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.
|
A |
B |
|
| Â Â Â Â 100.0 | Â Â Â Â 100.0 | |
| Â Â Â Â 110.0 | Â Â Â Â 150.0 |
50% |
| Â Â Â Â 121.0 | Â Â Â Â 120.0 |
-20% |
| Â Â Â Â 133.1 | Â Â Â Â 170.0 |
42% |
| Â Â Â Â 146.4 | Â Â Â Â 130.0 |
-24% |
| Â Â Â Â 161.1 | Â Â Â Â 161.1 |
24% |
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:
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)
