# Compound Growth and How It Is Calculated ## Key Takeaways

• Compound annual growth rate (CAGR) is a useful metric by which to gauge the average return of assets that rise and fall in value over time.
• CAGR can also be used to compare the performance of a group of similar assets.
• However, CAGR should not be used to determine investment risk.

The true power of investing is derived from the amount of time an investment is given to grow. Yes, the size of the capital investment also plays a role. However, growth is achieved when interest earns interest. This compounding effect can snowball over time, causing the principal investment and the interest gained from that investment to grow simultaneously.

This brings us to the idea of compound growth and how it is calculated.

## What is Compound Growth?

In the simplest terms, compound growth is defined as an investment’s average growth rate over a specific period. Essentially, it is the returns earned on the original investment amount, added to subsequent earnings on the combined amounts as earnings are reinvested. This can create many multiples of the original investment over the long term.

For example, if an investor takes a \$2,000 position in an opportunity at an annual growth rate of 6%. They would have \$2,120 at the end of the first year. Reinvesting that return, they would earn 6% on the \$2,120 the following year, giving them a total of \$2,247.20. Assuming a consistent annual 6% rate of growth, the investment would be returning over \$650 annually over a 30-year period.

This is the power of compounding

However, few things grow continuously in the real world. There are periods of intense growth and moderate growth, as well as some with no growth at all.

The reality is that true compound growth is rare. However, measuring it can still be important to investors. Calculating the average growth rate of an investment over a certain period can provide investors with a metric by which they can compare various investing opportunities. This can help them determine the potential of a given opportunity.

### Compound Annual Growth Rate

The compounded annual growth rate (CAGR) is considered one of the most accurate means of calculating the returns of an investment that’s likely to fluctuate in value over time. CAGR is a good way to gain insights into how different investments have performed over a given period, or against a specific benchmark.

Within this, however, it is important to note that the CAGR represents a “smoothed” rate of return. Rather than a reckoning of the growth an investment achieved in any specific year, the CAGR reflects the average growth rate of an investment over an extended period.

### Calculating a CAGR

A CAGR calculation is achieved by first dividing the value of an investment at the end of a prescribed period by its value at the start of that interval. The quotient of that calculation is then raised to an exponent of one, divided by the number of years under consideration. From the result of that calculation, one is subtracted, the result of which is then multiplied by 100 to determine the percentage.

The formula is as follows:

CAGR = (EV/BV)1/n − 1×100

EV=Ending value

BV=Beginning value

n=Number of years​

To illustrate this, imagine a scenario in which \$10,000 was invested in a portfolio over a three-year period. The investment gained 30% the first year, which was reinvested, making the principal amount \$13,000 going into the second year. The investment then gained 7.69% the second year, which when reinvested, making the principal amount \$14,000 going into the third year. That amount realized a gain of 35.71% the third year, bringing the total to \$19,000.

While this scenario illustrates a great deal of volatility over that three-year period, the average growth rate was 23.86%

Using the formula above, this can be calculated as follows:

CAGR = (\$19,000/\$10,000)1/3 − 1×100 = 23.86%

### CAGR Uses

As mentioned above, CAGR can be useful for investors as a metric for comparing investment opportunities. While market volatility can mask the true performance potential of an asset, comparing its CAGR to other similar ones can result in a reasonable evaluation.

CAGR can also be used to help an investor determine the average rate of return they’ll need to achieve a particular goal. Say for example an investor knows that they will need \$100,000 in 18 years and they have \$30,000 to invest.

Needed Rate of Return = (\$50,000/\$15,000)1/18 − 1×100 = 6.90%

Based upon that calculation, they would need to find an investment returning 6.9% or better to achieve their goal.

### CAGR Limitations

Any discussion of CAGR must come back to the fact that it represents a smoothed rate of growth. In other words, the peaks and troughs of an investment’s performance curve are leveled out when calculating a CAGR. Thus, the calculation will not provide a true reflection of the volatility an investment experiences on its way to the calculated CAGR.

Further, the CAGR does not take into consideration additions and withdrawals from a portfolio over time. Adding to the principal amount over the period measured will artificially inflate the CAGR. The CAGR would be calculated based on the beginning and ending values, so the interim deposits would not be taken into consideration. Instead, they’d be seen as growth.

Similarly, withdrawals could lower the CAGR artificially.

It is also important to note that investors should be careful to understand that past performance is not always an indicator of future returns. As an example, a strong CAGR calculated over the three years leading up to the quarantines imposed by the COVID-19 pandemic would in no way be predictive of the market drops that occurred during the quarantine periods, or of the post-quarantine inflationary period.

A CAGR quote can also be used to mask periods of poor performance. Say for example an investment fund has a value of \$200,000 in year one, \$142,000 in year two, \$88,000 in year three, \$162,000 in year four and \$252,000 in year five. The 42% CAGR of the last three years of that scenario would look really good. However, the 4.73% CAGR over the entire five-year period is much less impressive.

### CAGR, Volatility, Portfolio Diversification and Alternative Investments

Going back to a previous point, calculating a compounded annual growth rate can smooth out periods of volatility. However, investors cannot afford to ignore volatility.

Thus, portfolio diversification is strong advice.

Varying the mix of asset classes held within a portfolio can help accomplish this. For example, fixed-price assets such as bonds, certificates of deposit and treasury notes usually respond to market volatility more favorably than publicly traded equities. This makes them useful when it comes to defending against potential instability. Alternative investments can also be potentially useful tools for portfolio diversification

Traditional portfolio asset allocation envisages a 60% public stock and 40% fixed income allocation. However, a more balanced 60/20/20 or 50/30/20 split, incorporating alternative assets, may make a portfolio less sensitive to public market short-term swings.

Real estate, private equity, venture capital, digital assets, and collectibles are among asset classes deemed “alternative investments.” Broadly speaking, such investments tend to be less connected to public equity, and thus offer potential for diversification.

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### In Summary

Compound annual growth rate is a useful metric when it comes to measuring the performance of an asset over a given period of time. However, it is not an accurate indicator of investment risk. In other words, the CAGR is but one of the tools an investor should apply to the evaluation of an investment opportunity. This rate should be also considered for retirement planning, for example.