CAGR explained
Compound annual growth rate, or CAGR, is one of the most important metrics of investing. Unlike a savings account or CD at a bank, most investments don’t pay pre-defined interest. In fact, investments can lose value, including principal. How do we calculate investment returns over time when investments fluctuate?
The answer is CAGR, which is something akin to the investing equivalent of interest. CAGR represents the annual return of an investment as if the returns were steady. The formula for CAGR is:
Where A is the final amount, B is the initial amount, and t is time in years. So CAGR is retrospectively calculated by plugging in the time period along with the initial portfolio balance and the final portfolio balance to see what the equivalent annual returns are over that time.
CAGR is not simply the arithmetic mean of your annual returns! For example, if an investment returns -50% (loses half its value) in year 1 and returns +100% (doubles in value) in year 2, the year 1 CAGR is indeed -50% and the year 2 CAGR is 100%. The arithmetic mean of the annual returns would suggest that over this 2-year period, the investment returned 25% ([-50%+100%]/2). But the actual CAGR over this 2-year period is 0% because the investment ended at the same value as it started!
There are a number of CAGR calculators readily available on the internet. Additionally, the RRI function allows you to calculate CAGR in Microsoft Excel. In this example, an investment took 10 years to double in value from $1,000 to $2,000:
The function needs 3 variables: RRI (number of years, initial amount, final amount)
The RRI function tells us that the CAGR over this time is 7.18%. It doesn’t matter how the investment ended up at $2,000 after 10 years (in other words, the investment could have soared to $1 million in year 5 and crashed back to $2,000 by year 10); the returns are still equivalent to 7.18% interest annually. By the way, in the example above you can also see the “rule of 72” in action, where the time it takes for an investment to double in value is roughly equal to 72/interest. So, at 7.2% interest it takes about 10 years for an investment to double in value, and at 10% interest it takes about 7.2 years to double.
So in essence, CAGR “smoothes out” volatility and provides a number that can be used for comparisons and calculations. And CAGR can change dramatically depending on the time period used for calculation. For example, the CAGR of the S&P 500 is astonishing from 2009 to 2020 (around 14.5%), but less impressive from 2007 to 2020 (around 9%). From 2000 to 2020, it is even worse at a paltry 6.3% or so. This makes sense, as the market has been on an uninterrupted bull run for the past decade, but experienced 2 catastrophic crashes in the decade prior. The investor who started in 2009 probably has a much different view of the market’s overall performance than the investor who started in 2000.
When you research any fund or ETF, the fund will publish information about historical CAGR, calculated for the past 1, 3, 5, and 10 years (if the fund has been around for that long), as well as since inception. Using the formula above, you can also calculate CAGR for any investment that does not publish this information, such as individual stocks, or the price of a commodity. The following table shows the 1, 3, 5, and 10 year historical CAGR of a few popular investments over the past 10 years:
Of course, the future CAGR of any investment is unknowable. However, as I discussed in my book, the historical CAGR of the S&P 500 (and the overall domestic stock market) is around 9 to 10% when calculated out to 40 years, 50 years, or even longer. Once we look past short-term volatility (short-term in this case can be as long as a decade!), the long-term returns have been steady. This is why the stock market keeps people awake at night, but actually makes for a good long-term investment.
While it might be tempting to view CAGR interchangeably with interest, however, it is not. Although CAGR calculations are agnostic to the performance fluctuations of an investment during a time period (again, only the initial amount and final amount during that time matters), one fascinating phenomenon of CAGR is that the sequence of returns is still highly important. For more on this topic, see my follow-up article on sequence of returns and why it matters.
Happy investing!
