Consider an investment with the returns over 4 years as shownhere:

Year. 1 2 3 4

16% 11% 10% 10%

a. What is the compound annual growth rate (CAGR) for this investment over the 4 years?

b. What is the average annual return of the investment over the 4 years?

c. Which is a better measure of the investment's pastperformance? If the investment's returns are independent and identically distributed, which is a better measure of theinvestment's expected return next year?

Explanation:

Assume the initial invest at the beginning is $100.

The investment at end of year 4 is:

100 x 1.16 x 1.11 x 1.1 x 1.1 = 155.80

a) CAGR over the 4 years = (155.8 / 100 ) ^ (1/4) = 11.72%

b) Average annual return over 4 years = (16% +11% + 10% +10%) /4 = 11.75%

c) Since the returns over the 4 year period are not much volatile, average annual return is a better measure.

If the investment's returns are independent and identically distributed, Average annual return will be the better measure because there is no correlation between returns over the years and thus there is no point to take into consideration the compounding effect by using CAGR.

A) -0.111

B) 11.75%

C) Take the first year measures for next year investment, as it gave the highest returns.

Explanation:

A) The compound annual growth rate is calculated as

(EB÷BB)^1/n - 1

EB is the ending balance

BB is the beginning balance

n is the number of years

Therefore;

(10% ÷ 16%)^1/4 - 1

(0.625)^1/4 - 1 = (0.625)^0.25 - 1

0.88914 - 1 = -0.111

Because the growth rate is negative, that means the investment did not grow, but rather the growth dropped with -0.111

B) The average annual return for this investment is to calculate the mean value for the of the annual returns

(16% + 11% + 10% + 10%) ÷ 4 = 11.75%

That means the average returns for 4 years is 11.75%

C) The better measure for the next year investment, is the measures that was taken in the first year, as it gave the investment the highest return since 4 years ago.

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