Compound Annual Growth Rate - CAGR

Loading the player...

What is the 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year.

To calculate compound annual growth rate, divide the value of an investment at the end of the period in question by its value at the beginning of that period, raise the result to the power of one divided by the period length, and subtract one from the subsequent result.

This can be written as follows:


Compound Annual Growth Rate (CAGR)

CAGR can also be calculated using Investopedia's own Compound Annual Growth Rate Calculator.

BREAKING DOWN 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially an imaginary number that describes the rate at which an investment would have grown if it had grown at a steady rate, which virtually never happens in reality. You can think of CAGR as a way to smooth out an investment’s returns so that they may be more easily understood.

Don't worry if this concept is still fuzzy to you – CAGR is one of those terms best explained through example. Suppose you invested $10,000 in a portfolio on Jan 1, 2005. Unsurprisingly, your portfolio would likely grow at an inconsistent rate. Let us assume that by Jan 1, 2006, your portfolio had grown to $13,000. Let us also assume that it then grew to $14,000 by the same time in 2007, and spiked during that year, ending up at $19,500 by Jan 1, 2008.

To calculate the CAGR of your portfolio from the period from Jan 1, 2005 to Jan 1, 2008, you would divide the final value of your portfolio by the portfolio’s initial value ($19,500 / $10,000 = 1.95). Next, you would  raise the result to the power of 1 divided by the number of years (1 / 3 = 1/3 or 0.3333). Finally, you would subtract 1 from the resulting value.

Doing the math, you would calculate:

[(19,500 / 10,000)^(1 / 3)] – 1

= (1.95 ^ 0.3333) – 1

= 1.2493 – 1

= 0.2493, or 24.93%.

Thus, the compound annual growth rate of your three-year investment is equal to 24.93%, representing the smoothed annualized gain you earned over your investment time horizon.

Uses of the Compound Annual Growth Rate (CAGR)

CAGR is a relatively simple metric, since it merely measures the average rate of an investment’s growth over a variable period of time. Because of this simplicity, this metric is a flexible one and thus has a variety of uses.

Most simply, CAGR can be used to calculate the average growth of a single investment. Because of market volatility, the year-to-year growth of an investment may be difficult to interpret. For example, an investment may increase in value by 8% in one year, decrease in value by 2% the following year and increase in value by 5% in the next. With inconsistent annual growth, CAGR may be used to give a broader picture of an investment’s progress.

CAGR may also be used to compare investments of different types with one another. For example, suppose in 2010 you put $10,000 into a savings account with a fixed annual interest rate of 1%, growing to a value of $10,100 in 2011, $10,201 in 2012 and $10,303.01 in 2013. Say that in 2010, you wanted to pursue other investment options but, fearing market volatility, you only invested $5,000 this time, into a portfolio with a varying growth rate. Suppose that the portfolio grew in value to $5,114 in 2011, dropped to a value of $5,098 in 2012 and grew to $5,437 in 2013. Although the portfolio grew at an inconsistent rate and even lost value in 2012, the investment’s CAGR between 2010 and 2013 was 2.83% ((5,437/5,000)^(1/3) - 1 = 1.0874^0.3333 – 1 = 1.0283 – 1 = 0.0283 = 2.83%), substantially higher than the interest rate of the savings account. The portfolio, then, proved to be the more profitable investment.

CAGR can also be used to track the performance of various business measures of one or multiple companies alongside one another. For example, over a five-year period Big-Sale Stores’ market share CAGR may be 1.82% but its customer satisfaction CAGR over the same period might be -0.58%. In this way, comparing the CAGRs of measures within a single company may reveal that company’s strengths and weaknesses. However, comparing those CAGRs with those tracking the same measures in other companies may help situate this data within the scope of the market. For example, Big-Sale’s customer satisfaction CAGR might not seem so low if compared with SuperFast Cable’s customer satisfaction CAGR of -6.31% during the same period.

Limitations of 'Compound Annual Growth Rate - CAGR'

Like any metric, CAGR should not be used alone, but rather should be used alongside other metrics as well. This is because, like any metric, CAGR is not without its drawbacks.

The simplest limitation of CAGR is that because it calculates the smooth average of growth over a period, it ignores volatility and implies that the growth during that time was steady. Yet, this is never actually the case. As such, you should never take CAGR at face value — also check the values each year that go into calculating CAGR.

Another limitation of using CAGR in assessing investments is that, no matter how steady the growth of a company or investment has been over a period of time (even if you have checked the individual annual values), CAGR is a purely historical metric. What this means is that even if an investment’s growth has been very consistent over a five-year period, you cannot safely use CAGR to assume that the investment will continue to grow at the same rate during the following year or years, as market volatility and other factors may come into play and affect that investment’s rate of growth.

A third limitation of CAGR is a limitation of representation. Say that an investment fund had values of $100,000 in 2010, $71,000 in 2011, $44,000 in 2012, $81,000 in 2013 and $126,000 in 2014. If the fund managers told you in 2015 that the fund’s CAGR was a whopping 42.01% over the past three years, they would not be lying. They would, however, be omitting some very important information about the fund’s history, including the fact that the fund’s CAGR over the past five years was a much more modest 4.73%.

For more on the Compound Annual Growth Rate (CAGR), see: Compound Annual Growth Rate: What You Should Know.

  1. MAR Ratio

    A measurement of returns adjusted for risk that can be used to ...
  2. Effective Annual Interest Rate

    Effective Annual Interest Rate is an investment's annual rate ...
  3. Periodic Interest Rate

    The interest rate charged on a loan or realized on an investment ...
  4. Annual Percentage Yield - APY

    The effective annual rate of return taking into account the effect ...
  5. Stated Annual Interest Rate

    The return on an investment that is expressed as a per-year percentage, ...
  6. Average Annual Growth Rate - AAGR

    The average increase in the value of an individual investment ...
Related Articles
  1. Markets

    The Most Accurate Way To Gauge Returns: The Compound Annual Growth Rate

    The compound annual growth rate, or CAGR for short, represents one of the most accurate ways to calculate and determine returns for individual assets, investment portfolios and anything that ...
  2. Financial Advisor

    The 15 Fastest-Growing RIAs

    Registered investment advisors are consolidating their business and assets. Here are 15 of the fastest-growing RIAs.
  3. Managing Wealth

    Learn Simple And Compound Interest

    Interest is defined as the cost of borrowing money, and depending on how it is calculated, can be classified as simple interest or compound interest.
  4. Insights

    Why to Watch Southeast Asia's Internet Economy

    The world’s fastest growing internet region currently has a booming base of 260 million Internet users, growing at a rate of approximately 14% five-year CAGR.
  5. Markets

    Morgan Stanley On the Trends in Asset Management (MS)

    Learn about trends in the asset management industry and future prospects for its growth, according to a May 2016 Morgan Stanley report.
  6. Markets

    5 Stock Market Metrics Explained

    Learn how to evaluate a company's performance using metrics such as ROE, EPS and P/E ratio.
  7. Investing

    How To Calculate Your Investment Return

    How much are your investments actually returning? Find out why the method of calculation matters.
  8. Markets

    Explaining Growth Rates

    Growth rate refers to the amount a specific variable or measure has grown over a specified time, whether related to one company or an entire economy.
  9. Investing

    Accelerating Returns With Continuous Compounding

    Investopedia explains the natural log and exponential functions used to calculate this value.
  10. Managing Wealth

    Overcoming Compounding's Dark Side

    Understanding how money is made and lost over time can help you improve your returns.
  1. What is the formula for calculating compound annual growth rate (CAGR) in Excel?

    The concept of CAGR is relatively straightforward and requires only three primary inputs: an investments beginning value, ... Read Answer >>
  2. Why is the compound annual growth rate (CAGR) misleading when assessing long-term ...

    The compound annual growth rate (CAGR) measures the return on an investment over a certain period of time. Below is an overview ... Read Answer >>
  3. How do you calculate CAGR?

    Find out how to understand and use the compound annual growth rate formula, and find out why it helps put an uneven performance ... Read Answer >>
  4. What are the main differences between compound annual growth rate (CAGR) and internal ...

    The compound annual growth rate (CAGR), measures the return on an investment over a certain period of time. The internal ... Read Answer >>
  5. How does the compound interest concept vary between a basic savings account and an ...

    I understand compound interest as it relates to a basic savings account. If you get 5% interest on $1000 each year, it will ... Read Answer >>
  6. How do I use the rule of 72 to calculate continuous compounding?

    Find out why the rule of 72 does not accurately reflect the growth caused by continuous compounding, and which number can ... Read Answer >>
Hot Definitions
  1. Dove

    An economic policy advisor who promotes monetary policies that involve the maintenance of low interest rates, believing that ...
  2. Cyclical Stock

    An equity security whose price is affected by ups and downs in the overall economy. Cyclical stocks typically relate to companies ...
  3. Front Running

    The unethical practice of a broker trading an equity based on information from the analyst department before his or her clients ...
  4. After-Hours Trading - AHT

    Trading after regular trading hours on the major exchanges. The increasing popularity of electronic communication networks ...
  5. Omnibus Account

    An account between two futures merchants (brokers). It involves the transaction of individual accounts which are combined ...
  6. Weighted Average Life - WAL

    The average number of years for which each dollar of unpaid principal on a loan or mortgage remains outstanding. Once calculated, ...
Trading Center