which of the followingstatements about return distributions is least likely correct? a. if skew > 0 => mean > median b. if skew > 0 => average magnitude of positive deviations from the mean is larger than the average magnitude of negative deviations from the mean. c. if kurtosis > 3 & the analyst uses statistical models that do not account for the fatter tails, the analyst will overestimate the likelihood of very bad or very good outcomes. correct answer is c (is not correct). c should read " … UNDERestimate the likelihood …" but then, why is b correct?
I am not sure if you are saying that C or B is correct, but I believe choice B is not a correct statement (and therefore the answer) If skew is > 0, the huge bulge is to the right(idk how you are technically supposed to state that, but that is how I think of it). That means that most of the results are centered around that bulge. Therefore, most of the devations that are positive from the mean (which would be near the bulge, to the right of the peak) would be small in magnitude, in comparison to the deviations that are negative, which would be pretty far from the mean (large in magnitude). I hope this very very technical analysis helps!
this is exactly my reasoning, too however, q bank say the answer we are supposed to give is c. this implies that b is “correct” (because the question asked for the least likely correct answer).
I think you guys have problems with your Skewness and Kurtosis concepts. Let me attempt to correct them first. Skewness: is a measure of the asymmetry of the distribution. There are three types 1. no skewness or normal 2. positive or right skewed ( Bulge to the left) 3. negative or left skewed (bulge to the right) Yes the bulge leans in the opposite direction of the name. e.g. a positively skewed distribution has a mean greater than median or the average value is more than the value at the center. Because the right side with less but extreme deviations, totals more than the left side with many but small deviations. Kurtosis: is the measure of the peakedness of the distribution. The three types are 1. normal k=3 2. high peaked or kurtosis more than 3 3. low peaked or kurtosis less than three All students usually know these facts about kurtosis correctly but what they don’t know is that A distribution with kurtosis more than 3 or leptokurtic has a more acute peak (that is, a higher probability than a normal distribution of values very close to the mean) AND fatter tails (that is, a higher probability than a normal distribution of values very far from the mean). It is shaped like an up side down ‘T’ A distribution with kurtosis less than 3 or platykurtic has a peak lower than normal (that is, a lower probability than a normal distribution of values very close to the mean) AND thinner tails (that is, a lower probability than a normal distribution of values very far from the mean). And higher probability of values lying at moderate distances from the mean. It is shaped like dome. Now, this may seem different from what you have learned, but this is right and you can recheck it with your curriculum. Now, looking at the question we have to find the wrong statement. Everybody agrees that A is correct. B is also correct because is skewness is greater than 0 then we are dealing with positive or right skewness in which the bulge leans to the left and therefore, average magnitude of positive deviations from the mean is larger than the average magnitude of negative deviations from the mean C is the wrong statement as a leptokurtic or more peaked distribution has fatter tails and does account for extreme deviations. enjoy
Great explanation my friend. Thanks!!