Compound Annual Growth Rate (CAGR) measures the annual growth rate of an investment over a specified time period longer than one year, assuming the investment compounds annually. The standard mathematical formula for CAGR is CAGR = (Ending Value / Beginning Value)^(1 / n) - 1, where n represents the total number of years.
Unlike simple average returns, CAGR provides a smoothed geometric mean rate that reflects true wealth accumulation over volatile periods. Simple averages fail to capture compounding: if an investment gains 100% in Year 1 (growing $100 to $200) and loses 50% in Year 2 (falling from $200 to $100), the simple average return is (100% - 50%) / 2 = +25.0%. However, your actual net return is 0%, which CAGR correctly accurately measures: (100 / 100)^(1/2) - 1 = 0.0%.
Step-by-step CAGR calculation example
Suppose an initial investment of $15,000 in an index fund grows to $32,000 over a 7-year holding period. To calculate CAGR, divide the ending value by the starting value: $32,000 / $15,000 = 2.1333. Next, raise this figure to the power of 1/7 (0.142857): (2.1333)^0.142857 = 1.1141. Subtracting 1 yields a CAGR of 0.1141, or 11.41% annually.
This 11.41% CAGR indicates that a steady annual return of 11.41% would produce the exact same final balance of $32,000 from a $15,000 starting investment over 7 years. This metric enables standardized comparison between different asset classes -- such as comparing real estate, stocks, and business ventures across varying holding periods.
Limitations of CAGR and cash flow assumptions
While CAGR is a primary performance metric, it hides path dependency and intra-period volatility. Two portfolios might achieve identical 10.0% CAGRs over a decade, but one may experience severe 40% drawdowns along the way while the other experiences steady single-digit annual gains. CAGR measures starting and ending balance endpoints, ignoring intermediate risk exposure.
Furthermore, CAGR assumes a single initial lump-sum investment with zero interim capital additions or withdrawals. If you regularly deposit or withdraw funds over the investment lifespan, you must compute the Internal Rate of Return (IRR) or Money-Weighted Rate of Return instead of standard CAGR. You can experiment with compounding timelines using an ROI calculator or compound interest calculator.