- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 6. Confidence Intervals for the Population Mean

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**CFA Practice Question**

A retail client of yours is interested in knowing how low an annual return a major stock index might have, as a once-in--twenty-years event. The index in question has had an annual return of 11% with a standard deviation of 22%. You believe these returns have been normally distributed. What is the lowest return that could be expected once in twenty years?

A. -11.0%

B. -25.2%

C. -32.1%

**Explanation:**Once in twenty years is 1/20 = 5%. So, the client seeks the 5th percentile return. This could be obtained by computing a 95% confidence interval. However, since our information will be based at the mean, we should seek the 90% confidence interval, where the other 10% is split between the lower and upper bounds of the distribution. That way, we can obtain the lower 5% figure. The lower bound of the 90% confidence interval is 11% - 22%*1.645 = -25.2%.

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**User Contributed Comments**
10

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

ehc0791 |
Good question! |

aakash1108 |
Very good! |

Yurik74 |
I just guessed it and strangely got the right result. -11 seemed too close to mean for this probabilty, 32.1 & 45.7 - too far, so the option was 25.2; glad my intuition was good but better know for sure |

homersimpson |
why do we need to multiply 1.645 in the end? can anyone pls help? |

jayj001 |
Because 90% confidence interval has values more than 1 standard deviation away i.e. 1.645 standard deviations away |

arendb |
I had C as my answer, based on 95% confidence interval. Can someone please explain why we are using 90% confidence interval in this instance? I don't understand. |

Schuyler3 |
2 tailed 90% and 1 tailed 95% both have a value of 1.645 |

gtt240 |
Why didn't we divide the standard deviation by the square root of n to create a standard error? |

merc10112 |
Same question as gtt240... |

Wilko |
I think the reason we do not use the standard error, but the given standard deviation is because we are dealing with the actual index and not a sample of the index. We are working with a population not a sample. |