Compound Annual Growth Rate (CAGR)

Compound annual growth rate (CAGR) is a financial metric that calculates the rate of return of an investment over a specific period. It’s a widely used indicator of investment performance and is often used to compare the performance of different investments.

How to Calculate CAGR

Calculating CAGR involves the following steps:

1. Calculate the beginning and ending values: Calculate the beginning and ending values of the investment.
2. Calculate the number of years: Calculate the number of years the investment was held.
3. Calculate CAGR: Use the formula: CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) – 1

A Worked Example

Say you invest $1,000. In year one it triples to $3,000, a 200% gain. In year two the market corrects and you lose half, ending with $1,500.

The simple average of the two yearly returns is 75%: the average of up 200% and down 50%. But $1,000 growing at 75% a year for two years would be $3,063, and your account holds $1,500. The average lies because it ignores compounding.

CAGR tells the truth: (1500 / 1000)^(1/2) – 1 = 22.5%. That is the steady rate that gets you from $1,000 to $1,500 in two years. Same ending value, honest number.

CAGR vs. Average Annual Return

The arithmetic average almost always overstates results when returns are volatile, and the more volatile the ride, the bigger the gap. Use CAGR to compare two investments over the same period. Never use it to predict the path: it describes a smooth ride that never actually happened.

Interpretation of CAGR

A high CAGR indicates that an investment has performed well, while a low CAGR indicates that an investment has underperformed.

Significance of CAGR

CAGR is significant because it:

• Gives a single number that summarizes an investment’s performance over time
• Lets investors compare different investments over the same period on equal footing
• Helps set realistic expectations for long-term planning

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Limitations of CAGR

While CAGR is a useful metric, it has its limitations:

• Ignores volatility: CAGR ignores the volatility of an investment and may not reflect its true risk.
• Describes a rate that never actually happened: no single year grew at the CAGR. It is a hypothetical steady rate, useful for comparison, not a description of the ride.
• Does not account for fees: CAGR does not account for fees and expenses associated with an investment.

Alternatives to CAGR

Other financial metrics that can be used to evaluate investment performance include:

• Return on investment (ROI): Calculates the return of an investment divided by its cost.
• Internal rate of return (IRR): Calculates the rate of return of an investment based on its cash flows.
• Modified internal rate of return (MIRR): Calculates the rate of return of an investment based on its cash flows and assumes that cash flows are reinvested at a specified rate.

Conclusion

Compound annual growth rate (CAGR) is a powerful metric that can help investors understand investment performance and make informed investment decisions. By understanding its definition, calculation, and significance, investors can gain a deeper understanding of the investments they hold.