- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 9. Shortfall Risk and Roy's Safety-First Criterion

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**CFA Practice Question**

An analyst has a client with a $1,000,000 portfolio. The client may need to liquidate $100,000 of the portfolio at the end of a particular year. The client does not want to invade the initial capital of $1,000,000. The table below summarizes different investment allocations.

What is the probability that the return on the safety-first optimal portfolio will be less than the shortfall level R

_{L}? Assume normality.A. 27%

B. 30%

C. 33%

**Explanation:**The probability is 33% that the return on the safety-first optimal portfolio will be less than the shortfall level, R

_{L}. The optimal z-value on X was 0.435.

Thus, P(RA < 10) = N (-0.435)). The reading on the table at 0.44 is 0.6700.

The solution is thus 1 - 0.6700 = 33%.

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**User Contributed Comments**
7

User |
Comment |
---|---|

danlan |
0.435=(20-10)/23 for X, which is higher than (10-10)/23 for Y and (13-10)/18 for Z |

dimanyc |
my problem is "reading on table at 0.44". There won't be a table at exam and 27,30,33 are too close to guess (although i guessed that part right! :) |

achu |
No reasonable tester would require memorization of the normal table. Use an online version of the table when doing these problems; assume you'd get a table excerpt on a real test for such a problem! |

homersimpson |
Looks like Y is the only one that falls short out of the three. So 1/3=33%. No z table required. |

Anevasee |
Can someone expand on the solution please? What is R_{L}? |

megageorge |
RL is 10% minimum that client wants to earn (100k/1mln) |

megageorge |
how we can get our test statistics without amount of n? |