Compound Annual Growth Rate (CAGR)

The compound annual growth rate is a number that represents a steady level of growth from a beginning value to an ending value. It can be thought of as a way to smooth out uneven returns.

To calculate the CAGR of an investment over a period of n years, you would take the nth root of the total percentage return.

Consider a beginning investment of $100 and an ending investment of $161. 161/100 = 1.61. The fifth root of 1.61 is equivalent to 1.61 to the power of 1/5, or 1.1. Subtracting 1 (100% or the initial investment) gives 0.1, or 10%. The CAGR in this case is 10%.

Since the CAGR smooths out uneven returns, it fails to account for the risks taken to achieve the return.  Any series of returns that starts at 100% and ends at 161% five years later will have a 10% CAGR, such as the investments in column A and Column B below.



     100.0      100.0
     110.0      150.0


     121.0      120.0


     133.1      170.0


     146.4      130.0


     161.1      161.1


Column A actually grew at 10% per year. Column B had large positive gains in some years and large negative gains in others, but ended at the same value. Many investors would prefer the investment in Column A due to its greater predictability and equivalent terminal value.

For more information, see all articles on: Fundamental Analysis, Investing in Stocks, Performance Measurement

See also:
  • Money-Weighted Rate of Return
  • The Gordon Growth Model
  • Time Weighted Rate of Return vs. Money Weighted Rate of Return
  • Implied Growth Rates
  • Neoclassical Growth Theory
  • Technical Analysis Explained : The Successful Investor's Guide to Spotting Investment Trends and Turning Points

    The Intelligent Investor: The Classic Text on Value Investing

    Financial Statement Analysis: A Practitioner's Guide, 3rd Edition

    Managing Investment Portfolios: A Dynamic Process (CFA Institute Investment Series)

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