Question

An investor earns 6 percent, -1 percent, and 3 percent for years 1,2 , and 3 , respectively. Find the annualised geometric rate of return, expressed as a percentage, to two decimal points. DO NOT include the % sign. (Eg. if your calculated answer is 99.99%, enter 99.99.)

Answer 1

The annualised geometric rate of return over the three years is approximately 2.53%.

Step-by-step explanation:

To calculate the annualised geometric rate of return, we use the formula for the geometric mean:

1. Add 1 to each percentage return, remembering to convert the percentages to decimals first. This step accounts for the negative return in year 2, by adding 1 to the actual return, which avoids negative or zero values in the multiplication that follows.
2. Multiply these adjusted returns together. For example, (1 + 0.06) * (1 - 0.01) * (1 + 0.03).
3. Take the nth root of the result from step 2, where n is the number of periods (3 years in this case).
4. Subtract 1 from the result of step 3 and then multiply by 100 to convert back to a percentage.

Performing these steps, we get:

• (1 + 0.06) = 1.06
• (1 - 0.01) = 0.99
• (1 + 0.03) = 1.03

Multiplying these together yields: 1.06 * 0.99 * 1.03 = 1.07778

Taking the cube root (since we have 3 years) gives us the 3rd root of 1.07778, which is approximately 1.0253.

Finally, subtracting 1 and converting to a percentage, we have (1.0253 - 1) * 100 = 2.53%