Introduction to CAGR

By Pinyo, on August 28, 2007

On books, web sites, and blogs (including this one) you may have come across references such as the S&P 500 has grown 13% 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 states an annualized return, most likely he is referring to CAGR, or Compound Annual Growth Rate. The S&P 500 did not return a steady 13% gain each year — in reality, some years it went up and some down. In the graph below, you can see the S&P 500 percentage growth adjusted for dividend yield. You can see that the growth rate is different each year. In fact, in 5 out of the 30 years it actually went down (table column F).

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

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

For example, S&P 500 from 1977 to 2007 (adjusted for dividend yield)

CAGR = (3351.66/ 95.10) ^ (1 / 30) – 1 = 12.61%

Graphically, it is a graph smoothing function. In the graph below, you can see S&P 500 growth — blue line (table column B) represents investment growth, and green 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 (orange, table column D) and S&P 500 plus dividend (purple, table column H).

From the table below, you can see that CAGR of S&P 500 plus dividend yield from 1977 to 2007 was 12.61%. Of course, your actual return can be very different from this scenario. For example, if invested from 2000 to 2007, your CAGR would be a mere 3.24%!

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
3. Link to CAGR Spreadsheet

Here are a few things I learned about CAGR over the years:

• It is a good measure of performance for a specified time period
• It may have no bearing for my specific investment period. For instance, I started investing in 1996, so my CAGR would have been 8.34% if I had invested in an S&P 500 index fund.
• It does not say anything about investment volatility — i.e., CD has CAGR of about 5% with no volatility but S&P 500 has its good years and bad years

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

This article was featured in the Carnival of Personal Finance #116 – NSA Edition hosted by Advanced Personal Finance.

Read more about

Get free updates

    via Twitter
    via Facebook
    via RSS or Email

Share this article

• 
• 
• 
• 
• Share

Pinyo is the brain behind Moolanomy personal finance blog and a few other web sites. If you like this article, please subscribe for free daily email updates.

All posts by Pinyo

Please share your comment:

Comment Rules: Constructive criticism is welcomed. Please use your PERSONAL name or initials and not your business name or URL, as the latter comes off like spam and I'll most likely delete your comment. Have fun and thanks for adding to the conversation! Here's our comment policy and guidelines.

3 blogs that link to this article:

If your trackback does not show in 24 hours, please resend to this trackback URI.

1. Advanced Personal Finance » Blog Archive » Carnival of Personal Finance #116 - NSA Edition
2. Quit Your Job, Collect Credit Cards, Save With Grocery Deals: My Carnival Picks » Money and Personal Finance Blog In Silicon Valley
3. A Compound Annual Growth Rate (CAGR) Calculator | Stock Research Pro