A gain of 50% followed by a loss of 50% averages 0%, but 10,000 ends at 7,500. The steady yearly rate that gives the same result, the compound annual growth rate or CAGR, is a loss of 13.4% a year.
Each year’s return applies to the amount at the start of that year. The loss applies to 15,000, not 10,000, so it takes away 7,500, more than the 5,000 the gain added.
A four-year example
The four returns below average 5%, but 10,000 grows to 11,475, a steady 3.5% a year.
| Year | Return | Balance at the end of the year |
|---|---|---|
| 1 | +20% | 12,000 |
| 2 | −10% | 10,800 |
| 3 | +25% | 13,500 |
| 4 | −15% | 11,475 |
What the example leaves out
Both examples leave out fees, taxes and money added or taken out along the way. When money goes in or out at different times, the rate that accounts for the timing is the XIRR, which the calculator also works out.