Example:For the last three years the return for Acme Corporation common stock have been -9.34%, 23.45%, and 8.92%. Find the geometric mean.
Take the cube root of (-.0934 + 1)(.2345 + 1)(.0892 + 1) = The cube root of 1.21903. On your TI calculator, enter 1.21903 and hit the yxkey, then enter .3333 = to get of 1.06825. Now you must subtract this number from one to get an answer of 6.825%.
Weighted meanis a special case of the mean that allows different weights on different observations.?
Example:A portfolio consists of 50% common stocks, 40% bonds, and 10% cash. If the return on common stocks is 12%, the return on bonds is 7%, and the return on cash is 3%, what is the return to the portfolio?
Weighted mean = [(0.50 *0.12) + (0.40 * 0.07) + (0.10 * 0.03)] = 0.091, or 9.1%
The medianis the mid-point of the data when the data is arranged from the largest to the smallest values. Half the observations are above the median and half are below the median. To determine the median, arrange the data from highest to the lowest and find the middle observation.
Example:The five-year annualized total returns for five investment managers are 30%, 15%, 25%, 21%, and 23%. Find the median return for the managers.
First, arrange the returns from hi to lo: 30, 25, 23, 21, 15.