### CFA Practice Question

There are 434 practice questions for this study session.

### 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%.

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.