CAGR: Compound Annual Growth Rate

The mean annual growth rate of an investment over a specified period longer than one year.

Definition§

CAGR, or Compound Annual Growth Rate, refers to the mean annual growth rate of an investment over a specified period longer than one year. Unlike absolute returns, CAGR represents one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time.

Formula§

The CAGR formula is expressed mathematically as:

$$\text{CAGR} = \left( \frac{V_{\text{final}}}{V_{\text{initial}}} \right)^{\frac{1}{n}} - 1$$

where:

• $V_{\text{final}}$ = the final value of the investment
• $V_{\text{initial}}$ = the initial value of the investment
• $n$ = number of years

Types of Growth Rates§

Simple Growth Rate§

Simple growth rate calculates the percentage increase or decrease of an investment from beginning to end without compounding.

Annualized Growth Rate§

Annualized growth rate considers compounding and therefore represents a more realistic growth measure over time.

Special Considerations§

Volatility§

CAGR does not account for investment volatility within the period analyzed, hence it is more suited for steady investments.

Time Horizon§

Longer time horizons smooth out anomalies, making CAGR more reliable for long-term investments than short-term ones.

Examples§

CAGR Calculation Example§

If an investment’s initial value is $1,000 ( $V_{\text{initial}}$) and its value after 5 years ( $n=5$) is $2,000 ( $V_{\text{final}}$), the CAGR is calculated as:

$$\text{CAGR} = \left( \frac{2000}{1000} \right)^{\frac{1}{5}} - 1 \approx 0.1487 \text{ or } 14.87\%$$

Historical Context§

Origin and Application§

CAGR has become a standard measure in finance and investment analysis since the establishment of modern portfolio theory in the mid-20th century.

Applicability§

Investment Performance§

CAGR provides investors a clear view of investment performance ignoring the market volatility within the period.

Financial Projections§

Businesses use CAGR for long-term financial projections due to its ability to represent compound growth accurately.

Comparisons§

CAGR vs. Average Annual Growth Rate (AAGR)§

While both measure annual growth, AAGR does not account for compounding, providing potentially less accurate results compared to CAGR.

CAGR vs. IRR (Internal Rate of Return)§

IRR considers both the size and timing of cash flows, making it more comprehensive but also more complex than CAGR.

Related Terms§

• Absolute Return: The total return of an investment over a specific period.
• Geometric Mean: Another method of calculating average growth rates incorporating compounding.
• Market Volatility: The rate at which the price of investments increases or decreases for a given set of returns.

Frequently Asked Questions§

Is CAGR a Good Measure of Investment Performance?§

Yes, CAGR effectively measures an investment’s performance over time, but it should be used in conjunction with other metrics due to its inability to account for interim volatility.

How Long Should the Time Period Be for CAGR Calculation?§

Ideally, the time period should be long enough to smooth out short-term volatility and anomalies, typically longer than one year.

Can CAGR Be Negative?§

Yes, if the final value of the investment is less than the initial value, the CAGR will be negative, indicating a decline in value.

References§

1. Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.

Summary§

CAGR, or Compound Annual Growth Rate, is a crucial metric for investors and financial analysts, representing the mean annual growth rate of an investment over a specified period. Despite its limitations in considering interim volatility, CAGR remains a cornerstone in long-term financial analysis, investment performance measurements, and financial projections.