I have a question, when you need to calculate a variance for a 7-year period returns of a portfolio, what type of variance should you use if the question does not indicate which one to use? For instance, 2000 5.5% 2001 -8.7% 2002 13.0% 2003 24.0% 2004 -5.6% 2005 2.3% 2006 12.0%
i think you should calc population var for this example because we are looking at whole 7yrs. Var=110.5 I hope exam will be clear enough to know which one to calculate.
thanks, are you from baruch?
yes, are u too?
yea, just graduated this past semester. How about you?
2nd yr mba. how’s prep going for you?
it’s going good, but i stumbled upon the cfai mock got a 63.3%… need to study hard…
you should calculate sample variance because you are given a sample of returns (not population which is the whole set of possible returns)
maratikus Wrote: ------------------------------------------------------- > you should calculate sample variance because you > are given a sample of returns (not population > which is the whole set of possible returns) Completely agree, but “the answer” may be different…
^ Hmmmm. I think that the variance required here is the population variance. You only need to calculate the sample variance if you know that the data is part of a sample set. I’d go with population variance because there is nothing in the question that alludes to sampling. Would agree though that the question is not set up clearly enough considering the topic.
Remember that it is not about sampling, it’s about bias and how you get the mean. In this case, you would certainly calculate X-bar which should lead you to use the sample variance. Your only way out of that is to say that X-bar is the same as the population mean because the entire distribution is comprised of these observed numbers and they are all equally likely. Somewhere in the middle of that last sentence you should start mumbling and looking down.
That’s pretty confusing. Joey, On the test will it say Sample or make a clear distinction of which needs to be calculated?
Joey, are you saying that because you are assuming that the set of 7 numbers above is not the whole population? (On review it probably makes sense to assume that a set of 7 performance data points is only a sample and therefore to use the sample variance). I understand your point above and I’d be interested to understand your thoughts on the following example then. If I were to ask what the variance of the set {2,3,4,5,6,7,8,9} was. What would the answer be: 1). If you knew that the population set was the number system of positive integers between 2 and 9 inclusive? 2). If you knew that the population set was the number system of positive integers between 1 and 10 inclusive? In 1, if would calculate the popn. variance because I would have mu. In 2, the sample variance, because I would only have Xbar. My point was that the question doesn’t specifically tell you whether it is referring to scenario 1 or scenario 2, leading to assumptions being made. Critique away …
BishBosh Wrote: ------------------------------------------------------- > Joey, are you saying that because you are assuming > that the set of 7 numbers above is not the whole > population? (On review it probably makes sense to > assume that a set of 7 performance data points is > only a sample and therefore to use the sample > variance). > > I understand your point above and I’d be > interested to understand your thoughts on the > following example then. > > If I were to ask what the variance of the set > {2,3,4,5,6,7,8,9} was. What would the answer be: > Clearly a sample. Calculate the sample variance. > 1). If you knew that the population set was the > number system of positive integers between 2 and 9 > inclusive? > Not relevant. > 2). If you knew that the population set was the > number system of positive integers between 1 and > 10 inclusive? > Not relevant. > > In 1, if would calculate the popn. variance > because I would have mu. > I don’t know mu unless you tell me that they are equally likely and then I would calculate the variance of the distn. > In 2, the sample variance, because I would only > have Xbar. > > My point was that the question doesn’t > specifically tell you whether it is referring to > scenario 1 or scenario 2, leading to assumptions > being made. > > > > > Critique away … At the end of the day, you should almost always calculate the sample variance. If your conclusions depend on the difference between the sample variance and the population variance, you shouldn’t be making them.
so the answer is?
there’s also one similar in the mock exam, the questions does not address which variance we should use. under this circumstances, what should be our approach?
They just aren’t going to ask you to calculate a variance on the exam and have a sample variance be right and a population variance be wrong. Are they going to penalize you for calculating a biased estimator? 1) Who says all estimators ought to be unbiased? 2) Since we don’t use the sample variance for anything in particular, shouldn’t we be concerned with the bias of the sample standard deviation? The sample std dev is biased. 3) The population variance is the MLE under normality and MLE’s are good things to have. 4) Neither one is admissable etc, etc.