Question

A stock had returns of 16 percent, 4 percent, 8 percent, 14 percent, -9 percent, and -5 percent over the past six years. What is the geometric average return for this time period?

Answer 1

To calculate the geometric average return for a time period with multiple returns, we need to multiply all the returns together and then take the geometric mean.

In this case, the returns are 16%, 4%, 8%, 14%, -9%, and -5%. To calculate the geometric average return, we can follow these steps:

1. Convert the returns into decimal form by dividing each return by 100:
16% = 0.16
4% = 0.04
8% = 0.08
14% = 0.14
-9% = -0.09
-5% = -0.05

2. Multiply all the returns together:
0.16 * 0.04 * 0.08 * 0.14 * -0.09 * -0.05 = 0.00048384

3. Take the nth root of the result, where n is the number of returns. In this case, n is 6:
∛0.00048384 = 0.0382 (rounded to four decimal places)

4. Convert the result back to percentage form by multiplying by 100:
0.0382 * 100 = 3.82%

Therefore, the geometric average return for this time period is approximately 3.82%.