 # Portfolio Standard Deviation

This question out of Q-bank stumped me, can anyone explain to me what the correct answer is and why? Assets A (with a variance of 0.25) and B (with a variance of 0.40) are perfectly positively correlated. If an investor creates a portfolio using only these two assets with 40 percent invested in A, the portfolio standard deviation is closest to: A) 0.3400. B) 0.3742. C) 0.7616. D) 0.5795.

perfect +ve correlation beta = 1 variance = .4^2 ( .25) + .6^2 * .4 + 2 (.4) (.6) (1) sqrt(.25) * sqrt (.4) = .3358 std deviation = .5795 choice D

I think it’s D

I agree with Cpk123 accept the beta would be rho actually at least if I am not wrong beta is market correlation

That’s right! Apparently I am just missing something… The equation in the Schweser materials says that the equation is: [(w1^2)(o1^2) + (w1^2)(o1^2) + 2(w1)(w2)(o1)(o2)(cov)]^1/2. So why isn’t the .25 and .4 squared? And why are we taking the sqrt of these in the last part of the equation?

bcos problem says 0.25 and 0.4 are VARIANCE. They throw u off in Portfolio Management by giving you Variance, asking for Std Dev. by rho - florinpop means correlation coefficient. Yes - it’s rho - not beta - my bad.

cos they’re variance and not standard deviation, as mentioned in the question… ya, positively perfectly correlation means correlation coefficient is +1, it’s different from beta

look at the equation on page 218 from Schwester books Hope it the same I have an older version 0.25 and 0.4 are variances so you have to calculate the standard deviation

I knew it had to be something silly but I just couldn’t see it. Might be time to call it a night Thanks everyone!!

.25 and .40 do not need to be squared, because these are given as the variances of the two assets (the std deviations squared). And if you do not take the square root at the end, you will have the portfolio variance, instead of the portfolio std deviation.

Just to confuse everyone: Another way to do this problem is to say that if they have correlation = 1, you can rewrite them as levered investments in the same security X with variance = 1. So A = Sqrt(.25)X and B=Sqrt(0.4)X so the whole portfolio is 0.6*Sqrt(.25)*X + 0.4*Sqrt(0.4) X = 0.5795 X => D Note: If X has std dev s then A*X has std dev A*s.

Joey I believe it must be .4 * sqrt (.25) + .6 * sqrt (.4) = .5795

^ yep. Mistyped that (since my equation doesn’t come out to 0.5795).