Compound annual growth rate

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Compound annual growth rate (CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. [1] [2] CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of various data values, such as revenue growth of companies, or of economic values, over time. [3]

Contents

Equation

For annual values, CAGR is defined as:

where is the initial value, is the end value, and is the number of years.

CAGR can also be used to calculate mean annualized growth rates on quarterly or monthly values. The numerator of the exponent would be the value of 4 in the case of quarterly, and 12 in the case of monthly, with the denominator being the number of corresponding periods involved. [4]

Applications

These are some of the common CAGR applications:

See also

Related Research Articles

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The volatility tax is a mathematical finance term first published by Rick Ashburn, CFA in a 2003 column, and formalized by hedge fund manager Mark Spitznagel, describing the effect of large investment losses on compound returns. It has also been called volatility drag, volatility decay or variance drain. This is not literally a tax in the sense of a levy imposed by a government, but the mathematical difference between geometric averages compared to arithmetic averages. This difference resembles a tax due to the mathematics which impose a lower compound return when returns vary over time, compared to a simple sum of returns. This diminishment of returns is in increasing proportion to volatility, such that volatility itself appears to be the basis of a progressive tax. Conversely, fixed-return investments appear to be "volatility tax free".

References

  1. Mark J. P. Anson; Frank J. Fabozzi; Frank J. Jones (3 December 2010). The Handbook of Traditional and Alternative Investment Vehicles: Investment Characteristics and Strategies. John Wiley & Sons. pp. 489–. ISBN   978-1-118-00869-0.
  2. root. "Compound Annual Growth Rate (CAGR) Definition | Investopedia". Investopedia. Retrieved 2016-03-04.
  3. Emily Chan (27 November 2012). Harvard Business School Confidential: Secrets of Success. John Wiley & Sons. pp. 185–. ISBN   978-1-118-58344-9.
  4. "How is average annual growth calculated?". Bureau of Economic Analysis. January 11, 2008.
  5. 1 2 3 "Compound Annual Growth Rate CAGR: Summary and Forum". www.12manage.com. Retrieved 2019-05-02.
  6. "How is average annual growth calculated?". Bureau of Economic Analysis. January 11, 2008.