# Quanto..

The S&P 500 index has expected return of 9% per year with standarddeviation of 15%. Assuming that returns are normally distributed, what is the range of returns that can be expected over one year with a 95% level of confidence?

9% (+/-) 1.96*15% [-20.4%, 38.4%]

It is correct. My question is “I get confused sometime”: When we use the standard error to caulate the confidence interval?

You use the standard error when you are not told that the distribution is normal (generally they will say sample mean, sample standard deviation, and give you the number of observations N)

When you are using a Sample to make a prediction of the Population Parameters, use the Std Error of the Sample Mean. This is because (this is not mathematical, it is something you have to think about) you are using a smaller # to predict a much larger #. So your error term needs to reflect that difference. in the above, the S&P 500 index is the population itself. So no need for the Std Error of the “sample” because they have given you the entire Population Mean and std. If they had instead given you the mean of 30 companies on the S&P 500 is 9% and their sample std dev is 15% --> your answer would have changed to 9 +/- 1.96 * 15/sqrt(29) instead of the above. Hope this answers your question. CP

strangedays Wrote: ------------------------------------------------------- > It is correct. > > My question is “I get confused sometime”: > > When we use the standard error to caulate the > confidence interval? good one – I think when you are looking at a sample, you use SEE ? they gave us no sample size here, so we can eschew it r(standard error) right away.