# Compound Annual Growth Rate (CAGR) Calculation and Examples

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You may have come across references such as the S&P 500 has grown 10% annually for the past 30 years or something to that effect. You may wonder what that means and where did they get that number. When someone mentions an annualized return, most likely he is referring to the Compound Annual Growth Rate or CAGR.

The S&P 500 did not return a steady 10% gain each year and it never will. In reality, some years it went up and some down, and even this is an average over the course of the year — the actual market goes up and down every micro-second that it is open for trading! In the graph below, you can see the S&P 500 percentage growth and dividend yield.

You can see that the growth rate is different each year. In fact, in 8 out of the 30 years, the S&P 500 lost value (table column F).

## How to Calculate CAGR

Mathematically, CAGR measures the rate of change in value between two points in time. The formula is express as:

CAGR = (ending value ÷ beginning value) ^ (1 ÷ years) – 1

For example, the S&P 500 from 1989 to 2018 (adjusted for dividend yield)

CAGR = (4,559.41 ÷ 277.72) ^ (1 ÷ 30) – 1 = 9.78%

Graphically, it is a graph smoothing function.

In the graph below, you can see S&P 500 growth — the green line (table column B) represents investment growth, and the purple line (table column G) represents investment growth plus dividend yield. Notice that the two lines trend upward, but go up and down each year.

The two smooth lines represent CAGR of S&P 500 (green dotted line, table column D) and S&P 500 plus dividends (purple dotted line, table column H).

From the table below, you can see that the CAGR of the S&P 500 growth plus dividend yield from 1989 to 2018 was 9.78%. Of course, your actual return can be very different from this scenario. For example, if invested from 2000 to 2008, your CAGR would be -3.70%!

Notes:

1. S&P 500 index data points reflect the last trading day of the year
2. Yield data from S&P Earnings: 1960-Current

Here are a few things important things about CAGR:

• It is a good measure of performance for a specified period
• It is easily manipulated by adjusting the period being measured. For instance, I can make the annual return higher or lower by cherry-picking different periods:
• 10 years = 13.15% (2009 to 2018) – right after the Financial Crisis of 2008
• 20 years = 5.59% (1999 to 2018) – right before the Dot Com Bubble of 2000
• 30 years = 9.98% (1989 to 2018)
• It does not say anything about investment volatility — i.e., a Certificate of Deposit has CAGR of about 2% with no volatility, but the S&P 500 has its good years and bad years

What else do you know about CAGR that you can share with us?

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## Compound Annual Growth Rate (CAGR) Calculation and Examples

by Pinyo Bhulipongsanon time to read: 2 min
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