Arithmetic vs. Geometric Average
When evaluating investment performance, it's critical to understand that not all "averages" are created equal. The math of money depends on compounding, which can make simple averages misleading.
Arithmetic Average Return
This is the simple mathematical average of your annual returns. You simply add up the returns and divide by the number of years. While easy to calculate, it does not reflect the actual wealth generated because it ignores the order and compounding of gains and losses.
Geometric Average (Time-Weighted)
The geometric average is the "true" rate of return. It represents the constant annual growth rate that would be required to reach the same final portfolio value. This is the standard used by mutual funds and professional investors because it accounts for the volatility and compounding of your money.
The "Volatility Drag"
The geometric average is almost always lower than the arithmetic average. This difference is known as volatility drag. For example, if you lose 50% one year and gain 50% the next, your arithmetic average is 0%, but your geometric average is -13.4% because you actually lost 25% of your total wealth.
Cumulative Return
The cumulative return is the total aggregate growth over the entire period. It tells you exactly how much your initial principal has grown (or shrunk) from the start to the end of the sequence.