Question

Consider the following five monthly returns. The arithmetic average monthly return over this period is 3.40​% and the geometric average monthly return over this period is 3.30​%. Explain the difference between the arithmetic average return and the geometric average return. Are both numbers​ useful? If​ so, explain​ why? 6​% negative 3​% 7​% 8​% negative 1​% Choose the correct answer below.

A. The arithmetic average return is the best estimate of what you would earn in the​ future, so this is the number you care about. The geometric average return is useless.

B. The geometric average return is what you would have actually achieved if you had held the​ stock, so this is the number you care about. The arithmetic average return is useless.

C. There is no difference between arithmetic and geometric average returns. The two are just different methods to get the same answer.

D. Both numbers are useful. The geometric average return tells you what you would actually make if you held the stock over this period. You can use thearithmetic average return over the period as an estimate of the expected return. If you use this​ estimate, it is what you would expect to make in the next period

Answer 1

The answer will be option "d" - Both numbers are useful. The geometric average return tells you what you would actually make if you held the stock over this period. You can use the arithmetic average return over the period as an estimate of the expected return. If you use this​ estimate, it is what you would expect to make in the next period.

Explanation:

gn = (1+rc)^(1/n) - 1

In the above formula gn = geometric average return, rc = cumulative return over the entire period, n = no. of equal subset periods.

Arithmetic return = sum of all returns/n

The geometric mean differs from the arithmetic average, or arithmetic mean, in how it is calculated because it takes into account the compounding that occurs from period to period. Because of this, investors usually consider the geometric mean a more accurate measure of returns than the arithmetic mean. This, however, does not mean that arithmetic average is useless. It is useful but in a different manner than goemetric average return.