What Is CAGR (Compound Annual Growth Rate)?

CAGR is the standard way to express what an investment actually returned, and the reason it exists is that the intuitive alternative — averaging the annual returns — is not merely imprecise but systematically overstates results in a way that grows with volatility.

This guide covers the CAGR formula, how to calculate annualized return over any period, the difference between CAGR and average annual return, volatility drag, and the limitations that make CAGR insufficient on its own.

Last updated: 2026-09-05

Short Answer

CAGR is the constant annual rate that would turn a starting value into an ending value over a given period: (Ending ÷ Beginning)^(1 ÷ Years) − 1. It is the correct way to state an investment's return, because averaging annual returns overstates results whenever returns vary.

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What It Means

Compound annual growth rate is the constant annual rate of return that, compounded over the holding period, would produce the observed ending value from the observed starting value. The formula is CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Years) − 1. An investment growing from $10,000 to $18,000 over five years has a CAGR of 1.8^0.2 − 1 = 12.5%. This does not describe any individual year; it is the smooth-path equivalent of whatever sequence actually occurred. Annualized return is the same idea generalized to any period length: raise one plus the total return to the power of the number of such periods in a year, then subtract one. A 6% return over six months annualizes to 1.06² − 1 = 12.36%, not 12% — the difference is the second half-year compounding on the first half-year's gains.

Quick Answer

Use CAGR whenever you need to compare investments held for different lengths of time, or to state what something actually returned. Never average annual returns to do this: because returns compound multiplicatively, the arithmetic mean describes an outcome that did not occur. A gain of 50% followed by a loss of 50% averages to zero but leaves you with 75 cents on the dollar. The size of the error is approximately half the variance, so it is negligible for stable assets and very large for volatile ones. What CAGR cannot tell you is anything about the path, the risk taken, or the effect of your own deposits and withdrawals — which is why it belongs alongside maximum drawdown and the Sharpe ratio rather than on its own.

For the full framework, see Annualized Return & CAGR.

How to Calculate and Interpret Annualized Return

Five steps that cover the calculation and the checks that keep the resulting number honest.

1. Calculate CAGR from the two endpoints: divide the ending value by the beginning value, raise the result to the power of one divided by the number of years, and subtract one. For periods that are not whole years, use the exact fraction — a 3.5-year holding uses an exponent of 1 ÷ 3.5. Include reinvested dividends in both values, or the figure measures price appreciation rather than total return.
2. Annualize shorter periods geometrically, never by multiplying. A 3% quarterly return annualizes to 1.03⁴ − 1 = 12.55%, not 12%. Then treat the result with appropriate skepticism: annualizing a single quarter assumes three more quarters exactly like it, which is why performance reporting standards discourage annualizing anything under twelve months. A short-period annualized figure is a unit conversion, not a forecast.
3. Compare CAGR against the arithmetic average to measure volatility drag. The gap between the two is driven by volatility and is approximately σ²/2 and tells you how much compounding is being eroded by variability. A portfolio whose average return is 12% but whose CAGR is 8% is losing four points a year to volatility — a strong argument that reducing variability would improve returns, not just comfort.
4. Test the sensitivity of the result to the dates chosen. CAGR depends entirely on two values, so shifting the window across a market peak or trough can move it several percentage points with no change in the underlying investment. Recalculate across several start dates, or look at rolling returns, before accepting any single figure — particularly one selected by whoever is presenting it.
5. Read CAGR alongside risk measures before drawing a conclusion. Pair it with maximum drawdown to see the worst decline actually endured and with the Sharpe ratio to see return per unit of risk. Whether any excess return reflects skill or factor exposure is the separate question alpha addresses. A 25% CAGR over three years with a 55% drawdown and a 15% CAGR over twenty years with a 25% drawdown are not comparable, and the smaller number is usually the better investment.

Time-Weighted vs. Money-Weighted Return

CAGR expresses a time-weighted return: it deliberately ignores deposits and withdrawals so it measures the investment in isolation. This is the right choice for comparing funds, since a manager does not control when investors add or remove money. Money-weighted return, calculated as an internal rate of return, incorporates the size and timing of every cash flow and measures what actually happened to your capital. The two diverge whenever contributions are uneven — an investor who added heavily just before a drawdown will have a money-weighted return well below the fund's published CAGR, while one who added at a low will do better than the headline. Neither figure is wrong; they answer different questions. When comparing investment options, use time-weighted CAGR. When assessing your own results, calculate the money-weighted return, because that is the number describing your money.

Return Pattern	Arithmetic Average	Actual CAGR	Why They Differ
+50%, −50%	0.0%	−13.4%	$100 → $150 → $75; losses need larger gains to recover
+10%, +10%, +10%	10.0%	10.0%	No variation, so the two measures agree exactly
+30%, −10%, +20%	13.3%	12.2%	Moderate volatility opens a ~1 point gap
+80%, −40%, +60%	33.3%	24.6%	High volatility drags compounded growth far below the average

CAGR Example: Why the Average Misleads

Two portfolios, both averaging 10% annual returns over 20 years on $100,000:

Portfolio A: 10% average return with 12% annualized volatility. Volatility drag of roughly 0.7 points gives a CAGR near 9.3%, growing $100,000 to approximately $591,000.
Portfolio B: 10% average return with 30% annualized volatility. Volatility drag of roughly 4.5 points gives a CAGR near 5.5%, growing $100,000 to approximately $292,000.
The arithmetic averages are identical. The ending values differ by roughly $299,000, entirely because of the difference in variability.
The path matters behaviorally as well: Portfolio B's larger swings make it substantially harder to hold for twenty years, so the realized gap for most investors is wider still than the arithmetic suggests.

Averaging the annual returns would report both portfolios at 10% and conceal a $299,000 difference. This is why CAGR is the only defensible way to state a multi-year return, and why volatility belongs in any comparison of long-run outcomes.

Key Takeaways

• CAGR = (Ending ÷ Beginning)^(1 ÷ Years) − 1 — the constant annual rate that reproduces the actual total result.
• Never average annual returns; compounding is multiplicative, and the arithmetic mean overstates results in every case where returns vary.
• Volatility drag is approximately σ²/2 — at equal average returns, the less volatile portfolio genuinely compounds to more money.
• CAGR uses only two endpoints, so it is highly sensitive to the start and end dates chosen; rolling returns give a far more honest picture.
• CAGR says nothing about the path, the risk, or the effect of your own cash flows — read it alongside maximum drawdown, Sharpe ratio, and money-weighted return.

For the full framework, examples, and FAQs, read Annualized Return & CAGR.

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Common Mistake

The most consequential thing CAGR reveals is not the return itself but volatility drag. Geometric return is approximately the arithmetic mean minus half the variance, which means two portfolios with the same average annual return but different volatility do not end up with the same money — the calmer one ends up with more, and the gap widens with the square of volatility. At a 10% average return, moving volatility from 12% to 30% costs roughly 3.8 percentage points of compounded annual growth. Over twenty years that is the difference between roughly six times your money and roughly three times it, with no difference in average return at all. This is the mathematical reason risk management is a return strategy rather than a comfort measure.

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FAQs

What is the CAGR formula?

CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Number of Years) − 1. For an investment that grew from $25,000 to $40,000 over six years: (40,000 ÷ 25,000)^(1 ÷ 6) − 1 = 1.6^0.1667 − 1 ≈ 8.15%. Use exact fractional years for periods that are not whole, and make sure both values reflect total return with dividends reinvested rather than price alone — omitting dividends can understate a broad equity CAGR by roughly two percentage points a year, which compounds into a very large error over long periods.

What is the difference between CAGR and average annual return?

Average annual return sums the yearly returns and divides by the number of years; CAGR calculates the constant compounded rate connecting the start and end values. They agree only when every yearly return is identical, and CAGR is always lower otherwise. The canonical example is +50% followed by −50%: the average is 0%, but $100 becomes $150 and then $75, a CAGR of −13.4%. The size of the divergence is approximately half the variance of returns, so it is small for stable assets and substantial for volatile ones. Since the arithmetic average describes a result that never occurred, CAGR is the figure to use for any claim about actual performance.

Is CAGR the same as annualized return?

In practice they are used interchangeably, with a slight difference in emphasis. CAGR specifically describes growth between two endpoints over multiple years. Annualized return is the broader operation of converting a return from any period into an annual-equivalent rate, which includes annualizing a month or a quarter as well as computing a multi-year CAGR. Both use geometric compounding rather than simple multiplication. The distinction that actually matters is not between these two terms but between either of them and the arithmetic average, which is a genuinely different and consistently more optimistic calculation.

What are the limitations of CAGR?

Three significant ones. It uses only two endpoints, making it highly sensitive to the dates chosen — a window beginning at a market bottom flatters the result by construction, which is why rolling returns across many start dates give a more honest picture. It contains no risk information: a 30% CAGR earned through a 60% drawdown and a 12% CAGR earned through a 20% drawdown look like the former is better, and usually it is not. And because it is time-weighted, it excludes the effect of your own contributions and withdrawals, so it will differ — often substantially — from what your account actually earned. CAGR is a summary of where an investment ended, never a description of what holding it cost.