What Is Compound Annual Growth Rate (CAGR)?

Compound annual growth rate, or CAGR, is a backward-looking metric that examines a company’s or an asset’s performance over a specified period of time. Using the CAGR formula, investors can calculate the rate of return that would have been necessary for the asset to grow from its initial value to its final value for that period of time.

CAGR is a simple metric that smoothes out price volatility and assumes all profits are reinvested in order to arrive at an annual average growth rate. Because it’s essentially an average of an asset’s returns, the CAGR formula can be used to compare the performance of disparate investments over the same time period.

While convenient, the CAGR doesn’t tell the entire story of an asset’s performance, because it averages the annual return. The actual performance of most investments is not a straight progression but varies from year to year, sometimes dramatically.

CAGR also takes into account compound interest, and assumes the reinvestment of all profits or other income from an investment, which may not be part of an investor’s strategy.

Having a grasp of what the definition of CAGR is, how it works and what it means can help you invest in ETFs, stocks, bonds and a wide range of assets.

Understanding the CAGR Definition

As an investment metric, CAGR offers a summary of the annual return of a given investment, as though it had grown at a consistent rate every year.

As such it can be useful in comparing how different assets have performed over long periods of time, or how they’ve performed under different market conditions, such as a bull market versus a downturn. It is just one of many important metrics, such as net present value.

As with most investment metrics, however, it comes with some blind spots. Two investments with similar CAGRs may differ in other ways, such as their volatility — a factor that investors may want to consider when buying stocks or other securities.

When investing online, CAGR can be a good starting place. But it doesn’t take into account other factors that affect an asset’s returns, such as underlying revenues, its role in the global economy, or competition in the space. It can help evaluate performance, but is far from the final word.

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The CAGR Formula and How to Calculate It

Here is the formula you can use to calculate CAGR:

1.    Start by dividing the value of an investment at the end of the period you’re tracking by its beginning value.

2.    Take the result, and raise it to an exponent of one, divided by the total number of years that you are tracking.

3.    From that result, subtract one.

4.    Take that number and multiply it by 100 to reach the final CAGR percentage return.

Another way to write the formula is:

CAGR = (Ending value/beginning value) ^ (1/no. of periods) – 1 x 100

A Simple CAGR Example

To understand how you might use the CAGR, imagine a hypothetical portfolio of $1,000 that you invested for three years, and then wanted to check its performance.

In the first year, it delivered $200 in returns, raising the amount invested to $1,200, for a 20% return. Assume that year, and every year after, you reinvested the returns.

The next year, your portfolio grew to $1,300, an increase of $100, or 8.33%.

Then in the third and final year, the portfolio reached a value of $1,600, growing by $300 or 18.75%.

As an investor, that last year might leave you with the impression that the portfolio was doing really well, with a nearly 19% return. But the CAGR can’t tell you the full story of an investment’s or a portfolio’s performance, which is how much returns varied from year to year.

Using the CAGR Formula

To find the actual compound annual growth rate for your portfolio, you’d start with $1,000 as the beginning investment and $1,600 as the ending investment. You’d divide the ending value by its beginning value, then raise it to an exponent of one over the three years you’re tracking (⅓), also known as the cube root in this case.

Last, you’d subtract one from the result and multiply it by 100 to reach the final compound annual growth rate percentage of your portfolio.

CAGR = ($1,600 / $1,000)^1/3 – 1 x 100

In this example, the CAGR of your portfolio is 16.96%. That may come in handy, along with an investment calculator, as you compare potential investments for your portfolio.

Why Do Investors Use CAGR?

As a formula, CAGR can be used to calculate the average annual returns of anything from stocks to mutual funds to real estate to an art collection. It’s a useful tool because it applies to so many kinds of assets, and because it offers the perspective of time, which is valuable given the volatility of many assets.

For example, in the CAGR formula above, the compound annual growth rate at three years would be different than at five or 10 years, depending on the inputs. Let’s say you were tracking your portfolio over 10 years, and the ending value was $1,800 instead. Here, the compound annual growth rate would be 6.05% — showing slower growth over time.

Even if one asset goes up and down significantly from year to year, the CAGR can offer an insight into its overall performance. That can help investors manage a self-directed investing account.

Comparing Different Investments

By offering a single performance metric, compound annual growth rate is a shortcut to help investors evaluate the relative performance of different investments. It saves time, much like the rule of 72 (a formula that can help investors estimate how long it might take for an investment to double in value).

For example, a bond fund and a stock ETF are made up of different securities, and deliver returns in different ways. But by calculating the CAGR for each fund, an investor can compare their returns in a straightforward way.

The investor can use that comparison in many ways. They can use it to evaluate what’s working and what’s not in their portfolio, or how to shift their holdings, or to help decide how to allocate new assets.

Tracking Business Performance

Companies also use CAGR as a metric to track key performance indicators (KPIs) within their organization. These can include things like sales, operating costs, or even employee satisfaction. In a large organization, these metrics can be used to make strategic decisions.

When a company has access to a publicly traded competitor’s reported numbers, then a company may apply the CAGR formula to its competitor’s sales, revenues, and other metrics to see how they’re performing by comparison.

Limitations of the Compound Annual Growth Rate

One reason that CAGR is important to investors is that it’s a simple rendering of a given investment’s growth, smoothed over time — and that’s also its weakness. The whole story of any investment is always far more complex. Investment returns can vary widely from year to year, and volatility is something investors would be wise to take into account.

Compound annual growth rate is also limited in that it only speaks to the specific time span it tracks; it doesn’t reflect the performance of other years. Also, the formula doesn’t reveal any anomalous events that may have driven performance, and might be significant factors for investors to consider.

Investments aren’t the only things that vary from year to year — so do investors. And CAGR doesn’t take into account the amount or timing of any new investments or withdrawals from a given investment.

Volatility and Smooth Rate of Growth

The simplicity of a single CAGR number for a given time period is sometimes referred to as a smoothed rate of growth. That smoothing means that the CAGR necessarily leaves out the volatility that occurred on the way to reaching that number.

Aside from a few investments, such as bonds that are held to maturity, the actual return of any investment tends to vary from year to year. These swings can sometimes be dramatic. For this reason, relying too heavily on the CAGR to evaluate performance or new opportunities can create costly blindspots, simply because the compound annual growth rate ignores volatility.

For example, if an investor held a portfolio for five years, and added funds to the portfolio during the five-year period, then the CAGR would be inflated. The CAGR would calculate the rate of return based on the beginning and ending balances over the five years, and would essentially count the deposited funds as part of the annual growth rate, which would be inaccurate.

Impact of Adding or Withdrawing Funds

Another factor to consider with CAGR is that it assumes the investor will plow all the profits, yields or other income from an investment back into it.

But for most investors, some years they may invest more than they planned, while they may need to make withdrawals in other years. For that reason, the CAGR won’t necessarily reflect the money that an investor has made or would make on a given investment.

CAGR vs. Internal Rate of Return (IRR)

To address some of the shortcomings of CAGR, many sophisticated investors will use Internal rate of return (IRR) as a measurement for returns. IRR is more complex, and accounts for changing levels of cash moving in and out of a portfolio.

To arrive at IRR, investors have to conduct more detailed calculations than they do for CAGR. While investors can calculate CAGR by hand, using the steps described above, most investors will use Excel or portfolio accounting software to calculate the IRR.

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What Is Considered a Good CAGR?

As an investor, you generally want higher returns, i.e., higher compound growth rate. And the question of a good CAGR is similar to the question of how to measure good ROI. Simply put, there’s no single number that constitutes a good CAGR.

CAGR is a metric to track performance, and whether the growth rate it captures is good or not depends on the context. How much risk are you taking? What CAGRs are similar investments delivering? CAGR is valuable in comparing investments. But it can be misleading when comparing apples and oranges — like comparing technology stocks to municipal bonds.

The Takeaway

The definition of CAGR, or compound annual growth rate, is a metric that delivers a smoothed annualized rate of growth over a specific period. Investors can use it as a standardized shorthand to compare the performance of disparate assets in varying environments.

While it is a useful tool to track the performance of stocks, mutual funds, commodities, or other assets, it is only one such tool. As a single metric, CAGR overlooks important factors, such as volatility and the returns for investors who take money out or make new investments during a given period.

You can use CAGR to get a sense of an investment’s performance, but it’s important to do your research, and consider a wide range of factors before investing.

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FAQ

What is the difference between CAGR and a traditional growth rate?

The distinction is that CAGR accounts for the compounding of returns year upon year, while the average annual return does not. The average annual return is a simple arithmetic mean — you just add up the returns for each year and divide by the number of years.

Can a compound annual growth rate be negative?

Despite having “growth” in the name, CAGRs can be negative if the value of an investment declines in value over the given period. A CAGR can indicate an average annual loss rather than growth.

How does risk-adjusted CAGR work?

A risk-adjusted CAGR works like a regular CAGR, while adjusting an investment’s return for volatility or risk. It can be calculated in one of two ways, either by multiplying the CAGR by one minus the standard deviation, or by dividing the CAGR by a downside risk metric like maximum drawdown.

What is the difference between AAGR and CAGR?

The difference between AAGR and CAGR is that CAGR factors in the compounding of returns year upon year. The AAGR does not, and is arrived at by adding up the returns for each year and dividing it by the number of years.

How do you calculate CAGR for a fractional number of years?

You can calculate CAGR for a fractional number of years by using the standard formula, but when you divide the ending value by the beginning value, use the fractional number of years.

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