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A retail client of yours is interested in knowing how low an annual return a major stock index might have, as a once in a twenty year 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 low return that could be expected once in twenty years?
Correct Answer: B
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 9 0% confidence interval `is 11% - 22%*1.645 = -25.2%.