Question

A stock has had returns of −18.5 percent, 28.5 percent, 18 percent, −9.6 percent, 34.3 percent, and 26.5 percent over the last six years. what are the arithmetic and geometric returns for the stock? (do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places,
e.g., 32.16.) arithmetic average return % geometric average return %

Answer 1

The arithmetic average of a group of numbers is their sum divided by the number of them.

arithmetic average = (-18.5 +28.5 +18 -9.6 +34.3 +26.5)%/6 = 13.20%

(Please note that it is meaningless to compute an arithmetic average of percentages that have different base values, as these do. It may be a decent exercise in arithmetic, but the result has no real-world meaning whatever.)

_____

The geometric mean of a set of n numbers is the n-th root of their product. Because these are stock returns, we aren't really interested in the geometric mean of the given percentages. (Such a mean of a set including negative numbers has no meaning in any event.) What we want to find is the geometric mean of the year-to-year multiplier of stock values. Then we want to convert that back to a rate of return.

... ((1-.185)(1+.285)(1+.18)(1-.096)(1+.343)(1+.265))^(1/6) ≈ 1.89791917^(1/6) ≈ 1.112703

This multiplier value of 1.1127 corresponds to a

... geometric average return = 11.27%