The difference in one example
The cleanest way to see why these two numbers diverge is the classic up 100, down 50 case. Imagine you put 1,000 pounds into something that gains 100 percent in year one, taking it to 2,000 pounds, then loses 50 percent in year two. A 50 percent fall from 2,000 is 1,000, so you end exactly where you started. Your money has gone nowhere.
Now look at the two ways of describing that. The simple, or arithmetic, average return adds the yearly figures and divides by the count: plus 100 percent and minus 50 percent average to plus 25 percent a year. That sounds like a healthy return, yet your balance is unchanged. The CAGR, the compound annual growth rate, asks a different question: what single steady rate turns 1,000 into 1,000 over two years? The answer is 0 percent. The CAGR tells the truth, and the average flatters a result that was, in reality, flat.
Why the gap appears, and why it always favours the average
The reason is compounding combined with volatility. Percentage gains and losses are not symmetrical: a 50 percent loss needs a 100 percent gain to recover, because once you are down to half, you have to double just to get back. The simple average treats every percentage as equal and interchangeable, so it never sees this asymmetry. CAGR multiplies the years together rather than adding them, so it does.
This is not a quirk of one example. The CAGR is mathematically always less than or equal to the arithmetic average whenever returns vary at all, and the two are only equal when every year is identical. The size of the gap grows with volatility, which is why steady, boring returns show almost no difference between the two figures, while a wildly swinging investment can show a cheerful positive average sitting on top of a miserable CAGR. Whenever you see a fund or asset quoted with a big average annual return, it is worth asking whether that is a simple average dressing up a bumpier compounded reality.
A worked example with real numbers
Take four years of returns for a single holding: plus 30 percent, minus 20 percent, plus 25 percent, then minus 10 percent. The arithmetic average is simple: add 30, minus 20, 25 and minus 10 to get 25, then divide by 4, giving plus 6.25 percent a year. That is the number a careless summary might headline.
Now follow the actual money. Start with 10,000 pounds. After plus 30 percent it is 13,000. After minus 20 percent it is 10,400. After plus 25 percent it is 13,000 again. After minus 10 percent it ends at 11,700. To find the CAGR, divide the end by the start, 11,700 divided by 10,000, which is 1.17, then raise it to the power of one quarter and subtract one. That works out to about 4.0 percent a year. So the same four years are either 6.25 percent or 4.0 percent depending on which measure you use, and only the 4.0 percent CAGR actually reproduces the 11,700 pound balance you are holding. You can check figures like these with our CAGR calculator, which takes a start value, end value and number of years and returns the compounded rate.
When each measure is the right tool
CAGR is the measure to trust when you want to know what actually happened or to compare two investments over the same window. Because it collapses a messy run of years into one honest compounded rate, it lets you line up a fund against an index, or one savings product against another, on equal terms. It is also the rate the Rule of 72 expects: if you want to estimate how long an investment takes to double, feed in the CAGR, not the flattering average.
A simple average still has uses. It can give a quick feel for a typical year, and it is the correct input for certain forward looking models that deliberately work with expected single period returns. The mistake is using it to describe what you earned over multiple years, because there it systematically overstates the result. A useful habit: quote CAGR for past performance, and be suspicious of any headline average return that is not labelled clearly.
- Comparing real past performance: use CAGR.
- Estimating doubling time or long run growth: use CAGR.
- Describing a single typical year in rough terms: a simple average is fine.
- Accounting for deposits and withdrawals: neither, use a money weighted return.
Putting it to work
The practical takeaway is to read return figures carefully and always ask which one you are looking at. If a product advertises an average annual return, that number can be legitimately higher than the growth you would have banked, especially for volatile assets, so reach for the CAGR before you judge. When you are weighing up a lump sum investment against its total gain, our ROI calculator gives you the overall percentage return, and the compound interest calculator lets you project a steady CAGR forward to see where a pot might land.
None of this changes how an investment behaves; it changes how clearly you see it. CAGR is simply the more honest lens, smoothing the journey into a single rate that genuinely reconciles your start and end balances. This is general educational information, not financial advice; for decisions that matter, model your own figures or speak to a qualified, regulated adviser.