What compounding is, and why the curve bends
Compounding is earning returns on your past returns, not just on your original capital. In year one you make a return on your starting balance. In year two you make a return on the starting balance plus year one's gains, so the base you are growing is already bigger. Every period after that builds on a larger base than the one before it.
That is why a compounding growth curve bends upward instead of climbing in a straight line. A fixed percentage applied to a growing balance produces bigger and bigger dollar gains, even though the rate never changes. Give it enough years and the curve steepens dramatically, which is why time is the single most powerful ingredient in the whole equation.
CAGR: the one number that tells the truth
To describe compounded growth with a single figure, you use the Compound Annual Growth Rate, or CAGR. It is the smoothed annual rate that takes you from a starting value to an ending value over N years, as if you had grown by the exact same percentage every year. It ignores the bumps along the way and answers one clean question: what steady rate would have produced this result?
So this account did not grow by some vague “a lot over five years.” It grew at a compound rate of about 9.86% per year. That single figure lets you compare two accounts, two funds, or two strategies on equal footing, regardless of how choppy the ride was in between.
Why the average return lies
CAGR is not the same thing as the average, or arithmetic mean, of your yearly returns, and the average almost always overstates your real result. The reason is volatility. When returns swing, the average adds up the percentages and divides, but your money does not work that way, because each year's result is applied on top of the last.
The classic trap: a year of +50% followed by a year of −50%. The arithmetic average is 0%, so it looks like you broke even. But run the actual dollars. Start with $100. Up 50% takes you to $150. Down 50% takes you to $75. You did not break even, you lost 25% of your money. CAGR reports the truth here at roughly −13.4% per year, because that is the steady rate that turns $100 into $75 over two years. The average said zero; the account said down a quarter.
Volatility drag, the fee nobody quotes
That gap between the average and the real compounded rate has a name: volatility drag. The bigger the swings, the wider the gap, and it only ever works against you. A loss needs a larger gain to undo it, because the gain has to work on a shrunken base. Down 50% requires a 100% gain just to get back to even. That asymmetry is baked into compounding, and it is exactly why volatile equity curves quietly underperform their own advertised averages.
Why consistency compounds better than swings
Put it all together and the lesson is counterintuitive but exact: consistent, smaller returns compound better than wild swings with the same average. Two strategies can post the identical arithmetic mean, and the smoother one will end with more money every single time, because it pays less volatility drag along the way. This is another reason drawdowns and volatility are the enemies of long-run growth, not just the source of a bumpy ride. The steady hand does not merely feel calmer; it finishes richer.