An analyst gathered the following information about the net profit margins of companies in two industries: Net Profit Margin Industry K Industry L Mean 15.0% 5.0% Standard deviation 2.0% 0.8% Range 10.0% 15.0% Compared with the other industry, the relative dispersion of net profit margins is smaller for Industry: A. L, because it has a smaller mean deviation. B. L, because it has a smaller range of variation. C. K, because it has a smaller standard deviation. D. K, because it has a smaller coefficient of variation.
A not true because you can’t find the mean deviation from info given (among other reasons) B not true because 15 > 10 C not true because 2 > 0.8 Which leaves D which is also true because 2/15 < 0.8/5
I think the important thing for this question is not to get distracted from what the question is asking (i.e., it’s asking about relative dispersion (also called coefficient of variation) and not standard deviation or range measures). (That’s a good thing to remember generally for CFA Exam questions). Cv = ó^2 / ì = Cv(K) = 2.0/15 = 0.13 Cv(L) = 0.8/5 = 0.16 So the answer is D, because Cv(K) < Cv(L) (0.13 < 0.16) Cv provides a method of measuring intrinsic variation in a population because increases in variance caused by increases in means are appropriately adjusted in a common percentage scale. This makes it a more favoured measure of dispersion (or risk) relative to the SD (ó^2). Feel free to correct me if I’m wrong.
Yes, you are absolutely correct Farina. Coefficient of variation (CV) measures the amount of dispersion in a distribution relative to the distribtuion’s mean, it eanbles us to make a direct comparison of dispersion across different sets of data. (D) is the correct answer.