Formula

What Is Compound Annual Growth Rate (CAGR)?

The Compound Annual Growth Rate (CAGR) is a widely used financial metric that represents the smoothed, annualized rate of return an investment would have achieved if it had grown at a steady rate over a specified period longer than one year, with profits reinvested at the end of each year. As a concept within investment performance analysis, a sub-category of financial metrics, CAGR helps investors understand the average growth trajectory of various assets or business metrics. Unlike a simple average, CAGR accounts for the compounding effect of returns, providing a more accurate picture of growth over multiple periods.

History and Origin

The concept of compounding, fundamental to CAGR, has roots tracing back to ancient civilizations, including Babylon, where "interest on interest" was recognized and mathematical problems involving it were solved¹³, ¹⁴. Early forms of compound interest calculations were documented by mathematicians like Leonardo Fibonacci in 1202 A.D. in his Liber Abaci, where he explored how invested sums could grow over time¹¹, ¹².

The widespread adoption and analysis of compound interest, however, advanced significantly after 1500 with the availability of printed books, which facilitated the spread of mathematical techniques. During this period, mathematicians such as Trenchant and Stevin published the first compound interest tables, followed by Witt in 1613, who further demonstrated their practical applications. Towards the close of the 17th century, interest calculations were integrated with age-dependent survival rates, laying the groundwork for actuarial science⁹, ¹⁰. The Compound Annual Growth Rate (CAGR) builds upon these historical mathematical foundations, offering a standardized way to measure growth over multiple periods by incorporating the power of compounding.

Key Takeaways

• CAGR provides a smoothed average annual growth rate, assuming returns are reinvested over the period.
• It is particularly useful for evaluating the performance of investments or business metrics over multi-year horizons.
• CAGR helps compare the growth of different investments, even if their actual year-to-year returns are volatile.
• The metric does not reflect actual year-to-year volatility or interim performance fluctuations.
• It assumes a constant growth rate, which is rarely the case in real-world investment scenarios.

Formula and Calculation

The formula for Compound Annual Growth Rate (CAGR) is:

Where:

• Ending Value: The investment's value at the end of the period.
• Beginning Value: The investment's value at the start of the period.
• Number of Years: The total duration of the investment in years. This can also represent the number of compounding periods if the period is not measured in years (e.g., quarters or months, adjusted to years).

This formula effectively calculates the geometric mean of growth rates, providing a single, consistent annual growth rate that would take the investment from its beginning value to its ending value over the specified time frame.

Interpreting the CAGR

CAGR is interpreted as the annualized rate at which an investment would have grown if it had compounded at a steady rate over the specified period. A positive CAGR indicates growth, while a negative CAGR signifies a decline. For instance, a 10% CAGR over five years means that, on average, the investment grew by 10% each year, assuming all profits were reinvested.

When evaluating an investment portfolio, a higher CAGR generally suggests better historical performance. However, it is crucial to consider the context, including the initial investment amount, the duration, and any additional contributions or withdrawals. Investors often use CAGR to compare the historical performance of different mutual funds, stocks, or other assets, providing a standardized basis for comparison despite fluctuating yearly returns.

Hypothetical Example

Consider an investor who placed $10,000 into a growth-oriented fund five years ago.

• Year 1: The fund increased by 15%, reaching $11,500.
• Year 2: It then dropped by 5%, to $10,925.
• Year 3: It gained 20%, reaching $13,110.
• Year 4: It gained 8%, reaching $14,158.80.
• Year 5: Finally, it gained 12%, ending at $15,857.86.

To calculate the CAGR for this investment:

1. Beginning Value: $10,000
2. Ending Value: $15,857.86
3. Number of Years: 5

Using the formula:

This indicates that, over the five-year period, the investment grew at an average annual rate of approximately 9.66%, accounting for the compounding effect. This smoothed rate helps assess the overall growth trend, even with fluctuating yearly returns. The actual diversification of the fund's holdings would also impact these returns.

Practical Applications

CAGR is a versatile metric applied across various areas of finance:

• Investment Analysis: Investors use CAGR to evaluate the historical growth of individual stocks, mutual funds, or entire portfolios over specific periods, helping them compare different investment options.
• Business Performance: Companies often use CAGR to measure the growth of sales, revenue, market share, or other key performance indicators over multiple years, especially in financial modeling and strategic planning.
• Economic Analysis: Economists and analysts may use CAGR to analyze trends in macroeconomic data, such as Gross Domestic Product (GDP) or inflation, available from sources like the Federal Reserve Economic Data (FRED) from the St. Louis Fed⁶, ⁷, ⁸. This helps in understanding long-term economic shifts.
• Regulatory Compliance: Financial advisors and asset managers frequently use CAGR in their performance reporting. Recent updates to the SEC Marketing Rule, for instance, have provided new SEC guidance on how performance, including metrics like CAGR, must be presented to clients, particularly regarding the display of gross versus net returns⁴, ⁵.

Limitations and Criticisms

Despite its utility, CAGR has several important limitations that users must understand:

• Ignores Volatility: The most significant criticism of CAGR is that it presents a smoothed growth rate, effectively ignoring the year-to-year volatility and fluctuations an investment experienced², ³. An investment with a high CAGR might have had significant drops and recoveries, which CAGR does not reveal. This can be misleading when assessing the actual risk management profile.
• Assumes Reinvestment: CAGR assumes that all profits are reinvested back into the investment, which may not always be the case for an investor. Withdrawals or additional contributions during the period can distort the perceived growth rate.
• Sensitivity to Time Horizon: The calculated CAGR is highly dependent on the chosen beginning and ending points. Selecting different periods can result in drastically different CAGR values, making it possible to misrepresent performance if the timeframe is cherry-picked.
• Not a True Return Rate: CAGR is a "representational" figure rather than a true rate of return because it doesn't account for the variability of returns. It implies a steady, consistent growth that rarely occurs in real markets. As noted by Alpha Theory, while valuable, CAGR does not tell the "whole story" of a return stream¹.

Compound Annual Growth Rate (CAGR) vs. Simple Annual Growth Rate

The key difference between Compound Annual Growth Rate (CAGR) and Simple Annual Growth Rate lies in how they treat returns over multiple periods.

The Simple Annual Growth Rate (also known as arithmetic mean return) is calculated by taking the average of the yearly growth rates. For example, if an investment grows by 10% in Year 1 and 20% in Year 2, the simple average growth rate would be (10% + 20%) / 2 = 15%. This method does not account for the effect of compounding, meaning it assumes that the principal amount remains constant each year, and interest is not earned on previously accumulated interest.

In contrast, Compound Annual Growth Rate (CAGR) considers the compounding effect. It calculates the geometric mean of the annual growth rates, effectively showing the average annual growth rate assuming that returns generated in one year are reinvested and contribute to the base for the next year's returns. CAGR provides a more realistic representation of an investment's growth over time, as financial investments typically involve compounding. While the simple average can be useful for understanding individual period performance, CAGR is generally preferred for assessing long-term investment performance because it reflects how an initial investment would have grown with compounding.

FAQs

What is a good CAGR?

There is no universal "good" CAGR, as it depends heavily on the asset class, market conditions, and investment objectives. A CAGR of 7-10% might be considered good for a broadly diversified asset allocation over the long term, while high-growth private equity investments might target significantly higher CAGRs. It's best to compare an investment's CAGR to its peers and relevant benchmarks.

Can CAGR be negative?

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

Is CAGR the same as average annual return?

No, CAGR is not the same as a simple average annual return. CAGR is a geometric mean, which accounts for the compounding effect, whereas a simple average annual return is an arithmetic mean of yearly returns and does not consider compounding. CAGR provides a more accurate picture of the actual wealth accumulation from an investment over multiple periods.

Why is CAGR important for long-term investments?

CAGR is particularly important for long-term investments because it smooths out the fluctuations and volatility inherent in market returns. Over extended periods, the power of compounding significantly impacts total returns, and CAGR effectively captures this by showing a consistent, equivalent annual growth rate that accounts for interest earning interest.