Question on Ra.P1.T1.AMENC.26.32.Chapter4.V5

[jim1.jiang]

27.1 Assume a two-asset portfolio. Asset A has volatility of 20% and Asset B has volatility of 30%. The returns of the two assets have a correlation of 0.4. If each asset is weighted 50% (equally-weighted portfolio), what is the portfolio volatility?

a) 19.4%
b) 20.1%
c) 21.1%
d) 25.9%

27.1. C (21.1%) P(volatility) = SQRT[ weight_A^2*variance(A) + weight_B*variance(B) + 2*weight_A*weight_B*Covariance(A,B)] = SQRT [50%^2*20%^2 + 50%^2*30%^2 + 2*50%*50%*20*30%*0.4] = SQRT [0.0445] = 21.1%

Should 0.4 be covariance instead of correlation?

STDp = SQRT(w^2 * STD1^2 + (1 - w)^2 * STD2^2 + 2(w)*(1 - w)*Cov(R1,R2))

Where Cov(R1,R2) = Corr(R1,R2)STD1STD2

 

[Alex_1]

Hi, I think it is correct that 0,4 is the correlation and not the covariance. The formula above states that Cov = Corr x Std 1 Std 2. In the covariance term above it should be 20% instead of 20 but otherwise this looks correct to me. Thanks.

 

[David Harper CFA FRM]

Thanks @Alex_1 for noticing the missing (%)
Hi @jim1.jiang fyi, source is here @ https://forum.bionicturtle.com/threads/l1-t1-27-correlation-impact.3451/
fyi, you can look at XLS here @ https://www.dropbox.com/s/y4wbtosu80r81rc/T1.27_portfolioVariance.xls

It looks like the 0.4 is okay, as Alex says, because the final term shown is 2*weight(A)*weight(B)*volatility(A)*volatility(B)*correlation(A,B) where correlation(A,B) is the given 0.40. So this final term is equal to 2*weight(A)*weight(B)*volatility(A)*volatility(B)*correlation(A,B) = 2*weight(A)*weight(B)*covariance(A,B) because covariance(A,B) = volatility(A)*volatility(B)*correlation(A,B), so we get the same answer of 21.5% with:
= ... SQRT [50%^2*20%^2 + 50%^2*30%^2 + 2*50%*50%*0.0240 where covariance(A,B) = 0.0240 = 20%*30%*0.40