The table below gives the deviations of a portfolio's annual total returns from its benchmark's annual returns,for a 6-year period ending in 2011. The arithmetic mean return and median return are the closest to _______.
A) mean = -2.00% and median = -4.28%.
B) mean = -2.00% and median = -1.67%.
C) mean = -1.67% and median = -0.56%.
D) mean = -1.67% and median = 0.56%

Question

The table below gives the deviations of a portfolio's annual total returns from its benchmark's annual returns,for a 6-year period ending in 2011.  The arithmetic mean return and median return are the closest to _______.
A) mean = -2.00% and median = -4.28%. 
B) mean = -2.00% and median = -1.67%. 
C) mean = -1.67% and median = -0.56%. 
D) mean = -1.67% and median = 0.56%

Quizplus · Accepted Answer

To find the arithmetic mean return, we need to sum all the deviations and divide by the number of observations. Sum of deviations = (-4.5) + (-1.2) + (-2.6) + (-1.5) + (-0.6) + (5.5) = -5.9. Number of observations = 6. Therefore, the mean deviation = -5.9/6 = -0.9833 or approximately -0.98%. Since the benchmark is assumed to have a return of zero, the portfolio's return is the same as the mean deviation, which is approximately -0.98%. To find the median return, we need to arrange the deviations in ascending order: -4.5, -2.6, -1.5, -1.2, -0.6, 5.5. The middle value is the median. Since there are an even number of observations, we take the average of the two middle values: (-1.5 - 1.2)/2 = -0.56%. Therefore, the closest values to the arithmetic mean and median are -0.98% and -0.56%, respectively. The closest answer choice is C.

The Table Below Gives the Deviations of a Portfolio's Annual