Erick Santana

CAGR: Compound Annual Growth Rate Explained

6 min read

CAGR: Compound Annual Growth Rate Explained

The Compound Annual Growth Rate (CAGR) is one of the most important metrics in finance and investing, providing a standardized way to measure and compare the performance of investments over different time periods. Unlike simple averages, CAGR accounts for the compounding effect, making it an essential tool for portfolio analysis and performance evaluation.

What is CAGR?

CAGR represents the mean annual growth rate of an investment over a specified period longer than one year. It describes the rate at which an investment would have grown if it had grown at a steady rate, compounding annually. CAGR smooths out the volatility of returns to show what the consistent annual return would have been.

The CAGR Formula

The mathematical formula for CAGR is:

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

Or expressed mathematically:

CAGR = (V_f / V_i)^(1/n) - 1

Where:

  • V_f = Final value
  • V_i = Initial value
  • n = Number of years

Practical Examples

Example 1: Stock Investment

Suppose you invested 16,000 over 5 years:

CAGR = (10,000)^(1/5) - 1 CAGR = (1.6)^(0.2) - 1
CAGR = 1.0986 - 1 = 0.0986 or 9.86%

This means the investment grew at an average annual rate of 9.86%.

Example 2: Portfolio Performance

A portfolio starts with 85,000 over 7 years:

CAGR = (50,000)^(1/7) - 1 CAGR = (1.7)^(0.1429) - 1 CAGR = 1.0844 - 1 = 0.0844 or 8.44%

Example 3: Comparing Investments

Investment A: 2,500 over 10 years CAGR_A = (1,000)^(1/10) - 1 = 9.60%

Investment B: 2,000 over 6 years
CAGR_B = (1,000)^(1/6) - 1 = 12.25%

Despite Investment A having a higher absolute return, Investment B has a superior CAGR.

Why CAGR Matters

Standardized Comparison

CAGR enables fair comparison between investments with different time horizons and volatility patterns. A 50% return over 10 years looks very different from a 50% return over 2 years when expressed as CAGR.

Smoothing Volatility

Real investment returns are rarely smooth. CAGR helps investors see through short-term volatility to understand the underlying long-term growth pattern.

Future Projections

While past performance doesn’t guarantee future results, CAGR provides a baseline for projecting potential future growth, especially useful in financial planning and efficient_frontier analysis.

CAGR in Portfolio Theory

Modern Portfolio Theory Integration

In Markowitz modern portfolio theory, CAGR serves as the return component when constructing efficient portfolios. When plotting the efficient_frontier, portfolio managers use:

  • Y-axis: Expected CAGR (return)
  • X-axis: Standard deviation (risk)

This creates a visual representation of the risk-return tradeoff for different portfolio allocations.

Performance Measurement

CAGR is essential for:

  • Benchmarking: Comparing portfolio performance against market indices
  • Manager Evaluation: Assessing active management effectiveness
  • Risk-Adjusted Returns: Computing metrics like the Sharpe ratio

Limitations of CAGR

Volatility Blind

CAGR doesn’t account for the volatility experienced during the investment period. Two investments with identical CAGRs might have vastly different risk profiles.

Consider these two scenarios over 3 years:

  • Investment A: 1,200 → 1,728 (CAGR: 20%)
  • Investment B: 500 → 1,728 (CAGR: 20%)

Both have the same CAGR, but Investment B is much more volatile.

No Risk Adjustment

CAGR doesn’t consider the risk taken to achieve returns. A 10% CAGR from government bonds represents a very different risk-return profile than a 10% CAGR from cryptocurrency investments.

Timing Sensitivity

CAGR calculations are sensitive to the start and end dates chosen, which can significantly impact results, especially for volatile investments.

Advanced CAGR Applications

Geometric vs. Arithmetic Mean

CAGR represents the geometric mean of returns, which is always lower than the arithmetic mean for volatile investments. This difference increases with volatility:

Geometric Mean ≤ Arithmetic Mean

The equality holds only when returns are constant (zero volatility).

CAGR in Risk Management

Portfolio managers use CAGR in conjunction with other metrics:

  • Maximum Drawdown: Largest peak-to-trough decline
  • Calmar Ratio: CAGR divided by maximum drawdown
  • Sortino Ratio: CAGR divided by downside deviation

Multi-Period Analysis

For complex investment scenarios, analysts might calculate CAGR for different sub-periods to understand performance patterns across market cycles.

Calculating CAGR in Practice

Using Spreadsheets

In Excel or Google Sheets:

=POWER(Ending_Value/Beginning_Value, 1/Years) - 1

Using Python

def cagr(beginning_value, ending_value, years):
    return (ending_value / beginning_value) ** (1/years) - 1
 
# Example
result = cagr(10000, 16000, 5)
print(f"CAGR: {result:.4f} or {result*100:.2f}%")

Using R

cagr <- function(beginning_value, ending_value, years) {
  (ending_value / beginning_value) ^ (1/years) - 1
}
 
# Example
result <- cagr(10000, 16000, 5)
cat("CAGR:", sprintf("%.4f or %.2f%%", result, result*100))

CAGR vs. Other Return Metrics

Simple Annual Return

Simple return = (Ending Value - Beginning Value) / Beginning Value / Years

This doesn’t account for compounding and can be misleading for multi-year periods.

Internal Rate of Return (IRR)

IRR considers the timing of cash flows, making it more appropriate for investments with intermediate cash flows (dividends, contributions, withdrawals).

Time-Weighted Return

Used when there are external cash flows during the investment period, providing a measure of investment performance independent of cash flow timing.

Best Practices

When to Use CAGR

  • Comparing investments over different time periods
  • Evaluating long-term investment performance
  • Financial planning and projection scenarios
  • Portfolio optimization and efficient_frontier construction

When to Supplement CAGR

  • Include volatility measures (standard deviation, maximum drawdown)
  • Consider risk-adjusted metrics (Sharpe ratio, Sortino ratio)
  • Analyze sub-period performance for market cycle insights
  • Account for taxes and transaction costs in real-world scenarios

Conclusion

CAGR is a fundamental metric that provides crucial insights into investment performance by capturing the power of compounding. While it has limitations—particularly its inability to reflect volatility and risk—CAGR remains indispensable for portfolio analysis, performance comparison, and financial planning.

Understanding CAGR enables investors to make more informed decisions when evaluating investment opportunities, constructing portfolios, and setting realistic expectations for long-term wealth building. When used alongside other financial metrics and incorporated into frameworks like the efficient_frontier and Markowitz optimization, CAGR becomes a powerful tool for systematic investment management.

Graph View

Backlinks