Fri 19 Jan 2007

**Who:** This post is for people who want to know what the compound annual growth rate (CAGR) is. This post will be helpful for those who want to know more about CAGR, its benefits, and its drawbacks.

**What:** This post will discuss what CAGR is and the mathematics behind calculating it. There will also be a discussion of the utility one can get out of using CAGR as a part of financial analysis.

**What is it?**

The Compound Annual Growth Rate (CAGR) is a number which provides an average yearly growth rate for an investment over time. Since most investment returns vary from year to year, just knowing how much the investment returned over a single, short period of time is not very helpful. Knowing how much an investment returned in 2001, 2002, 2003, and 2004 individually will be more helpful. However, wouldn’t it be nice to have an average return per year over that period of time? Yes it would, and that is what a compound growth rate does. In the example below, we will take the average of the individual yearly returns for an investment over 4 years to see if this gives us the overall growth rate over the course of the 4 years. **Hint:** It doesn’t.

Example 1 shows that if you average the individual yearly growth rates, you obtain a 27.88% rate of growth per year. If you apply this 27.88% growth rate over four years, you would expect the final value of a $1,000 investment to be $2,674 when in actuality it is it only $2,000. As you can see, we need a better way to figure out the average yearly growth. This is where CAGR comes in. In example 2 below, the Excel-ically inclined can see a quick review of how CAGR is calculated.

**The Formula**

For those of you who do not like Excel and/or prefer mathematically formulas, I have created this little image for you (I did it in MS Paint; more fun than I thought). If you haven’t figured it out, S = starting value, E = ending value, and Y = the number of years over which the investment grew from S to E.

**Ok, I know what it is. Why do I care?**

The CAGR is an excellent way to intuitively understand how much an investment is returning over a given period of time. If an investment isn’t giving you good returns, why waste your time with it? Since everyone knows this, the section will be very short. If you take one thing out of this section, let it be this: *By itself, the compound annual growth rate is almost useless when evaluating an investment. Only with proper context can we correctly utilize CAGR to make an informed devision.*

**I already knew all that stuff. Tell me something I don’t know.**

There are a boatload of problems with CAGR. I will highlight some of the problems here because I have found that many new investors and intermediate investors alike make a lot of these mistakes. In the long run, these mistakes can have devastating effects on one’s portfolio.

- What is a good return? Stop! Before you answer that question, read what AFR thinks about what constitutes a good return. The point is that out of context, individual return numbers mean nothing. If I offered you a 100% return, would you jump on the opportunity? What if I then said that the investment was a bet on black in roulette? Would you still take it? Remember, always contextualize your returns.

- CAGR says *nothing* about the volatility of the underlying investment. If I offered you 3 investments A, B, and C with 10%, 20%, and 30% CAGR over the last 3 years respectively, which one would you choose? Think about your answer and then look at the charts below. If you compare the Sharpe Ratios of these investments (assuming 5% risk free rate), you can see that investment A is clearly a superior choice in terms of mathematical risk/reward. The moral of the story here is that you should always compare the returns with the risk that they require you to take.

- What if we took the example above and looked at the CAGR over 15 years as opposed to just 3 years. You may find that investments A, B, and C have CAGRs of 5%, 19% and 10% respectively over 15 years. Would this change your choice of investment from A to B? All else being equal, it would probably change my mind. You’ve all heard the phrase “past performance is no guarantee of future results.” This is ESPECIALLY true for statistics that reflect information over a SHORT period of time. Asset classes/sectors tear up the market for short periods of time and then shrivel (Tech stocks in the late 90’s anyone?). The moral of the story here is that we should be careful to scrutinize a long history of the performance of an investment as opposed to viewing only a short period of data.
*Note: I am not claiming that historical performance is even a good way to pick investments, long term history is just better than short term history (generally), thats all!*

**The Bottom Line**

The title of the post says it all… Beware. Realize that the compound annual growth statistic (the one you see on all the websites which show returns of various funds over time) has a very specific usage. Utilizing the ratio out of context to make a financial decision has many drawbacks. Remember that the CAGR of an investment cannot be determined to be “good” or “bad” without a discussion of risks involved and remember that CAGR is often used to fool investors to jump into investments that have soared recently. Keep the CAGR in your bag of tricks, but make sure it’s not all that you’ve got in there.

Popularity: 18%

### One Response to “Compound Annual Growth Rate: Beware”

### Leave a Reply

You must be logged in to post a comment.

January 24th, 2007 at 8:45 am

[…] Compound Annual Growth Rate: Beware […]