CAGR (Compound Annual Growth Rate)

CAGR eliminates the distortion caused by volatility and compounding math when comparing investments across different time periods. The formula is:

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

Where n is the number of years.

**Example:** A crypto portfolio grows from $10,000 to $40,000 over 5 years. CAGR = ($40,000 / $10,000)^(1/5) - 1 = 4^0.2 - 1 = 1.3195 - 1 = 31.95% per year

This means $10,000 growing at exactly 31.95% each year for 5 years would reach $40,000. The actual year-by-year returns could be wildly different (+200%, -60%, +80%, -30%, +150%) but the CAGR smooths this to the equivalent steady rate.

**Why CAGR matters for crypto:** Crypto returns are highly volatile and non-linear. Bitcoin's year-by-year returns have included +1,318% (2017), -73% (2018), +92% (2020), +59% (2021), -65% (2022). Saying "Bitcoin returned X% on average" using simple average returns is misleading because simple averages don't account for compounding effects of losses.

**CAGR vs. simple average return:** If an investment goes up 100% in year 1 and down 50% in year 2: - Simple average: (+100% + -50%) / 2 = +25% average annual - CAGR: (1 × 2 × 0.5)^(1/2) - 1 = 1^0.5 - 1 = 0% — you broke even

The CAGR of 0% is the accurate answer. The 25% simple average is misleading.

**Using CAGR in strategy comparison:** When comparing crypto strategies, always use CAGR over the same time period. A strategy that delivered 200% total return over 4 years (CAGR ~31%) is inferior to one that delivered 150% total return over 2 years (CAGR ~50%), even though the total return is lower.

**CAGR alongside risk metrics:** CAGR alone does not account for risk. Combine it with: - Maximum drawdown (Calmar ratio = CAGR / MDD) - Volatility (Sharpe ratio uses annualized standard deviation) - Downside deviation (Sortino ratio)