CAGR (Compound Annual Growth Rate)

Quick Definition

CAGR (Compound Annual Growth Rate) is the rate at which an investment would have grown each year if it had grown at a steady annual rate over a given period. It smooths out the volatility of year-to-year returns into a single representative annual figure, making it the standard metric for comparing investment performance across different time periods.

CAGR = (Ending Value / Beginning Value)^(1/Number of Years) - 1

What It Means

CAGR answers the question: "If this investment grew at the same rate every year, what would that rate have been?"

Real investments do not grow at a steady rate — they have great years and terrible years. CAGR ignores the path and focuses on the outcome: how much did $1 become, expressed as an equivalent annual rate?

This makes CAGR the only fair way to compare:

• An investment that returned 50% in year 1, -20% in year 2, and 30% in year 3
• An investment that returned 18% each year for 3 years

Both might produce similar total returns, but CAGR reveals the equivalent annual growth rate for each.

CAGR Formula and Calculation

CAGR = (Ending Value / Beginning Value)^(1/n) - 1

Where n = number of years

Example 1: Basic Stock Investment

• Beginning value: $10,000
• Ending value: $18,500
• Time period: 6 years
• CAGR = (18,500 / 10,000)^(1/6) - 1 = (1.85)^0.1667 - 1 = 10.8%

Example 2: S&P 500 Long-Term

• S&P 500 value in 1994: ~470
• S&P 500 value in 2024: ~5,000
• Time period: 30 years
• CAGR = (5,000 / 470)^(1/30) - 1 = (10.64)^0.0333 - 1 = 8.3% (price only, no dividends)
• With dividends reinvested: approximately 10.5%

Example 3: Revenue Growth (Business Metric)

• Company revenue in 2019: $500M
• Company revenue in 2024: $850M
• CAGR = (850 / 500)^(1/5) - 1 = (1.70)^0.2 - 1 = 11.2% annual revenue growth

CAGR vs. Average Annual Return: A Critical Distinction

These are not the same, and the difference matters enormously:

Scenario: A $10,000 investment with these annual returns:

• Year 1: +50%
• Year 2: -40%
• Year 3: +30%

Simple average: (50% + (-40%) + 30%) / 3 = 13.3% average annual return

Actual calculation:

• After Year 1: $10,000 × 1.50 = $15,000
• After Year 2: $15,000 × 0.60 = $9,000
• After Year 3: $9,000 × 1.30 = $11,700

CAGR = ($11,700 / $10,000)^(1/3) - 1 = 5.4%

The simple average was 13.3% but the actual annualized return was only 5.4%. This gap is called volatility drag — large losses require proportionally larger gains to recover. Losing 50% requires a 100% gain just to break even.

This is why CAGR is the honest measure and simple averages can be misleading.

CAGR Benchmarks: What Good Looks Like

The S&P 500's ~10.5% CAGR is the benchmark that active managers, hedge funds, and individual stock-pickers must surpass to justify their approach over passive index investing.

The Power of Small CAGR Differences

Small differences in CAGR compound into enormous wealth differences over long periods:

$10,000 invested for 30 years:

The difference between a 7% and 10% CAGR over 30 years is the difference between 7.6x and 17.4x your money — more than double the outcome from a 3 percentage point difference.

This is why minimizing fees (which directly reduce CAGR) is so powerful. A 1% expense ratio that reduces your CAGR from 10% to 9% turns a $174,494 outcome into $132,677 — a $41,817 difference on a $10,000 investment.

CAGR for Business Analysis

CAGR is used extensively to communicate company growth rates:

Investors typically pay premium P/E multiples for companies with high revenue and earnings CAGR because high growth rates, if sustained, justify high current valuations.

Key Points to Remember

• CAGR = (End/Start)^(1/n) - 1 — the annualized equivalent return over any period
• CAGR always tells the truth about returns; simple averages overstate returns due to volatility drag
• The S&P 500's historical ~10.5% CAGR (with dividends) is the benchmark for all investments
• Small CAGR differences compound into massive wealth differences over decades
• A 1% fee reducing CAGR from 10% to 9% costs $41,817 over 30 years on a $10,000 investment
• CAGR is used for both investment returns and business revenue/earnings growth measurement

Common Mistakes to Avoid

• Using simple average returns instead of CAGR: Fund companies sometimes advertise average annual returns that are higher than the actual CAGR. Always verify which is being quoted.
• Comparing CAGR over different time periods: A 10-year CAGR of 15% during a bull market tells a different story than a 30-year CAGR of 10% through multiple cycles.
• Projecting historical CAGR indefinitely: Past performance does not guarantee future results. Using the S&P 500's historical 10% CAGR for 50-year projections is a reasonable planning assumption, not a guarantee.

Frequently Asked Questions

Q: How do I calculate CAGR on a calculator? A: Divide ending value by beginning value. Press the y^x or x^y key, then enter 1 divided by the number of years. Press equals. Subtract 1. Multiply by 100 for the percentage. For example: $18,500 / $10,000 = 1.85. Press y^x, enter 0.1667 (for 6 years = 1/6). Result: 1.108. Subtract 1: 0.108. Multiply by 100: 10.8% CAGR.

Q: What is the difference between CAGR and IRR? A: CAGR measures the growth of a single lump-sum investment. IRR (Internal Rate of Return) handles multiple cash flows at different times — useful for investments with ongoing contributions or distributions, like real estate or private equity.

Q: Is a higher CAGR always better? A: Generally yes, but not without considering risk. A 20% CAGR with extreme volatility (losing 60% some years) may produce worse risk-adjusted outcomes than a 12% CAGR with steady, moderate volatility. The Sharpe ratio measures return relative to risk.