How this number is made
The arithmetic average adds the four returns and divides by four. The geometric average is the compound rate that produces the same four-year result. The geometric number is the one that matches wealth. The arithmetic number is larger whenever the returns are not identical, and people quote it because it looks better.
- Type each year as a percent. A loss is negative.
- Four years is the form. It is not a claim that four years is a full market cycle.
Formula
Arithmetic = the sum of the returns ÷ 4. Geometric = (the product of 1 + each return) ^ (1 ÷ 4) − 1.
Worked example
With the figures already in the form, geometric average is 4.78%.
Questions
Which one should I use?
Geometric, if the question is how the account compounded. Arithmetic, if the question is the typical year in a simple average.
What if a year lost everything?
A −100% return makes the geometric result −100%. The product includes a zero.