I got myself confused on question 11 page 556 of book 1. The question was construct 90 % confidence
levels for a mean return of 1.07% and standard deviation 2.38. They used the standard deviation as the sample error and this confused me. Is this because they explicticly say in the question 'base your estimates of future period monthly return parameters on the sample mean and standard deviation.
in such case there is no need to calculate the standard error.
This is a good case. Confidence intervals construction requires standard error, which is the standard deviation divided by the square root of the number of observations. So, if the question gives you standard deviation, you must calculate the standard error before the CI calculation.
However, what happens if the question does not specify “n” or to use the standard deviation as like it was the standard error? I think calculate it as it is asked, because thats the info you have. In this case the question specify to use that info to calculate CI.
I think that at least the questions won’t go in a contradiction way, so read very well the questions.
Regards
Not necessarily.
If you’re creating a confidence for the mean of a population, or for a given percentage of the population, you need the standard error.
If you’re creating a confidence interval for an arbitrary member of the population (e.g., next month’s return), you use standard deviation, not standard error.