Average versus compound
Type yearly returns in percent, separated by commas, to compare the simple average with what the money actually did.
CAGR = (ending ÷ starting)^(1 ÷ years) − 1. It ignores the path in between, so two investments with the same CAGR can have had very different ups and downs.
Examples
Berkshire Hathaway, 1965 to 2024. Warren Buffett's 2024 shareholder letter put the compounded annual gain in Berkshire's market value per share at 19.9% from 1965 through 2024, against 10.4% for the S&P 500 with dividends. Those two rates look like a gap of about two to one. Over 60 years, compounding turned it into an overall gain of about 5,500,000% for Berkshire against about 39,000% for the index.
The Nasdaq after 2000. The Nasdaq Composite peaked above 5,000 in March 2000 and fell about 78% by October 2002. To get back to even after a 78% fall, an investment has to grow about 4.5 times. The index did not close above its 2000 high again until 2015. Any average of yearly returns over that stretch hides how long the money was underwater.
Explain it like I'm 13
Say you have 100 points in a game. One round you win 50% more, so you have 150. Next round you lose 50%, which is half of 150, so you have 75. The "average" of +50 and −50 is zero, but you lost a quarter of your points.
CAGR is the honest number. It asks: if you had grown by the same amount every round, what amount would get you from where you started to where you ended?
Questions
What is CAGR?
Compound annual growth rate: the single steady yearly rate that would take a starting value to an ending value over a number of years.
Why is CAGR lower than the average return?
Losses hurt more than gains help. A 50% gain followed by a 50% loss averages 0%, but leaves you with 25% less money. CAGR shows what really happened to the money.
What is the rule of 72?
Divide 72 by the yearly rate to estimate how many years it takes to double. At 8% a year, about 9 years.