KIM FINANCE

CAGR (Compound Annual Growth Rate)

1. Definition

CAGR is a metric that represents the mean annual growth rate of an investment over a specified time period longer than one year.

While investment values fluctuate over time, CAGR smooths out this volatility. It describes the rate at which an investment would have grown if it had grown at a steady rate, assuming the profits were reinvested at the end of each year (compounding).

2. The Basic Formula

CAGR determines the theoretical steady growth rate required to get from the beginning value to the ending value over a specific period ($n$).

$$ CAGR = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1 $$

3. Key Logic (vs. Arithmetic Mean)

A common mistake is using the "Arithmetic Mean" (simply averaging the yearly returns). This method fails to account for the effects of compounding and negative returns.

Example: The Trap of Arithmetic Mean

Suppose you invest $1,000. In the first year, it gains +50%, and in the second year, it loses -50%.

  1. Actual Asset Movement:

    • Year 1: $1,000 \rightarrow $1,500
    • Year 2: $1,500 \rightarrow $750
    • Result: A loss of $250 (-25%).

  2. Arithmetic Mean Calculation (Misleading):

    • $(+50\% - 50\%) \div 2 = \mathbf{0\%}$
    • Mathematically, the average return looks like 0%, but in reality, you lost money.

  3. CAGR Calculation (Correct):

    • $\left( \frac{750}{1000} \right)^{\frac{1}{2}} - 1 \approx \mathbf{-13.4\%}$
    • This accurately reflects that your wealth decayed at a rate of -13.4% per year.

4. Why It Matters

5. Limitations