What is CAGR and how is it different from average return?

CAGR (Compound Annual Growth Rate) is the geometric mean return — the smooth annual rate that takes a beginning value to an ending value over a given period. Arithmetic average is the simple sum of annual returns divided by years. They differ whenever returns vary across years. A portfolio that earns +50% then -50% averages 0% arithmetically but loses 25% over the period (CAGR ≈ -13.4%). CAGR is the honest performance measure; arithmetic average flatters volatile returns.

How do I calculate CAGR?

CAGR = (Ending Value / Beginning Value)^(1/Years) − 1. For a $10,000 investment growing to $18,000 over 5 years: (18,000/10,000)^(1/5) − 1 = 1.8^0.2 − 1 = 1.1247 − 1 = 12.47% annual CAGR. The exponent (1/Years) is the key step — it converts total growth into an annualized rate.

CAGR doesn't capture volatility, drawdowns, or sequence of returns. Two investments with identical CAGRs can have wildly different risk profiles. For investments with cash flows in and out (contributions, withdrawals), use IRR or time-weighted return instead. CAGR is also misleading over very short periods (under 3 years) where the geometric mean is dominated by single-year noise.

What is the Rule of 72?

A back-of-envelope estimate: years to double an investment ≈ 72 ÷ annual return percent. At 8% return, money doubles in 9 years. At 12%, in 6 years. The rule is exact at about 7.85% and accurate within a tenth of a year for returns between 5% and 15%.

What's a typical long-term CAGR for stock indexes?

S&P 500 with reinvested dividends from 1957-2024: roughly 10.5% CAGR nominal, 7.0% real (inflation-adjusted). U.S. small-cap (Russell 2000) ~11% nominal. International developed (MSCI EAFE) ~8% nominal. Emerging markets (MSCI EM) ~9% nominal but with far higher volatility.

Is CAGR before or after fees?

Both versions exist. 'Gross of fee' CAGR is the raw investment return; 'net of fee' is after manager fees and expense ratios. For mutual funds and ETFs, published CAGRs are net of fund expense ratios. For separate accounts and hedge funds, both are typically disclosed. Always confirm which is being quoted.

Finance

Annualized Rate of Return Calculator

Calculate the compound annual growth rate (CAGR) of any investment.

Beginning Value ($)

Ending Value ($)

Holding Period (years)

Formula:
CAGR = (Ending / Beginning)^(1/Years) − 1
Total Return = (Ending − Beginning) / Beginning × 100

CAGR is the geometric mean of annual returns — the single number that honestly summarizes how an investment performed across time. Headlines and marketing materials prefer the arithmetic average because it always looks higher; reality, regulators, and CFA charterholders use CAGR.

CAGR vs arithmetic average

Imagine a portfolio earns +60% in year 1 and -40% in year 2. Arithmetic average = (60 − 40) / 2 = 10%. Sounds great. Reality: $100 → $160 → $96. Total return: -4%. CAGR over two years: (96/100)^0.5 − 1 = -2.02%. The arithmetic average lied by 12 percentage points. The bigger the volatility, the bigger the lie — a phenomenon known as volatility drag or variance drain.

Worked example: $10,000 to $18,000 over 5 years

Total Return = (18,000 − 10,000) / 10,000 = 80%
CAGR = (18,000 / 10,000)^(1/5) − 1 = 1.8^0.2 − 1 = 12.47%/year
Rule of 72 doubling time at 12.47%: 72 / 12.47 ≈ 5.8 years
Projected forward 5 years at same CAGR: $18,000 × 1.1247^5 ≈ $32,400

Historical CAGRs across asset classes

Asset class	Period	Nominal CAGR	Real (after CPI)
S&P 500 (incl. dividends)	1957-2024	~10.5%	~7.0%
US small-cap (Russell 2000)	1979-2024	~10.7%	~7.2%
International developed (MSCI EAFE)	1970-2024	~8.5%	~4.5%
Emerging markets (MSCI EM)	1988-2024	~9.0%	~6.0%
US Bonds (Bloomberg Agg)	1976-2024	~5.4%	~2.0%
Gold	1971-2024	~7.8%	~3.2%
US Real Estate (Case-Shiller)	1987-2024	~4.1%	~1.4%
Inflation (CPI-U)	1957-2024	~3.5%	—

When CAGR isn't enough: TWR and IRR

CAGR works for buy-and-hold with no contributions or withdrawals. For accounts where you add money (dollar-cost averaging into a 401(k)) or withdraw (RMDs in retirement), two more rigorous measures exist:

Time-Weighted Return (TWR): Strips out the effect of cash flows to measure manager skill. The default reporting standard for mutual funds and separate accounts under GIPS.
Internal Rate of Return (IRR): Solves for the rate that makes NPV of all cash flows equal zero. Includes the effect of timing — when you added vs withdrew matters. The default for private equity, real estate, and personal finance scenarios with deposits/withdrawals.

Three CAGR pitfalls to avoid

Short horizons. CAGR over 1-3 years tells you very little about long-term return. Single-year noise dominates.
Cherry-picked dates. Starting in March 2009 and ending in February 2022 produces dramatically different CAGRs than the same investment from October 2007 to March 2009. Always disclose start/end.
Ignoring inflation. A 5% nominal CAGR during 3% inflation is a 2% real CAGR. Real returns are what matter for purchasing power.

FAQ

How does CAGR handle negative returns?

The formula works directly when ending value < beginning value (CAGR will be negative). It breaks if ending value goes through zero (e.g., complete loss) — apply common sense in that case.

How is CAGR annualized for partial years?

Use the fractional year in the exponent. 18 months = 1.5 years; CAGR = (End/Begin)^(1/1.5) − 1.

What's the highest sustainable CAGR ever?

Warren Buffett's Berkshire Hathaway: ~19.8% CAGR from 1965-2024, the gold standard for long-horizon performance. Renaissance Technologies' Medallion Fund reportedly ran ~40% net CAGR, but it's closed to outside capital.

Can CAGR exceed annual return?

No — CAGR is always less than or equal to the arithmetic average of annual returns (Jensen's inequality). Equality holds only when all annual returns are identical.

How does inflation affect CAGR?

Subtract inflation CAGR from nominal CAGR for an approximate real CAGR. Exact formula: (1 + nominal) / (1 + inflation) − 1.

Is CAGR the same as ROI?

No — ROI is total return (percent change in value). CAGR is the annualized equivalent. ROI of 80% over 5 years = CAGR of 12.47%.

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Sources

Educational only; not investment advice. Reviewed by Priya Venkatesan, CFA, on March 2, 2026.