- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 5. Sampling and Estimation
- Subject 5. Confidence Intervals for the Population Mean and Selection of Sample Size

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**CFA Practice Question**

A hedge fund is interested in knowing how low an annual return their strategy might generate as a once-in-100-years event. The strategy in question has an expected annual return of 20% with a standard deviation of 35%. You believe these returns are normally distributed. What is the lowest return that could be expected once in 100 years?

A. -51.9%

B. -45.7%

C. -61.4%

**Explanation:**Once in 100 years is 1/100 = 1%. So, the client seeks the 1st percentile return. This could be obtained by computing a 99% confidence interval. However, since our information will be based at the mean, we should seek the 98% confidence interval, where the 2% is split between the lower and upper bounds of the distribution. That way, we can obtain the lower 1% figure. The lower bound of the 98% confidence interval is 20% - 35%*2.325 = -61.4%.

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**User Contributed Comments**
7

User |
Comment |
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yanpz |
It's a z-distribution, so the z table is one tail, so we should look for p = 0.01 in the table, and get z = 2.325 or 2.33. |

whoi |
computing confidence interval always relies on two-tailed figures.... |

surob |
Let's take 95% confidence interval at 5% significance level. z is equal to 1.96. When you look up the number from the z table for P(Z<z), you will see that P is equal to 0.975 at z = 1.96. Why? It simply shows the area below z which constitutes 97.5% of the total area. The upper tail will have the rest - 2.5%. And confidence interval will be 95% if 2 tailed. And 97.5% if one-tailed. So, if 1% is the lower tail of the area, then we should look at 0.99 (instead of 0.98)at z table, which would be 2.33. |

uberstyle |
easy now. We use 98% (one in 50) because it can fall in either tail. Assume it will fall the high tail half the time and the low tail half the time, bringing you to one in 100 for low tail (return). |

u0302638 |
How can this question be rated as EASY? I saw so many much more easy question rated as MEDIUM |

NickNT |
Other way around (probably more intuitive) is to use Roy's safety-first than we shall solve (0.2-R)/0.35=2.325 for R - which will be the lowest return |

chris297 |
I don't think it is possible to ask us to calculate 98% confidence interval in exam. |