10x Compounding and an Exercise for the Student
Most investors are familiar with the “Rule of 72,” a formula for approximating the time it takes an investment to double at a given compounded annual return. The rule states that dividing 72 by the annual return equals the number of years to double. Conversely, the Rule of 72 can also determine the annual return by dividing 72 by the number of years. For example, it takes nine years to double an investment compounding at 8% a year (72/8% = 9 years). Similarly, the return required to double an investment in just six years is 12% (72/6 years = 12%).
Retirement is the primary goal of many investment plans. These long-range plans require more than just a doubling of an investment and involve time horizons that are longer than those easily estimated with the Rule of 72. Instead of increasing your investment by 2x, what if you wanted to increase it 10x? To make the planning process easier, I developed the “Rule of 240,” a formula for approximating the time and/or compounded return needed for an investment to increase by a factor of 10, or 10x compounding. The mathematical term for a factor of 10 is called an “order of magnitude.” It may be easier to think about it as “adding a zero” to your investment.
The methodology for using the “Rule of 240 Compounding” is the same as the Rule of 72. Namely, the number of years it takes to increase an investment by an order of magnitude, multiplied by the annual return is equal to 240. For example, an investment will take 20 years to add a zero ($100 will grow to $1,000) if the return is 12% a year (240/12% = 20 years). With an 8% annual return, it will take an investment 30 years to increase by a factor of 10.
Although the Rule of 240 is an estimation technique for 10x compounding, it is a reasonably accurate estimate. The Rule of 240 is accurate to within six months for all returns in the 6% to 15% range and is accurate to within 0.1% a year for all periods greater than 21 years.
What about inflation and taxes? The previous description referred to an “investment” gaining 10x, but in reality, the rule applies to anything in nature that compounds—including inflation.
Inflation at 3% a year would be 10x after 80 years (240/3). Or, if you prefer to think of it in terms of diminishing value, then your $1 will be worth only 10 cents in 80 years at 3% inflation. If a new car cost $4,000 in 1966 and $40,000 today, then automobile inflation can be estimated to be 240/50, or about 4.8% a year for the past 50 years. Granted, today’s $40,000 vehicle has more bells and whistles than a 1966 model, but the math behind the estimate is still valid.
As for inflation-adjusted investment returns, the Rule of 240 still applies. However, you will need to adjust the “nominal” return for the after-inflation “real” return. For example, a 12% nominal return takes 20 years to increase 10x. With 3% inflation, your 12% nominal return becomes a 9% real return, and the number of years to achieve a 10x inflation-adjusted return becomes 240/9= 26.7 years.
Tax impacts can be estimated in a similar fashion. If you are “paying taxes” as you go, then simply use your after-tax annual return instead of the nominal return. If you adjust your nominal return for both inflation and taxes, be prepared for disappointment because your time to achieve a 10x increase just became much longer.
You can also use the Rule of 240 to provide a reality check to anyone that believes a $100k investment account is going to magically turn into a $1 million retirement fund at 5% a year. With zero inflation, that lofty goal requires about 48 years (240/5). With 3% inflation, that 5% nominal return becomes only a 2% real return, and the time required to achieve 10x quickly extends to multiple lifetimes (240/2 = ??, the answer is left as an exercise for the student)
Note: This is an updated version of the article I first published in July 1999, and an expanded version of the Rule of 240 published in March 2015.
An Exercise for the Student
Each week I bring you my standard three-part EdgeCharts showing the momentum and relative strength rankings for sectors, factors, and global categories. I attempt to highlight any noteworthy changes and provide my analysis on the significance of those changes. Additionally, I monitor the overall structures for trend shifts, rotations, and specific market-environment patterns.
Today, we are doing something different. Instead of a single chart, I’m bringing you two of them: last week’s chart and today’s chart. Additionally, I am not going to provide any commentary or analysis on the changes. Today, it is up to you to decipher and analyze the variations. Or as they say, “the rest is left as an exercise for the student.” If you forgot what I said last week, you can read it here. In case you are worried—don’t be. I’ll be back next week with my regular insights.
The charts above depict both the relative strength and absolute strength of various market sectors, styles, and geographic locations on an intermediate-term basis. Each grouping is sorted (top to bottom) by relative strength. The magnitude of the displayed RSM value is a measure of absolute strength, which is our proprietary method of measuring and reporting the intermediate-term strength as an annualized value.
“Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.”
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