Quants (statistics) Question

Quick Question for you: A Manager forecasts a bond portfolio return of 10% and estimates a standard deviation of 4%. Assuming a normal returns distribution and that the manager is correct there is: A) 90% probability that the return will be between 3.2% and 17.2% B) 90% probability that the return will be between 2.16% and 17.87% C) 32% probability that the return will be between 6% and 14% The answer is B, but the question i have is this: Why, in this case, is the standard deviation of 4% used as the standard error? I thought the standard error was s/sqrt(n) Are the two interchangable?

How is the answer B? Is it meant to be a 95% probability ie 1.96 standard deviations on each side of the mean?

Sorry B) should read 95% prob…

I would say A is closest to correct interval. 90% probability in two-tailed test is between -1.65 and 1.65 st. dv. So true interval would be between 3.4 and 16.6. B interval is correct with 95% probability.

It was a typo, it should have been a 95% prob. The answer IS b, but that’s not what i’m asking… Usually for a confidence interval the formula is: is: X±Z(s/sqrt(n)). But in this case it seems acceptable to just put in the standard deviation of 4% rather than the Standard error… Why is this the case?

I’m not very good in statistics, but as far as I know, you have to use standard error when need to calculate the value of population mean from known sample mean. Here you have population mean and you’re asked to find interval in which particular percent of all values lie. If you were given sample mean and were asked find interval in which population mean lies, you would be using standard error. It’s a bit tricky, but I hope you’ll get it.

I’m very good in statistics, and as far as I know, you have to use standard error when need to calculate the variability of the sample mean. That is, when someone says that they take a sample of size n and then calculates a mean of the sample what is the probability the mean falls in some interval, you use standard error (divide by sqrt(n)). When you are asked the probability a single observation falls in an interval, just use standard deviation. Thus, Question asks about sample mean => Use standard error Question asks about single observation => Use standard deviation

Even if you were to use the standard error, where is the sample size given in the question?