Caveats In Compounding

“Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it.”
– Albert Einstein

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“Compounding is the most powerful force in the universe”
– Albert Einstein ‍

‍“My wealth has come from a combination of living in America, some lucky genes, and compound interest.”
– Warren Buffett

Compounding really is the 8th Wonder of the World. In a recent analysis, we were comparing the CAGR (Compound Annual Growth Rate) of two portfolios and noticed two unique qualities of compounding that are important to remember when using CAGR:
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1. Small differences in CAGR can compound to large differences over time

2. A 1% difference in two small CAGRs is not the same as a 1% difference in two large CAGRs

Small differences in CAGR can compound to large differences over time

‍Imagine you have two portfolios. One generating 8% per year and another 9%. The 1% difference seems trivial. Because of compounding, it is not.

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The 10-year performance difference is a non-trivial 20.8%. This means that finding investments that may seem marginally different when compared at the small scale of a year, can have profound differences over time.

One interesting fact was that the total difference over ten years was 20.8%, which is not the same as the 1% difference compounded over 10 years, which is 10.5%. This leads to the second unique quality…

A 1% difference in two small CAGRs is not the same as a 1% difference in two large CAGRs

If we bump the performance slightly up but keep the difference 1%, the total difference grows from 20.8% to 22.6%.

That 1% difference gets to compound a bigger base and thus results in a larger total return difference. This is counterintuitive. An investor may be indifferent between a 23% and a 24% return while being sensitive to a 2% versus 3% return. The later seems much more meaningful because the relative difference is 50%.

In the graph below, the difference between a 2% and 3% return is $12.5M (12.5% on $100M fund) over 10 years. The difference between a 23% and 24% return is $62.1M! They are both 1% differences, but they are not created equal.

Compounding is amazing but can be amazingly difficult to conceptualize. As an investor, your job is to be a professional compounder. Keep your tools sharp by remembering that CAGRs don’t tell the whole story. To get a better sense of the return stream, compare the CAGR to the total return for a period of time and then perform some basic sensitivity analysis. This allows the compounding impact on returns to present itself in a way that is easier to put into perspective and help you make better decisions.

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