FRM GARP Ques 6.12 accurate or not?

[bchauhan5]

This GARP solution does not make much sense - why are we not using the square root of the sample size in the denominator? GARP solution does not seem to make much sense and I have spent half a day re-reading the theory and searching online to find if this solution is accurate or not? Pls help!

GARP Ques - 6.12 - If you are given a 99% confidence interval for the mean return on the Nasdaq 100 of [2.32%, 12.78%], what is the sample mean and standard error? If this confidence inter-val is based on 37 years of annual data, assumed to be iid, what is the sample standard deviation?

GARP Sol -
The mean is the midpoint of a symmetric confidence interval (the usual type), and so is 7.55%. The 99% CI is constructed as [mn - c * sn ,mn + c * sn ] and so c * sn = 12.78% - 7.55% = 5.23%. The critical value for a 99% CI corresponds to the point where there is 0.5% in
each tail, or 2.57, and so sn =
5.23% 2.57
= 2.03%.

 

[Clay Carter]

This GARP solution does not make much sense - why are we not using the square root of the sample size in the denominator? GARP solution does not seem to make much sense and I have spent half a day re-reading the theory and searching online to find if this solution is accurate or not? Pls help!

GARP Ques - 6.12 - If you are given a 99% confidence interval for the mean return on the Nasdaq 100 of [2.32%, 12.78%], what is the sample mean and standard error? If this confidence inter-val is based on 37 years of annual data, assumed to be iid, what is the sample standard deviation?

GARP Sol -
The mean is the midpoint of a symmetric confidence interval (the usual type), and so is 7.55%. The 99% CI is constructed as [mn - c * sn ,mn + c * sn ] and so c * sn = 12.78% - 7.55% = 5.23%. The critical value for a 99% CI corresponds to the point where there is 0.5% in
each tail, or 2.57, and so sn =
5.23% 2.57
= 2.03%.

@bchauhan5 I think the confusion arises because GARP’s solution uses sn to denote the standard error, which already includes the sqrt(n) term in the denominator, but this is never stated explicitly. Once you see that I think the answer makes sense. So the standard error is 2.03% and the sample standard deviation is obtained by multiplying by sqrt(37).