The compound annual growth rate (CAGR) measures the “smoothed” rate at which an investment grows from a starting value to an ending value over time. It assumes growth compounds each year.
The formula is:
(where $n$ is the number of years). It is the most accurate way to compare the performance of different investments over the same period.
Formula:
> CAGR = (Ending Value / Beginning Value)^(1/n) − 1
Where:
- Ending Value = Final value of the investment
- Beginning Value = Initial value
- n = Number of years
- ^ (1/n) = The nth root of the ratio
Worked Example
You invested $10,000 in 2019. By 2024 (5 years), it grew to $18,000.
CAGR = ($18,000 / $10,000)^(1/5) − 1
= (1.8)^(0.2) − 1
= 1.1247 − 1
= 12.47% per year
This means your investment grew at an equivalent of 12.47% per year – even though the actual year-by-year returns may have fluctuated significantly.
CAGR vs Average Annual Return: An Important Difference
| Metric | Calculation | What It Shows |
|---|---|---|
| CAGR | Geometric mean (accounts for compounding) | True smoothed annual return |
| Average annual return | Simple arithmetic mean | Average of individual year returns |
Why they differ:
Year 1: +50% (portfolio goes from $10,000 to $15,000)
Year 2: −33% (portfolio drops from $15,000 to $10,050)
- Average return: (+50% − 33%) / 2 = +8.5% (looks positive)
- CAGR: ($10,050 / $10,000)^(1/2) − 1 = 0.25% (tells the real story)
The average is misleading here. CAGR reflects the actual compounded result – you barely broke even.
Calculating CAGR in Excel
=((Ending Value / Beginning Value)^(1/Years))−1
Or use the RATE function:
=RATE(n, 0, −Beginning Value, Ending Value)
Common Uses of CAGR
| Application | What It Measures |
|---|---|
| Investment returns | Portfolio or stock performance over multiple years |
| Revenue growth | How fast a company’s revenue is growing |
| Earnings growth | Earnings per share growth rate |
| Market size projections | Industry growth forecasts |
| Dividend growth | Rate of dividend increases over time |
CAGR Benchmarks for Context
| Asset Class | Historical CAGR (Long-Term) |
|---|---|
| S&P 500 (US stocks) | ~10% nominal / ~7% real |
| US bonds | ~3-5% |
| Real estate | ~4-8% |
| Gold | ~7-8% |
| Cash / savings | ~1-3% |
| Bitcoin (2013-2023) | ~100%+ (with extreme volatility) |
Limitations of CAGR
- Ignores volatility: Two investments with the same CAGR can have wildly different risk profiles
- Doesn’t show interim losses: A high CAGR can mask years of painful drawdowns
- Assumes reinvestment: CAGR assumes returns are reinvested – not always realistic
- Backward-looking: Past CAGR doesn’t guarantee future performance
Use CAGR alongside metrics like standard deviation, maximum drawdown, and Sharpe ratio for a complete picture.
The Bottom Line
Compound annual growth rate is the cleanest way to express multi-year growth as a single comparable number. It removes year-to-year noise and shows what growth actually compounded to. Use it to evaluate investments, benchmark business performance, and compare alternatives – just remember it’s a smoothed average, not a guarantee.
