CAGR vs average annual return

Two portfolios report the same "average annual return". One of them ends with more money than the other. The average was never the number that decided it.

This is not a subtlety. The two ways of summarising a series of returns can differ by a lot, they differ in a predictable direction, and the larger of the two is the one that tends to get quoted.

Two ways to average, one of which is not about money

The arithmetic average adds the yearly returns and divides by the number of years. It is what a spreadsheet gives you for AVERAGE, and it is what "average annual return" almost always means when someone says it out loud.

CAGR, the compound annual growth rate, is the single steady rate that would have turned your starting value into your ending value over the same period. It is a geometric average, and it is the one that describes what happened to your money.

The distinction only matters because returns compound. A 10% loss removes more than a 10% gain adds back, because the gain is applied to a smaller base. Averaging percentages throws that away.

The case that makes it obvious

You start with $10,000. Year one is +50%. Year two is −50%.

Step	Value
Start	$10,000
After +50%	$15,000
After −50%	$7,500
Arithmetic average	(+50% − 50%) ÷ 2 = 0%
CAGR	−13.4% a year, for two years

The arithmetic average says you broke even. You are down $2,500. Both calculations are correct arithmetic; only one of them is a description of your portfolio.

Nothing about this example is exotic. It is just large enough to see. The same effect operates on every ordinary sequence of returns, quietly, at a smaller size.

The gap only ever runs one way

This is the part worth internalising, because it turns a curiosity into a rule.

The arithmetic average is always greater than or equal to the CAGR, and they are equal only when every single period's return is identical. Any variation at all opens a gap, and the gap widens as the variation widens.

So the two numbers are not "two estimates that might differ either way". The average is a ceiling. If you are quoted an average annual return and want to know what it did to a balance, the honest answer is always "less than that", and how much less depends entirely on how bumpy the ride was, which the average itself does not tell you.

A practical consequence: two portfolios with the same average annual return but different volatility do not end with the same amount of money. The steadier one ends with more. That is arithmetic, not a claim about which is a better investment.

Where each one is the right tool

Neither number is wrong. They answer different questions, and the error is almost always using the average where the compound rate belongs.

Use	The right figure
What happened to my balance over the period	CAGR
What a typical single year looked like	Arithmetic average
Projecting a balance forward	CAGR
Comparing two return series over one period	CAGR

Projecting with an arithmetic average is the expensive version of this mistake: compounding a number that was never a compound rate overstates the outcome, and it overstates it more the longer the projection runs and the more volatile the assumption.

What CAGR still hides

CAGR is the better summary and it is still a summary. Three things it removes, each of which matters in a real portfolio:

• The path. Two portfolios with an identical CAGR can have had completely different journeys, one steady, one with a halving in the middle. If you had to sell during the halving, the identical CAGR describes an outcome you did not get.
• Sequence, once money is moving. A poor early stretch followed by a good one is not equivalent to the reverse if you were contributing throughout, or drawing down. CAGR is order-independent by construction; your balance is not.
• Whether it was your outcome at all. CAGR of a market series says what an untouched lump sum would have done. It says nothing about a portfolio you contributed to on a schedule, which is the question money-weighted return exists for.

Two ways people compute it wrongly

Annualising a short period

Taking a three-month return and raising it to the fourth power produces a confident annual figure from three months of noise. A good quarter becomes an implausible year, and the number is presented with the same authority as a ten-year figure. Annualising is a comparison device for periods long enough to be comparable; below a year it mostly manufactures precision.

Applying the formula to an account you contribute to

This is the common one, and it looks reasonable. Ending value divided by starting value, raised to one over the number of years, minus one, applied to an account you have been depositing into.

That figure is not a return. It attributes your deposits to investment growth. An account that doubled because you contributed as much again did not return 100%, and the formula cannot tell the difference, because it only sees two balances.

The fix is to compute a time-weighted return first, which breaks the history at each cash flow so contributions cannot distort it, and then annualise that. An annualised time-weighted return is a CAGR, a properly constructed one. That is also why it is the figure to use when comparing against a benchmark, which has no cash flows to distort.

What to keep track of

• Which of the two figures you are reading, on anything reporting a multi-year return. If it is not labelled, assume nothing.
• Cash flow dates and amounts, because they are the input that decides whether an annualised figure means anything.
• The period, stated exactly. A CAGR is defined by its start and end date, and two overlapping periods are not comparable summaries of the same portfolio.
• The whole portfolio, not one account. Annualising each account separately and averaging the results reintroduces the exact error this page is about.

To run your own numbers, the CAGR calculator does both figures at once: the rate from your two balances, plus the rate your money actually earned, with the gap between them labelled as the contributions.

Luum computes time-weighted and money-weighted return over fixed periods and labels which is which. The time-weighted vs money-weighted calculator runs a period through both in your browser, and how portfolio returns are calculated sets out the method.

This article explains two calculations. It is educational, does not recommend any security or strategy, and makes no claim about what any return will be.

Common questions

Is CAGR the same as average annual return?

No, and the difference is not small. Average annual return usually means the arithmetic average of the yearly figures, which ignores compounding. CAGR is the single steady rate that actually connects your starting value to your ending value. The average is always the higher of the two unless every year was identical, so the two labels describe genuinely different numbers.

Why is my CAGR lower than the average of my yearly returns?

Because variation between the years costs you, mathematically, and the arithmetic average does not record that cost. A gain and an equal-sized loss do not cancel: the loss applies to a larger base than the gain that follows it. The wider the spread of your yearly returns, the larger that gap will be, and it can only run in that direction.

Can I calculate CAGR on an account I contribute to every month?

Not with the simple start-and-end formula, which would count your deposits as growth. You need a time-weighted return, which splits the history at every contribution and withdrawal so that only the holdings' performance is measured, and then annualise that. The result is a valid CAGR; the shortcut on two balances is not.

Which figure should I use to project my portfolio forward?

The compound rate, if you use a single figure at all. Compounding an arithmetic average forward assumes a smoothness the underlying series never had, and it overstates the projected balance by more the longer and more volatile the projection. A range of outcomes is more honest than any single rate, and neither figure is a forecast.