In finance and investing, whether you’re looking at stocks or savings accounts, it’s often useful to calculate your returns to measure how you’re doing. One way is to calculate your compound annual growth rate or CAGR. The best way I’ve seen this defined is in the investopedia.com dictionary (hence the link), which says:
CAGR isn’t the actual return in reality. It’s an imaginary number that describes the rate at which an investment would have grown if it grew at a steady rate. You can think of CAGR as a way to smooth out the returns.
Here’s the general formula for calculating CAGR:
CAGR = (ending amount / beginning amount)(1 / # of years) – 1
When you look at mutual fund performances, the 1 year, 3 year, 5 year, and 10 year average annual returns you see are essentially CAGR calculations. For example, if you started out with an investment of $100 in your savings account, and after 5 years, this amount grew to $200, then your investment would have grown 100%. However, your compound annual growth rate would be 14.87%. In other words, if you had earned interest at a steady 14.87% each year for five years, you would have ended up with $200. I’ve included an excel template for calculating CAGR under the Tools & Calculators section of this website. (Update: I’ve added an online CAGR calculator.)
CAGR and mutual funds
I happened to find a website for a professional suite of tools called StyleAdvisor through Google one day while looking for mutual fund performance measures. They had an interesting writeup about one of their tools that measures how well mutual funds have performed in which they emphasized end-point bias in mutual fund performance. Basically, if a fund has underperformed for several years but has one really good year, its CAGR can still look very good because what’s happening essentially is that the returns of the one very good year are getting spread out (averaged) across all the other underperforming years. For this reason, it’s worth looking out for long-term and consistently good performance in a mutual fund by using rolling averages instead of focusing on average annual return rates. As a side note, it seems that StyleAdvisor does offer some good tools, but unfortunately their price tag shows they’re definitely geared toward institutional investors!
An interesting thought
After reading StyleAdvisor’s explanation, I realized the CAGR game might apply to stock investments as well. Suppose you invested in a stock or index. Then the longer you hold the stock, the greater the chance that you’d hit a year with abnormal returns (good or bad). Then, assuming you could find good companies or long-term prospects to invest in, and that the trend of the stock market tends to be upward instead of downward over long enough periods of time, it seems that you have a better chance of having good overall returns (as measured by CAGR) the longer you held the investments.
By the way, it seems to me that consistent and steady performance (or even matching the market) is underappreciated in the general investing community. People tend to focus on beating the market or trying to get double-digit returns without any real rationale or logical reasoning as to why this should be achievable. Jason Zweig, the commentator in the most recent edition of The Intelligent Investor, wrote something that really struck me, assuming it’s true:
Back in 1982, the average net worth of a Forbes 400 member was $230 million. To make it onto the 2002 Forbes 400, the average 1982 member needed to earn only a 4.5% average annual return on his wealth — during a period when even bank accounts yielded far more than that and the stock market gained an average of 13.2%. So how many of the Forbes 400 fotrunes from 1982 remained on the list 20 years later? Only 64 of the original members — a measily 16% — were still on the list in 2002. (p. 185)
Guess consistently good performance, even if underappreciated, is really worth seeking!
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AllThingsFinancial » Blog Archive » Day 4 - Basics of Investing
[…] Compound Annual Growth Rate (CAGR) […]
Meigs Hodge
I am trying to figure out the Excel commands in the formula, as they are different from the way Excel tells you to calcuate CAGR (XIRR)
What does the accent circumflex do in the formula? It is between the two quantities in parenthesis.
And what do the dollar signs do?
Ricemutt
@Meigs: I’m assuming you’re referring to the equations in the CAGR excel spreadsheet above (?) If so, the “^” is the way in Excel to denote raising something to a power. So, for example, 2*2*2 = 8 = 2^3 in Excel. (It’s also a common notation for several other applications/languages).
The “$” before something (like $B$3 for example) means make that cell “constant”. It’s really only used to make things easier when I copy-and-paste equations. (In Excel, if you copy and paste an equation across several rows or columns, the variables (cells) will automatically change relative to the position of the cutting-and-pasting, and by entering the “$” symbols, you keep the cell absolute.) In reality, I don’t think it impacts what you’re trying to figure out…just look at $B$3 as the same thing as “the contents of cell B3”.
I don’t know if it will help, but I also wrote a post about XIRR a couple of weeks ago that’s also on this site (just do a search for “XIRR” on the sidebar above). XIRR is an iterative function in Excel and there should be situations where XIRR and CAGR calculate the same thing, but I can’t come up with one right now as I’m logging in remotely from a library without access to Excel to demonstrate. A friend of mine claims to have determined that XIRR is essentially finding the impled rate at which your returns equal your investments assuming compounding on a daily basis. I’m not sure if that’s true.
Hope this helps more than it confuses, but feel free to write again.
AllFinancialMatters » Blog Archive » How to Compute Compound Annual Growth Rate - CAGR
[…] Ricemutt over at Experiments in Finance has written some wonderful posts (here, here, and here) on financial math. It was through her (I think Ricemutt is a “her,” but I’m not positive on that) posts that I discovered the meaning of Compound Annual Growth Rate or CAGR as it is commonly known. Yes, I was aware of CAGR but I never really thought about it much. I didn’t know it at the time that I put my Average vs. Geometric Average post together using an Excel spreadsheet, but CAGR and Geometric Average are the same thing. And, to top it off, I found a formula for calculating them that is MUCH easier than I previously understood. That’s good for all of us! […]
Using the Goal Seek function in Excel: a brief tutorial | Experiments in Finance
[…] CAGR, or compound annual growth rate, is one way to measure your annualized return given an initial amount, and ending amount, and a period of time. As regular readers might recall, the formula goes like this: […]
Henry
Sorry to impose. May I just check with you regarding the use of above mention formula CAGR.
Despite all the calculations. the result will not be meaning full unless I had something to compare with.
Normally the funds factsheet will show the offer to bid returns (%)- SGD over a period of years (1yr … 5yrs). Ironically, the manager would not tell you whether the data is derived from (CAGR). The generic term used is “annualised avg return”
Assuming the data is year-over-year growth rate, with dividend reinvested or (CAGR)
But how am I going to compare when I had invested on different time periods. Do I use XIRR, IRR to compare against CAGR. It does not make sense to me.
Can you enlighten me pls. I am confused…
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R K Gupta
Can you tell me any formula available in Excel to compute CAGR.
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