CFA Practice Question

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CFA Practice Question

You are given assets X, Y, and Z, which have expected returns of 5%, 10%, and 15% respectively, and standard deviations of return of 10%, 20%, and 35% respectively. Your client views any return below a level of 3% as unacceptable. Find the asset that minimizes the probability that the portfolio will fall below 3% annual return; what is the probability?

A. Z, 37%
B. X, 32%
C. Y, 36%
Correct Answer: C

To answer this question we must follow Roy's Safety-First criterion. First, we must find the shortfall level, R_l. Fortunately, this is already given to us in the question; it is 3%. Second, we compute the SFRatio for each asset in the portfolio: SFRatio = (E(R_p) - R_l) / sigma_p. For asset X, this ratio is (5%-3%)/10% = 0.2. For Y, we get (10% - 3%)/20% = 0.35 and for Z, we get (15% - 3%)/35% = 0.34. Third, find the standard normal cdf evaluated at the SFRatio for each asset. The probability of shortfall will be N(-SFRatio). For X, Y, and Z, these will be N(-0.2), N(-0.35), and N(-0.34). Since N(-0.2) = 1-N(0.2) and so on, we get 0.4207, 0.3632, and 0.3669 for X, Y, and Z, respectively. Thus, asset Y minimizes the probability that the return will fall short of 3%, with a probability of approximately 36%.

User Contributed Comments 13

User Comment
tanyak How is 1-N(0.2) = 0.4207?
dnguyen757 Z-score for 0.2 is 0.0793. Z-score for -0.2 is 0.5 - 0.0793 = 0.4207.
surob Do you know why we have to compute N(-0.2) or 1-N(0.2) instead of N(0.2)?
dave79 because here we have to find the cummulative probablity of values below 0.2 which lies in -ve side of the normal distribution curve and hence u check N(-veZ) or 1- N(Z)
StanleyMo -0.2 and 0.2 is symmetry, so N(-0.2) = 1 - N (0.2)
haosheng any shortcut other than Z-score?
CFAonTheBrain i dont get it. we get the z score EX: .2 which is .0793 then we subtract -1 ? or find the z-score for -.2 which is i dont know, and how do you get it?
salsa how do v compute N(.2)?
8thlegend If you are looking for the z score distribution its in the back of the CFA book A-67.

After calculating the SFratio, you are using that number like a z score, and using to find the probability.

.2 in the z-score is .5793. So it is likely that the Asset x will go up 57.93%.

The question wants to know what the probability of the asset going down. The z score that you find if the probably that it will go up so that is the reason why 1-N comes in.

so 1-.5739 = 0.427 => 42.27% that it will go down for asset x.

You need to do that with the rest 3
bundy Much more simple than that. Highest SF ratio is what you want. When you have calculated the SF Ratio and found Y to be highest you know the answer is C
DonAnd That is exactly what I did Bundy--->don't have unnecessary time to waste on the exam day.

Time is of the essence (1.5min per ques)
johntan1979 You all will turn out to be lousy asset managers if you always look for shortcuts like this.

It is important to consider the probability of Rp<RL when evaluating an investment to suit your client's risk tolerance.
ashish100 we'll cross that bridge when we get johntan1979

let us pass the mother of all exams first
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