While computing the average price of a stock or index over a period of time, I have the choice between using an arithmetic mean or a geometric mean. Which should I use and when?
I am reading a book on Trading Systems by Kaufman and he says:
The geometric mean has advantages in application to economics and prices. A classic example compares a tenfold rise in price from 100 to 1000 to a fall to one tenth from 100 to 10. An arithmetic mean of the 2 values 10 and 1000 is 505, while the geometric mean gives
G = (10 × 1000)^(1/2) = 100
and shows the relative distribution of prices as a function of comparable growth. Due to this property, the geometric mean is the best choice when averaging ratios that can be either fractions or percentages.
I am not able to understand what he means by that last part (from "relative distribution" onward.) Could somebody please explain?