Question

: If a stock has returns of 10 percent and 20 percent over 2 years, the geometric average rate of return can be calculated by:

A) Adding both returns
B) Taking the arithmetic mean
C) Multiplying both returns
D) Taking the harmonic mean

Answer 1

The geometric average rate of return for a stock with returns of 10% and 20% over two years is calculated by multiplying the return factors (1.10 and 1.20) and then taking the square root, resulting in approximately 14.87% average annual return. Option C.

Step-by-step explanation:

If a stock has returns of 10 percent and 20 percent over 2 years

The geometric average rate of return can be calculated by multiplying both returns and taking the nth root, where n is the number of periods.

Specifically, to find the geometric mean,

You use the formula √(p1 × p2 × ... × pn), where p1, p2, ..., pn are the return factors for each period.

The return factor is 1 plus the return (expressed as a decimal), so for a 10% return, the factor is 1.10 and for 20% it is 1.20.

Applying this to the returns given:

First, convert the percentage returns to factors: 10% becomes 1.10 and 20% becomes 1.20.

Next, multiply these factors: 1.10 × 1.20 = 1.32.

Finally, since we have two periods, take the square root (which is the second root):

√1.32 ≈ 1.1487, which corresponds to an average annual return of about 14.87%.

Thus, the correct answer is to multiply both returns (option C).