An analyst gathered the following annual return information about a portfolio since its inception on 1 January 2003: Year Portfolio return 2003 8.60% 2004 11.20% 2005 12.90% 2006 15.10% 2007 -9.40% The portfolio’s mean absolute deviation and variance of annual returns, respectively, for the five-year period are closest to: MAD Variance A. 6.83% 77.5 B. 6.83% 96.8 C. 7.68% 77.5 D. 7.68% 96.8

I think A but i can’t seem to recall the computation for MAD? can someone help

are you using n or n-1 in the denominator? Which one and why?

sum of the absolute difference between the mean and each return divided by N. In this case its a population…

I used n not n-1 b/c they say since inception so its not a sample, i’d assume its the population that we’re getting with portfolio returns.

saurya_s Wrote: ------------------------------------------------------- > are you using n or n-1 in the denominator? Which > one and why? u need to use n; since it is ALL returns since inception; not a sample.

Which mean do you use? Arithmetic or geometric?

arithmetic…

In the calculator, BAII, what is Sx and SigmaX. and what denominator do they use? S

The population of returns is not all the returns that were observable. The population of returns is all the returns that were possible. If you want an unbiased estimator of the variance, you need to use (n-1) in the denom.

Joey, what is the answer according to you? and their correspondence on tht BAII calculator?

JoeyDVivre Wrote: ------------------------------------------------------- > The population of returns is not all the returns > that were observable. The population of returns > is all the returns that were possible. If you > want an unbiased estimator of the variance, you > need to use (n-1) in the denom. oh! thank you…

Most likely the CFA guys were wrong… but for the exam purpose - “The population variance calculation is appropriate because the analyst is analyzing all the annual returns on the portfolio since its inception.”

Very silly.

JoeyDVivre Wrote: ------------------------------------------------------- > Very silly. from the feedback pdf they gave for Mock 1!

Joey, if you interpret it as all possible annual returns?

You would have to tell me that the distribution of all possible returns on the fund was limited to exactly 5 pts and that the only returns possible were 8.6% or 11.2% or … Thus there was 0 probability of a return between -9% and 8%. Right…

JDV, beg to differ with you… oh oh, someone is deferring with Joey! Aside from CFAI, the population for this problem is not about ALL possible values since you are clearly given all the population elements. To go by what you are suggesting, there are bsically NO populations out there to speak of, which is not true. Looking at the annual returns for the S&P 500 since the index started would be the POPULATION of annual returns for the S&P 500. We are NOT talking about annual returns in general, but about a specific population… I know what we you mean, you are looking at the values of the random variable called returns…but here we are not doing that. We have a well defined population, and we have to use it as such. If it would help, consider that these returns were stated as Low, Medium, and High returns. Would you call that a sample? No, it’s the entire population. I know I shouldn’t argue with a stats professor, but I think this is basic, and I believe it is correct.

I guess the crux of the matter is whether or not you are doing inferential statistics. If you have observed the entire population then there is no need for inference because there is nothing unknown. Almost any question about portfolios would be aimed at making inferences. For example, suppose that we were trying to decide whether the portfolio was getting riskier through the years. If we divide by n and the underlying distribution of returns is stable, we expect that our variance estimate will be biased downwards but the bias is diminishing so it will look like our portfolio is getting riskier. Anyway, it’s really best if you think that populations are unobservable and parameters about them are unknowable and the purpose of statistics is to make inferences about them.