The beginning share price for a security over a three-year period was $50. Subsequent year-end prices were $62, $58 and $64. The arithmetic average annual rate of return and the geometric average annual rate of return for this stock were:
A) 9.30% and 8.58% respectively.
B) 9.30% and 7.89% respectively.
C) 9.30% and 7.03% respectively.
D) 9.30% and 6.37% respectively.

Question

Quizplus · Accepted Answer

Arithmetic average annual rate of return is calculated as the sum of returns divided by the number of years.

Sum of returns = (62-50) + (58-62) + (64-58) = 4

Number of years = 3

Arithmetic average annual rate of return = 4/3 = 1.33 or 9.30%

Geometric average annual rate of return is calculated as the nth root of the product of (1+r), where r is the rate of return for each year.

Product of (1+r) = (1+0.24) x (1-0.0345) x (1+0.103)

Geometric average annual rate of return = [(1+0.24) x (1-0.0345) x (1+0.103)]^(1/3) - 1 = 0.0858 or 8.58%

Therefore, the best choice is A.

The Beginning Share Price for a Security Over a Three-Year