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question about CAPM

JamesVU2000

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Thread starter #1
why is correlation included to solve the problem? I cant see anything in the notes when we multiply the two terms x correlation?

Beta (i,M) = covariance(i, M)/variance(M) = 24%*15%*0.70/15%^2 = 1.12 <<- must know all of these steps! CAPM: E[R(i)] = Rf + Beta (i,M)*[R(M) - Rf] = 3% + 1.12*(8%-3%) = 8.60% PV (annual compounding) = $100/(1.086) + $100/(1.086)^2 = $176.87
thanks james
 

David Harper CFA FRM

David Harper CFA FRM (test)
Staff member
#2
HI @JamesVU2000 You've not sourced this so I don't have the context (@Nicole Seaman can you please move this thread once we know to what it refers?).

A fundamental, essential identity is that covariance(x,y) = correlation(x,y) * StandardDeviation(x) * StandardDeviation(y) such that "correlation is a standardized version of the covariance" per correlation(x,y) = covariance(x,y)/[StandardDeviation(x) * StandardDeviation(y)]. In the CAPM, β(i,M) = covariance(i, M)/σ^2(M) which, because covariance(i, M) = ρ(i, M)*σ(i)*σ(M), equivalently means that β(i,M) = [ρ(i, M)*σ(i)*σ(M)]/σ^2(M) = ρ(i, M)*σ(i)/σ(M). Because β(i,M) = ρ(i, M)*σ(i)/σ(M) we say "beta is correlation multiplied by (aka, scaled by) cross-volatility." Thanks,
 

David Harper CFA FRM

David Harper CFA FRM (test)
Staff member
#4
@JamesVU2000 Thank you. CAPM is found in three places in P1.T1 (Elton, Amenc, and Bodie) so it wasn't obvious to me. Each morning, Nicole and I hustle to answer questions, many of which can be moved to prior discussions (because most do not use search, as much as we try), so it saves us time if we have a direct reference. I typically do not have time to sift thru our notes to look for the match! Thanks,
 
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