# Standard Deviation of Return

Hi I’m working on the following problem and have different solution as the answer sheet. Volume 4 page 251 Month 1 2 3 4 5 6 Madison Corp: -0.04 0.06 -0.07 0.12 -0.02 0.05 Sophie Electric: 0.07 -0.02 -0.10 0.15 -0.06 0.02 Calculate Standard Deviation of Returns for each company. Well, according to the examples showed at the book, we can first calculate the variance of each and divide by n-1 to avoid statistical bias. The square root the variance to get the standard deviation of return. I tried to apply this approach. However, the answer sheet does not use n-1 (in this case should be 6months -1 = 5), instead it divides 6. Why is that? Thanks, -Hui

Yeah, a constant source of confusion. You did the problem correctly because the population is really all possible returns. There’s always some smersh about “you have all the observable data thus you have the population” which is a load of crap.

Because they treat the data as population not a sample. If it was a sample, they will say it in the problem.

I see. The difference btwn Population (entire group) and Sample (part of population) answered my question. Thanks much!!!

Here’s an interesting thing about this - the (n-1) vs n question comes up all the time. Nobody gets it because CFAI doesn’t really go into it and then puts examples like this in the book. However, the n-1 is about eliminating bias in the sample variance. But then we take the square root and talk about the sample standard deviation. But the theorem that X is unbiased for theta so Sqrt(X) is unbiased for Sqrt(theta) isn’t true and the sample standard deviation is biased for the population vol. So all this effort and we still screw it up…

Wow, so much twists. My main concern is what to do at real exam? I think CFA should be the one to clarify this issue and make consistant statements across the study material.

JoeyDVivre Wrote: ------------------------------------------------------- > Here’s an interesting thing about this - the (n-1) > vs n question comes up all the time. Nobody gets > it because CFAI doesn’t really go into it and then > puts examples like this in the book. However, the > n-1 is about eliminating bias in the sample > variance. But then we take the square root and > talk about the sample standard deviation. But the > theorem that X is unbiased for theta so Sqrt(X) is > unbiased for Sqrt(theta) isn’t true and the sample > standard deviation is biased for the population > vol. So all this effort and we still screw it > up… This is very true. I had to look it up in order to understand it a bit better. Oh, and by they way, it’s not theta, it’s miu.

What’s wrong with theta? I always use theta for unknown parameters.

Aren’t we suppose to use (n-1) for samples? I never quite understood this either.

CFABLACKBELT Wrote: ------------------------------------------------------- > Aren’t we suppose to use (n-1) for samples? > > I never quite understood this either. use n-1 if mean is unknown

JoeyDVivre Wrote: ------------------------------------------------------- > What’s wrong with theta? I always use theta for > unknown parameters. Sorry, I thought you were referring to the formula as it is stated in our texts. There it is miu. Of course, as you point out, on your own you could use theta, lambda, delta, beta, alpha, or heck even a smiley face if you’d like!!