 2nd row, IR should be residual return ÷ residual risk, not "residual risk [aka, alpha] ÷ residual return"

David Harper CFA FRM

David Harper CFA FRM
Staff member
Thank you @Nicole Seaman good find! To your point, I think the note is correct as it is @FRMNinjaLeonardo I think the confusion is that the last term (second bullet) contains σ(M) divisor, but this is the result of taking Jensen's alpha:

E(Rp) - Rf = α + β*[E(Rm) - Rf] where β = ρ*σ(p)/σ(m)
... but we assume ρ = 1 such that β is approximated by β ≈ σ(p)/σ(m) and Jensen's alpha:
E(Rp) - Rf = α + σ(p)/σ(m)*[E(Rm) - Rf] and then we can divide each side by σ(p):
(E(Rp) - Rf)/σ(p) = α/σ(p) + (σ(p)/σ(m)*[E(Rm) - Rf])/σ(p) but in the last term it cancels:
(E(Rp) - Rf)/σ(p) = α/σ(p) + (σ(p)/σ(m)*[E(Rm) - Rf])/σ(p) giving that final result:
(E(Rp) - Rf)/σ(p) = α/σ(p) + [E(Rm) - Rf])/σ(m)

Please note that we do not normally or necessarily assume ρ = 1. This is as assumption made by Amenc for purposes of this simplification where he invokes a certain definition of "well diversified." I would not want folks to think that "diversified" necessarily implies ρ(p, M) = 1.0, although we do have a definition of diversification as imperfect correlation.
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