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Basic Question 3 of 5
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?
B. X, 32%
C. Y, 36%
A. Z, 37%
B. X, 32%
C. Y, 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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Learning Outcome Statements
define shortfall risk, calculate the safety-first ratio, and identify an optimal portfolio using Roy's safety-first criterion
CFA® 2024 Level I Curriculum, Volume 1, Module 5.