A stock had returns of 9.62 percent, −14.65 percent, 19.85 percent, 25.35 percent, and 7.65 percent over the past five years. What was the geometric average return for this stock?

The geometric average return for this stock was 8.64%.

Explanation:

Geometric average return refers to the return which will result in the correct compounded dollars at the end of the time period.

Geometric average return can be computed using the following formula:

Geometric average return = {[(1 + r1)(1 + r2) ... (1 + rn)]^(1/n)} - 1 (1)

Where r is returns from year 1 to year n.

For the stock in the question, we have:

r1 = 9.62%, 0.0962

r2 = -14.65%, or -0.1465

r3 = 19.85%, or 0.1985

r4 = 25.35%, or 0.2535

r5 = 7.65%, or 0.0765

n = 5

Substituting the values into equation (1), we have:

Geometric average return = {[(1 + 0.0962)(1 - 0.1465)(1 + 0.1985)(1 + 0.2535)(1 + 0.0765)]^(1/5)} - 1

Geometric average return = {1.51310732605096^0.20} - 1

Geometric average return = 0.0864, or 8.64%

Therefore, the geometric average return for this stock was 8.64%.

a.