- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions
- Subject 7. The Standard Normal Distribution

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**CFA Practice Question**

An analyst wants to calculate a 95% confidence interval for the weighted-average of the projected mean return of a portfolio he manages. His latest calculations show that this portfolio has a weighted-average return of 8% and a variance of 36. What is the 95% confidence interval?

B. [-3.76%, 19.76%]

C. [-1.87%, 17.87%]

A. [-62.56%, 78.56%]

B. [-3.76%, 19.76%]

C. [-1.87%, 17.87%]

Correct Answer: B

The variance is 36, which corresponds to a standard error of 6%. The 95% confidence interval is given by: X-bar ± 1.96 x s = 8 ± 1.96 x 6.

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**User Contributed Comments**
11

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

Winner |
Can someone explain where the 6% figure comes from? |

tagr |
s = square root of variance => square root of 36 = 6 |

Bibhu |
In this sort of questions, no need to calculate both the limits. One limit is sufficient to pick up the correct results. |

bobert |
You use 6% because the SD is a measure of units from the mean, since the mean is expressed as a percentage, just divide it by 100. |

magicchip |
@Bibhu: be careful doing that. Work it out completely. |

tschorsch |
answering questions like this without spending much time allows you to spend more time on more complex problems since the given answers vary a lot, you can do things like this in your head the confidence interval is mean +/- 1.96 x stddev this is about mean +/- 2 std dev stddev is easy since 6x6 = 36 so interval = 8 - 2x6 = -4 to 8 + 2x6 = 20 How much time you spend on these depends on your confidence in these types of problems. If you are not strong in these areas, then by all means do all the math. We all have different abilities in different areas. Save time when you can. There will be other questions you will really have to think about that others will find obvious. |

boddunah |
nice trick for people who assume standard deviation was given but variance is given. need to look at question carefully. "variance" was given.not standard deviation. |

Masterguru |
nice trick tschorsch, thx |

irapp92 |
Not sure if this is how everyone solves the problem but it works for me and saves time (granted, not as much time as tschorsch's method) 1) Recall formula for finding Z is Z= (X- u)/ stdv 2) Check which variables are provided (in this case we have Z=1.96 (1.96=95% confidence), u=8, var=36 thus stdv= 6 (sqrt) 3) Plug into equation to see that we need to find X 4) Find the answer with the middle value (in this case -3.76) 5) Plug in -3.76 for X in the formula for step 1 6) If the calculator shows 1.96 you have your answer, if the result is >1.96; choose the lower answer (in this case C), if the result is <1.96; choose the higher answer (in this case A) May sound longer but after you do it a couple times it flows really fast and takes absolutely no brain power to do |

farhan92 |
i use irrap92's method but skip the last few steps! However, this method just makes more sense to me so best to go with what works for you instead of trying to learn toomany formulas |

Huricane74 |
95% CI = (1.96)*(.06) ± .08 |