why does schwser say AM is better than GM

CFA Level I
#1

Given rates of return on an index for the past 10 years, the arithmetic mean of these returns is:

A) statistically the best estimator of the next year’s rate of return. B) statistically the best estimator of the compound annual rate of return over multiple periods. C) the compound annual rate of return that would have resulted in the same change in wealth as the actual rates of return in the past years.

Click for Answer and Explanation

The arithmetic mean of past years’ returns is statistically a better estimator of the next year’s returns than the geometric mean. The geometric mean of past years’ returns is the compound annual rate of return that would have resulted in the same change in wealth as the compound individual years’ rates of return over the period. For estimating future multi-year returns, the geometric mean of past years’ returns is statistically a better estimator than the arithmetic mean.

#2

The asnwer was A.

When do we use GM?

#3

This question has a good chance of being 1 question on the exam.

What I would think for the exam is they give you past returns of a firm say in the past decade. From that it may be into two questions.

So say, you have solved and got 5.8% as the g.mean and 6 as the a.mean.

If they ask you, please forecast the value/return for one year, you use 1.06*Prev. value and contrastly, if they ask you please estimate the return of the stock/index/port in 3years’ time, use base value * 1.058^3.

Hope that helps.

Use a. mean for 1 year estimates and g. mean for multiple periods.