port mgmt question.

CFA Level II
#1

Rachel Stephens, CFA, examines data for two computer stocks, AAA and BBB, and derives the following results: Standard deviation for AAA is 0.50 Standard deviation for BBB is 0.50 Standard deviation for the S&P500 is 0.20 Correlation between AAA and the S&P500 is 0.60 Beta for BBB is 1.00 Stephens is asked to identify the stock that has the highest systematic risk and the stock that has the highest unsystematic risk. Stephens should draw the following conclusions: Highest Systematic Risk Highest Unsystematic Risk A) Stock AAA Stock AAA B) Stock BBB Stock BBB C) Stock AAA Stock BBB D) Stock BBB Stock AAA

#2

Beta for stock AAA is .6(.5)(.2)/(.2)=.3 D. Since stock B has a higher Beta it has higher systematic risk. Unsystematic risk would be total risk minus systematic. BBB = .5 - .2(1) = .3 AAA = .5 - .2(.3) = .44

#3

beta(AAA) = cor*stdev(portfolio)/stdev(market) = .6*.5/.2=1.5 since beta(AAA) > beta(BBB) and total standard deviation is same -> C

#4

maratikus, I thought beta was cov over the stdev of the market. Since corr=cov/(stdevi)(stdevj) wouldn’t beta = corr (stdev AAA)(stdev Market)/(stndev Market ?

#5

covariance / variance of the market (not Std dev)

#6

Excellent point! Then maratikus is right. Well done.

#7

I have made that mistake before. Never learn…

#8

I got 1.5 as the Beta for A. Is that what you guys are getting?

#9

Same thing

#10

So the answer is C then.

#11

I can’t see how it wouldn’t be.

#12

good job. The correct answer was C) Stock AAA Stock BBB First, compare the betas for the two stocks. The beta for AAA can be derived with the formula: Therefore, AAA has larger beta and greater systematic risk than stock BBB which has a beta equal to 1. To assess the unsystematic risk, note that total risk is measured by the standard deviation. Note that the standard deviations for AAA and BBB are identical. Therefore, AAA and BBB have identical total risk. Moreover, note that: total risk = systematic risk + unsystematic risk. We have already concluded that both stocks have identical total risk and that AAA has greater systematic risk. Therefore, BBB must have higher unsystematic risk.

#13

yep c

#14

Damn. Good question. Got that one wrong. Won’t screw that one up again.

#15

I actually worked this one out numerically, using market model mostly and the beta= Covariance/var(market) formula.

#16

cfasf1: the formula didnt come out in your post, can u please write it out if the format is funny? much appreciated

#17

oops, didn’t know that the formula was not in there. Beta AAA = (.60)(.50)/.20 = 1.5 Maratikus had it correct above.

#18

You can also use Cov/variance of the market = definition of beta Since cov=corr*sdAAA*sdMarket (.6)(.2)(.5)/(.2^2)=1.5 Same thing really