CAGR Formula: How to Calculate Compound Annual Growth Rate
⚡ Key Takeaways
- CAGR (Compound Annual Growth Rate) measures the smoothed annual rate of return for an investment over a specified period
- It eliminates year-to-year volatility to show what the equivalent steady growth rate would have been
- CAGR is calculated using only the beginning value, ending value, and the number of years
- It is more accurate than simple average return for comparing investments of different durations
- CAGR does not reflect risk or volatility, so it should be used alongside metrics like the Sharpe ratio
What Is CAGR?
CAGR (Compound Annual Growth Rate) is the rate at which an investment would have grown if it had grown at a steady rate each year. It smooths out the year-to-year fluctuations and provides a single, clean number that describes the investment's growth trajectory.
CAGR = (Ending Value / Beginning Value)^(1/Number of Years) - 1CAGR is the standard metric for comparing the performance of investments, portfolios, and business growth over different time periods. It is more accurate than a simple average return because it accounts for the compounding effect.
How to Calculate CAGR
Basic Calculation
You invested $10,000 five years ago, and your investment is now worth $18,000.
CAGR = ($18,000 / $10,000)^(1/5) - 1
CAGR = (1.80)^(0.20) - 1
CAGR = 1.1247 - 1
CAGR = 0.1247 = 12.47%
Your investment grew at a compound annual rate of 12.47%. This means that if the investment had grown by exactly 12.47% every single year, you would end up with the same $18,000.
Why Not Just Average the Returns?
Consider an investment with the following annual returns:
| Year | Return | Value (Starting at $10,000) |
|---|---|---|
| 1 | +50% | $15,000 |
| 2 | -30% | $10,500 |
| 3 | +20% | $12,600 |
Simple average return: (50% + (-30%) + 20%) / 3 = 13.3% CAGR: ($12,600 / $10,000)^(1/3) - 1 = 8.0%
The simple average (13.3%) is misleadingly high. The actual compound growth rate is only 8.0%. The difference exists because of the volatility drag: a 30% loss requires a 43% gain just to break even, not a 30% gain.
Pro Tip
Interpreting CAGR Values
| CAGR | Context |
|---|---|
| 3-5% | Typical for bonds and conservative investments |
| 7-10% | Historical long-term stock market average |
| 10-15% | Strong performance, beating the market |
| 15-25% | Excellent; top-tier fund manager territory |
| Above 25% | Exceptional but difficult to sustain long-term |
The historical CAGR of the S&P 500 (including dividends) is approximately 10% over the long term. Any investment or strategy that consistently delivers a CAGR above 10% is outperforming the market.
Using CAGR for Investment Comparison
CAGR's greatest strength is its ability to compare investments with different time periods and different volatility profiles.
Example: Comparing Two Investments
| Investment | Starting Value | Ending Value | Years | CAGR |
|---|---|---|---|---|
| Stock A | $5,000 | $12,000 | 7 | 13.3% |
| Stock B | $8,000 | $15,000 | 5 | 13.4% |
| Index Fund | $10,000 | $22,000 | 10 | 8.2% |
Despite different starting values, ending values, and time periods, CAGR allows direct comparison. Stock B has the highest CAGR, followed closely by Stock A. Both outperform the index fund.
CAGR for Business Metrics
CAGR is not limited to investment returns. It is widely used to measure growth in:
- Revenue CAGR: How fast a company's sales are growing
- EPS CAGR: How fast earnings per share are growing
- Dividend CAGR: How fast dividend payments are increasing
- Market growth: How fast an industry or market is expanding
Analysts frequently cite 3-year and 5-year revenue or earnings CAGR when evaluating companies. A company with a 20% revenue CAGR over five years is growing significantly faster than one with a 5% CAGR.
Limitations of CAGR
Ignores Volatility
CAGR shows only the beginning and ending points, not the journey between them. Two investments can have identical CAGRs but vastly different risk profiles:
Investment A: Steady 10% annually (low volatility) Investment B: +50%, -30%, +50%, -10%, +20% (high volatility)
Both might produce similar CAGRs, but Investment B involves far more risk and emotional stress. This is why the Sharpe ratio is a valuable complement to CAGR.
Ignores Cash Flows
CAGR does not account for dividends, interest, or additional contributions during the holding period. If you received dividends or added capital, the true performance differs from the CAGR calculation.
Assumes Compounding
CAGR assumes that returns are reinvested and compounded. If you withdrew returns rather than reinvesting them, your actual experience was different from the CAGR.
Endpoint Sensitivity
CAGR depends heavily on the starting and ending dates. An investment measured from a market peak to a market trough will have a low CAGR, while the same investment measured from a trough to a peak will have a high CAGR. Choose representative starting and ending points for meaningful analysis.
CAGR and the Rule of 72
The Rule of 72 is a quick estimation tool that tells you how long it takes for an investment to double at a given CAGR.
Years to Double ≈ 72 / CAGR (%)
Example: At 10% CAGR, an investment doubles in approximately 72/10 = 7.2 years
At 15% CAGR: 72/15 = 4.8 years
At 8% CAGR: 72/8 = 9 years
Frequently Asked Questions
Is CAGR the same as annual return?
No. CAGR is a smoothed, hypothetical rate that shows what a steady annual growth rate would produce the same result. Actual annual returns will vary above and below the CAGR from year to year. CAGR is the geometric mean of returns, while average annual return is the arithmetic mean.
What CAGR should I target as an investor?
Aim for a CAGR that beats the long-term market average (approximately 10% for the S&P 500) over a full market cycle. If your investment strategy consistently delivers a CAGR of 12-15% or more, you are outperforming the vast majority of investors and fund managers.
Can CAGR be negative?
Yes. If your investment's ending value is lower than the starting value, the CAGR is negative. For example, if $10,000 becomes $7,000 over 3 years, the CAGR is approximately -11.2%.
How do I use CAGR for evaluating stocks?
Look at the stock price CAGR over 3, 5, and 10 years. Compare this to the company's revenue and EPS CAGR over the same periods. If the stock price CAGR significantly exceeds the earnings CAGR, the stock may be becoming overvalued (expanding P/E ratio). If earnings CAGR exceeds price CAGR, the stock may be undervalued.
Is a high CAGR always good?
A high CAGR is positive but should be evaluated with context. Consider: over what time period? With how much volatility? From what starting point? A high CAGR from a market bottom is less impressive than the same CAGR from a market peak. Always pair CAGR with risk metrics like the Sharpe ratio for a complete picture.
Disclaimer
This is educational content, not financial advice. Trading involves risk, and you should consult a qualified financial advisor before making any investment decisions. Past performance does not guarantee future results.
Advanced CAGR Applications
Revenue CAGR for Company Analysis
When evaluating a company, revenue CAGR over 3-5 years is one of the most useful growth metrics. It shows whether the company's sales are accelerating, steady, or declining.
Compare revenue CAGR to EPS CAGR to understand how efficiently revenue growth translates to earnings growth:
- EPS CAGR > Revenue CAGR: The company is improving its margins and operating efficiency. Each dollar of revenue generates more profit over time.
- EPS CAGR < Revenue CAGR: Margins are compressing. Revenue is growing, but costs are growing faster. This may be temporary (investment phase) or concerning (competitive pressure).
- EPS CAGR = Revenue CAGR: Margins are stable. Growth is coming from top-line expansion rather than efficiency gains.
CAGR for Goal Setting
CAGR is useful for setting realistic trading and investment goals:
Future Value = Present Value x (1 + CAGR)^Years
Example: $25,000 account at 15% CAGR for 10 years
Future Value = $25,000 x (1.15)^10 = $25,000 x 4.046 = $101,136
This calculation shows the power of compounding. A $25,000 account growing at 15% CAGR becomes over $100,000 in 10 years. Even a modest CAGR, sustained over time, produces extraordinary results.
Comparing Investment Vehicles
CAGR allows fair comparison across different investment types:
| Investment Type | Typical CAGR Range | Risk Level |
|---|---|---|
| Savings account | 1-4% | Very low |
| Government bonds | 2-5% | Low |
| Corporate bonds | 4-7% | Low-moderate |
| S&P 500 index | 7-12% | Moderate |
| Growth stocks | 10-20% | High |
| Active trading | Varies widely | Very high |
This comparison highlights that active trading must deliver a meaningfully higher CAGR than passive index investing to justify the time, effort, and additional risk involved.
The Decay Effect of Losses
CAGR implicitly accounts for the asymmetric nature of losses. A 50% loss requires a 100% gain to recover, not a 50% gain. This is why strategies with large drawdowns tend to have lower CAGRs than strategies with smaller, more consistent gains, even if the average annual return is similar.
This mathematical reality underscores the importance of risk management and stop losses. Avoiding large losses is more valuable than capturing large gains, because large losses create a mathematical hole that requires disproportionate gains to fill. Protecting your capital is the single most important factor for long-term CAGR.
Frequently Asked Questions
What is the best way to get started with fundamentals?
Start by reading this guide thoroughly, then practice with a paper trading account before risking real capital. Focus on understanding the concepts rather than memorizing rules.
How long does it take to learn cagr formula?
Most traders can grasp the basics within a few weeks of study and practice. However, developing consistency and proficiency typically takes several months of active application.