Question

A 5-year investment has the following annual returns: +14%;

-12%; +6%; -10%; +30%. Using the proper method for calculating
investment returns, what is the investments annualized return?

Answer 1

To find the annualized return of the investment with specified annual returns, one should use the geometric mean. Upon calculation, the result is approximately 3.96%, which is the investment's annualized return over the 5-year period.

Step-by-step explanation:

To calculate the annualized return of a 5-year investment with the given annual returns of +14%, -12%, +6%, -10%, and +30%, we will use the geometric mean. The formula for calculating the annualized return (also known as the compound annual growth rate, CAGR) is:

((1 + r1) × (1 + r2) × ... × (1 + rn))^(1/n) - 1

Where 'r' represents the decimal form of each annual return and 'n' is the number of years. Applying these values:

((1 + 0.14) × (1 - 0.12) × (1 + 0.06) × (1 - 0.10) × (1 + 0.30))^(1/5) - 1

Calculating the above gives us the annualized return:

((1.14) × (0.88) × (1.06) × (0.90) × (1.30))^(1/5) - 1 = (1.21348928)^(1/5) - 1

=(1.0396449) - 1

= 0.0396449 or 3.96%

Therefore, the investment's annualized return is approximately 3.96%.