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Compound annual growth rate|

What Is Compound Annual Growth Rate?

The Compound Annual Growth Rate (CAGR) is a widely used financial metric that calculates the smoothed, annualized rate of return for an investment portfolio over a specified period longer than one year, assuming that all profits are reinvested. It falls under the broader category of Financial Metrics and is essential for understanding the consistent growth of an asset. Unlike simple annual growth, CAGR accounts for the compounding effect, where earnings generate their own earnings over time, providing a more accurate representation of an investment's performance. Financial professionals use CAGR to analyze historical returns and compare the performance of various investments over comparable time frames.

History and Origin

The concept of compounding, which underpins the Compound Annual Growth Rate, has roots dating back centuries. Early forms of calculating "interest on interest" were evident in ancient civilizations. The practice of charging interest on accrued interest allowed sums to grow exponentially. Over time, financial thinkers developed methods to quantify this growth. For instance, the "Rule of 72," a quick estimation of how long it takes for an investment to double, was cited by Luca Pacioli in 1494 in his Summa de arithmetica, reflecting an early understanding of compound growth. The power of compound interest has long been recognized as a fundamental principle in finance.10

Key Takeaways

  • CAGR represents the annualized average rate at which an investment grows over a multi-year period, assuming profits are reinvested.
  • It smooths out irregular year-over-year growth rates, providing a consistent measure for comparison.
  • CAGR is widely used to evaluate the historical performance of various assets, businesses, or investment portfolio components.
  • While a useful metric, CAGR does not account for the interim volatility or inherent risks of an investment.
  • For regulatory purposes, particularly in advertising investment performance, the Securities and Exchange Commission (SEC) has provided guidance on how performance metrics like CAGR should be presented alongside net returns.9

Formula and Calculation

The formula for the Compound Annual Growth Rate is as follows:

CAGR=(Ending ValueBeginning Value)1Number of Years−1\text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{\text{Number of Years}}} - 1

Where:

  • Ending Value = The investment's value at the end of the period.
  • Beginning Value = The initial principal investment at the start of the period.
  • Number of Years = The total duration of the investment in years.

This formula calculates the annual growth rate that, when compounded, would take the investment from its beginning value to its ending value over the specified period. It effectively measures the geometric mean of annual growth rates.

Interpreting the Compound Annual Growth Rate

Interpreting CAGR involves understanding that it provides a hypothetical, consistent growth path. A positive CAGR indicates that the investment has grown over the period, while a negative CAGR signifies a loss. When evaluating an investment, a higher CAGR generally suggests better historical performance. However, it's crucial to consider the context: a high CAGR might be associated with higher risk management or volatility. Investors often compare an investment's CAGR to relevant benchmarks or other investment opportunities to assess its relative success. For instance, comparing the CAGR of a stock to a market index over the same period can offer insight into its outperformance or underperformance.

Hypothetical Example

Suppose an investor, Sarah, purchases a growth stock for $10,000 at the beginning of 2020.

  • By the end of 2020, the stock's value rises to $12,000.
  • By the end of 2021, due to market fluctuations, it drops to $11,000.
  • By the end of 2022, the stock recovers and reaches $15,000.

To calculate the Compound Annual Growth Rate for Sarah's investment over these three years:

Beginning Value = $10,000
Ending Value = $15,000
Number of Years = 3

CAGR=(15,00010,000)13−1\text{CAGR} = \left( \frac{15,000}{10,000} \right)^{\frac{1}{3}} - 1
CAGR=(1.5)0.3333−1\text{CAGR} = (1.5)^{0.3333} - 1
CAGR≈1.1447−1\text{CAGR} \approx 1.1447 - 1
CAGR≈0.1447 or 14.47%\text{CAGR} \approx 0.1447 \text{ or } 14.47\%

This indicates that Sarah's initial principal of $10,000 grew at an average annual compounded rate of approximately 14.47% over the three-year period to reach $15,000. This smoothed rate helps Sarah understand the consistent growth, despite the actual year-to-year fluctuations in the mutual funds holding.

Practical Applications

The Compound Annual Growth Rate is a versatile metric used across various financial domains:

  • Investment Performance Analysis: Investors and financial analysts use CAGR to assess the historical performance of stocks, bonds, mutual funds, and other investment vehicles. It allows for direct comparisons between different investments over identical periods, helping to determine which has provided the most consistent growth.
  • Business Analysis: Companies use CAGR to measure the growth of key business metrics such as revenue, profits, market share, or customer base over multiple years, aiding in strategic planning and target setting.
  • Real Estate Valuation: In real estate investment, CAGR can illustrate the average annual appreciation of property values, providing a smoothed picture of growth over time.8
  • Financial Planning: Individuals and financial advisors incorporate CAGR into financial planning to project the potential growth of savings or retirement funds, assuming a consistent rate of return.
  • Economic Analysis: Economists and policymakers might use CAGR to analyze trends in economic indicators, such as Gross Domestic Product (GDP) or inflation, over extended periods. Even official economic rates, such as those published by central banks, may involve elements of compounding, as seen with the Secured Overnight Financing Rate (SOFR) index, which measures the cumulative impact of daily compounding.7
  • Benchmarking: Investment managers frequently use CAGR to compare their investment portfolio's performance against industry benchmarks or competitor funds, facilitating performance attribution.
  • Regulatory Reporting: While general advertising rules apply, the SEC Marketing Rule provides guidance for investment advisers on how to present performance information, often requiring clear disclosure of gross and net returns when displaying extracted performance to prevent misleading impressions.6

Limitations and Criticisms

While CAGR is a valuable tool, it has several limitations that users must consider:

  • Ignores Volatility: The most significant criticism of CAGR is that it presents a smoothed rate of growth, effectively disregarding the volatility and interim fluctuations an investment experiences. Two investments could have the same CAGR over a period but wildly different year-to-year returns, with one having significant ups and downs while the other grew steadily.5 This can mask periods of substantial loss or gain, which are crucial for assessing risk management.
  • Assumes Reinvestment: The calculation of CAGR inherently assumes that all profits generated are reinvested at the same rate, which may not always be feasible or intended by an investor. If an investor withdraws funds or adds new capital during the period, the actual effective rate of return on their invested capital will differ from the calculated CAGR.
  • Sensitive to Time Period: The calculated CAGR is highly dependent on the chosen beginning and ending points. A slight shift in the period can lead to a significantly different CAGR, especially for volatile assets.4
  • Does Not Account for External Cash Flows: CAGR does not factor in additional contributions to or withdrawals from the investment during the period. These external cash flows can distort the calculated rate, making it appear higher or lower than the true performance attributable solely to the investment's growth.

Therefore, CAGR should be used in conjunction with other metrics, such as standard deviation for volatility or maximum drawdown, to provide a more comprehensive view of an investment's performance and risk profile.

Compound Annual Growth Rate vs. Arithmetic Mean

The Compound Annual Growth Rate (CAGR) is often confused with the simple Arithmetic Mean (or average annual return) of returns. The key difference lies in how they account for compounding and the sequence of returns.

The arithmetic mean calculates the average of a series of annual returns by summing them up and dividing by the number of years. For example, if an investment has annual returns of +20%, -10%, and +15% over three years, the arithmetic mean would be (20 - 10 + 15) / 3 = 8.33%.

However, the arithmetic mean does not reflect the actual cumulative effect of these returns on the initial investment, particularly when losses occur. It fails to consider that percentage gains are applied to a smaller base after a loss. In contrast, CAGR is a geometric mean that considers the effect of compounding and provides the actual rate at which an initial investment would have grown to its final value. If an investment loses 30% in year one and gains 30% in year two, the arithmetic mean is 0%. However, the actual value would be less than the starting value because the 30% gain in year two is calculated on a smaller base. CAGR accurately captures this, showing a negative return in such a scenario.3 For historical performance analysis, especially over multiple periods with varying returns and volatility, CAGR offers a more realistic picture of the investment's true growth.1, 2

FAQs

What is a "good" Compound Annual Growth Rate?

There is no universal "good" CAGR, as it depends on the asset class, market conditions, and an investor's financial goals and risk tolerance. A CAGR of 10% for a stable bond investment might be considered excellent, while the same CAGR for a high-growth technology stock might be considered modest. It's best to compare an investment's CAGR to its peers and relevant market benchmarks over the same period.

Can Compound Annual Growth Rate be negative?

Yes, CAGR can be negative if the ending value of the investment is lower than its beginning value over the period. A negative CAGR indicates that the investment has lost value on an average annual compounded basis over the specified time frame.

Is CAGR the same as average annual return?

No, CAGR is not the same as the simple average annual return (arithmetic mean). CAGR accounts for compounding, meaning it considers that gains (or losses) in one year affect the base for the next year's returns. The simple average annual return does not consider this compounding effect, which can lead to a misleadingly higher average, especially with fluctuating returns.

Why is CAGR useful for long-term investments?

CAGR is particularly useful for long-term investments because it smooths out the year-to-year volatility that is common in financial markets. It provides a single, representative annual rate of growth that reflects the overall performance over an extended period, making it easier to compare investments with different asset allocation strategies or evaluate progress towards long-term financial goals through diversification.