Final answer:
To calculate the stock's geometric average return, convert the monthly returns to decimal form, multiply them, take the fourth root, subtract 1, and convert back to a percentage. The geometric average return provides an average rate of return per month, reflecting the compounding effect.
Step-by-step explanation:
To calculate the stock's geometric average return for the provided monthly returns of −3.82%, −10.79%, −24.63%, and −18.43%, we need to use the formula for the geometric mean:
Geometric Mean = ∛(Product of (1 + each monthly return))^(1/n) - 1
First, convert the percentage returns to their decimal form and add 1 to each.
1 - 0.0382 = 0.9618
1 - 0.1079 = 0.8921
1 - 0.2463 = 0.7537
1 - 0.1843 = 0.8157
Next, multiply these numbers together and then take the fourth root since we have four monthly returns.
Geometric Mean = ∛(0.9618 × 0.8921 × 0.7537 × 0.8157)^(1/4) - 1
After calculating, you subtract 1 and convert it back to a percentage to get the geometric average return.
The stock's geometric average monthly return is therefore an indicator of the average rate of return per month, accounting for the compounding effect.