Why returns compound

Two periods, one result

Start with 100. A 10% rise produces 110. A subsequent 10% decline is measured from 110, leaving 99. The compounded return is −1%.

Adding percentage changes would give zero and discard the changing base. The calculation is (1 + first_return) * (1 + second_return) - 1.

Build the curve

Start wealth at 1. For each period, multiply the previous wealth by 1 + return. Keep the intermediate values: a final return alone hides the path taken to get there. An empty return series leaves wealth at 1 and total return at zero.

Simple returns require a nonzero starting price. Our introductory tool requires positive prices. Do not silently replace a missing observation with zero: that creates an artificial loss and changes the next denominator.

Check the interpretation

Compounded historical performance describes this sample. It does not tell you the return to expect next, and it does not describe the drawdowns experienced along the way.

Calculate the example, write the function, then complete the free research.