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A stock has monthly returns of −3.82%,−10.79%, −24.63%, and −18.43%. What is the stock's geometric average return?

User Shen
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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.

User Eric Y
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