risk free, risky assets

CFA Level I
#1

When a risk free asset is combined with a portfolio of risky assets, is the variance of the resulting portfolio a weighted average of the returns variances of the risk free asset and of the porfolio of risky assets??? A.Yes B.No

#2

yes

#3

yes think about the portfolio variance formula, and set the standard deviation of the risk-free asset to 0

#4

because I think that the last part of the equation for portfolio variance will go to 0 because the st deviation for the risk free asset will be 0. Thus it should just be the weight of the risky asset multiplied by the variance (or st deviation) of the same assets.

#5

Actually, Schweser practice exams says the answer is NO. I also thought it was “yes”. I need to review this.

#6

yeah i guess it’s not because variance is still gonna be (w^2)(sd^2) i think i confused variance with standard deviation

#7

well, not the variance, the standard deviation is a weighted average. The variance is the squared w*stdv.

#8

Here is the equation: Portfolio Variance = (w1^2)(var1) + (w2^2)(var2) + (2(w1)(w2)(var1)(var2)(p1,2) If the risk free asset is asset 2, variance2 will be 0. Thus the second and third section should both go to 0. Right?

#9

variance is (st. dev.)^2 St. dev. is (variance)^(.5)

#10

right, but you have square w1, w2, cobined with the variances, so this is not a sum of weighted variances.

#11

yeah, and you are left with (w2*sd2)^2 which is not the weighted average of the returns variances but the squared weighted average of the returns variances edit:beaten

#12

Portfolio Variance = (w1^2)(var1) + (w2^2)(var2) is not a weight of variances, since your weights are squared.

#13

True, never thought that in depth on it. Just applied the formula. Sometimes I wish it was more computational… However if the covariance is 1, then it is a simple weighted average…correct. I want to be sure I keep this straight now

#14

and it is only the third term that dissapears, since risk free assets and risky assets have 0 correlation.

#15

i think 2 terms disappear what is the standard deviation of a risk-free asset?

#16

map1 Wrote: ------------------------------------------------------- > and it is only the third term that dissapears, > since risk free assets and risky assets have 0 > correlation. no, the second term must also disappear because the variance of a risk free asset is 0.

#17

so the final formula would be: portfolio variance = (w1^2)(variance) portfolio st. deviation = (portfolio variance)^(.5)

#18

right, you’re right.

#19

guess this would not be a simple weighted average because the weight gets squared on the risky assets. On the exam I guess I would need to write down the equation to visualize it.