### What Is Compounding?

Compounding is one of the most underappreciated concepts in finance and, when properly sustained over time, definitively the most powerful.

This edition of Investment Insights will cover compounding, arguably one of the most underappreciated concepts in finance. This is the second entry in a three-part series, the first of which covered volatility and the last of which will tie the two concepts together in a discussion of asset allocation. Like volatility, compounding is a foundational concept for the practice of protecting and building wealth and must be well understood to maximize your chances of achieving long-term success.

We will cover compounding much the same way we did volatility. We will begin with a contextually appropriate definition, go over its implications for protecting and building wealth, highlight some key lessons, discuss why it can be challenging to achieve and maintain and learn how to increase your odds of success to be as high as possible.

Along the way, several examples, both practical and theoretical, will help better illustrate this powerful arithmetic phenomenon. Consequently, this edition of Investment Insights will include far more charts than those that have come before.

Level-setting via Oxford Languages to begin, here is the conventional definition of the word compound.*1*

This definition is at the same time both accurate and limiting. Most people are likely familiar with compound interest, which the definition aptly describes. However, the concept of compounding and compound growth can actually be applied more broadly, to many different types of investments and situations. Thus, a more appropriate definition of compounding is realizing growth on top of previously realized growth, otherwise known as exponential growth (as opposed to linear growth). This dynamic is shown in the chart below.

Within this broader definition, stock prices certainly have the potential to compound in value over time, with gains earned on top of previous years’ gains in addition to the initial amount invested. Similarly, businesses can grow their free cash flow in a compound manner over time. As cash is reinvested in the business those investments generate additional free cash flow in subsequent years. In turn, this enables even greater reinvestment that then delivers even greater free cash flow in a virtuous cycle of sorts. This definition applies even in the natural world, where many types of organisms can exhibit exponential population growth. *2*

We can illustrate this definition practically using Capital Southwest Corporation as an example. Capital Southwest is a business development company. It borrows money to make loans to small businesses. Interest received on the loans, net of expenses, is distributed to shareholders as dividends. *3* As a result, this type of company typically carries a higher dividend yield than a traditional operating company, but this comes at the expense of lower potential for price appreciation. *4* This dynamic makes it the perfect example to illustrate how compounding works.

The chart below shows three data series. The first, bottom-most series is the value of $10,000 invested in Capital Southwest Corporation over time excluding dividends. The second series, in the middle on the chart, is the value of $10,000 over time assuming that dividends are received but not reinvested. The third series, on the top, is the value of $10,000 over time assuming that dividends are received and reinvested.

As shown, the return based on the stock price alone is just 12.9%. Including, but not reinvesting dividends, results in a higher return of 96.5%. However, including reinvested dividends the return is much higher, 138.4%. This last figure is an example of the benefits of compounding, as dividends are earned on previously received dividends. This exponential growth results in a ~20% higher ending value than if dividends were not reinvested.

From the perspective of protecting and building wealth, there are three important implications of compounding. First, slow and steady wins the race over time, every time. This can be seen in the chart below, which shows the performance of the NASDAQ 100 Index, through the headiest years of the Tech Bubble to the eventual aftermath, versus a boring old 6% compound annual return. *5* While the tech stocks raced out to a commanding lead during the euphoria, ultimately the slower, steadier investment prevailed. Perhaps there is good reason why the fable of the tortoise and the hare has been told and retold across millennia. *6*

Second, compounding takes time to work its magic. If you understand this, you can use it to your advantage. By starting to save for retirement early, you actually have to save less money overall than if you would start saving later in life. As the table below shows, to accumulate $1 million at age 70 you would have to save just $1,126 per year beginning at age 20. However, wait just ten years and the amount required more than doubles to $2,715. Wait even longer still and the necessary sums grow increasingly larger as compounding has less time to work its magic. *7*

Third, the corollary of compounding taking time to work its magic is that nothing much happens for a great while. I remember reading an article many years ago highlighting the fact that Warren Buffett had accumulated roughly half of his $100 billion plus fortune within the last ten years. *8* This seems impressive, but it is in fact a natural outcome of compounding. This can be shown using the “Rule of 72.”

The Rule of 72 is a mathematical shortcut for estimating roughly how many years it will take for an investment to double in value. To calculate this duration, divide 72 by the annual rate at which the investment is appreciating in value. For example, an investment returning 9% per year should roughly double in value every eight (72 / 9) years. *9* So for Warren Buffett’s wealth to have doubled over the last ten years, his investments must have appreciated 7.2% (72 / 7.2 = 10) per year. *10* When you put it that way, the achievement touted by the article seems relatively unimpressive. In fact, chances are that your net worth has roughly doubled over the last ten years as well.

Combining these three implications, compounding requires tremendous discipline over long periods of time where nothing much at all seems to happen until just before the end, when everything seems to happen almost all at once. *11* However, this only becomes reality if compounding is properly done, which is no small feat. If, as French mathematician Blaise Pascal put forth, “all men’s miseries derive from not being able to sit in a quiet room alone,” then we can begin to understand the challenges to actually achieving the desired outcome.

The first of these challenges are the psychological pressures standing in the way of achieving compounding. These psychological pressures stem from boredom and uncertainty. Boredom is quite simple, creating the urge to tinker or take unnecessary action. Each interrupts compounding (more on this later) and must be resisted. Uncertainty is more complex and results from the price volatility inherent in many types of investments. For even the best performing long-term investments, the path is rarely smooth and year-in, year-out returns are rarely equal to the long-term compound annual growth rate. More often there are extreme selloffs along the way that create significant pressure to sell your investments, which turns unrealized losses into realized losses and eliminates the potential for compounding to continue to occur.

Amazon Corporation’s stock is a great example of the latter pressure. Since its initial public offering in 1997, Amazon’s stock has compounded at a 33% annual rate. If you had invested $10,000 in Amazon’s IPO it would be worth $17,205,322 today, truly an incredible long-term outcome. However, between now and then Amazon’s stock suffered eight different selloffs in excess of 50%, including one in excess of 85% that lasted for nearly a year. *12* How many people actually had the intestinal fortitude to maintain a sizeable investment in Amazon, despite all the uncertainty, throughout all of these ups and downs? Likely very few I would bet, though I know of at least two. *13*

Another challenge to achieving compounding is simply maintaining a constant growth rate over extremely long periods of time. This is sometimes referred to as the law of large numbers, which is another way of saying that there are usually natural constraints on growth. We witness this dynamic in nature, where populations tend to grow exponentially for a period of time until resource limitations emerge and growth begins to slow before eventually leveling off. This dynamic also plays out in the business world. New products and businesses can grow quite rapidly initially for some time as they penetrate an existing market or create a new market. Eventually, however, the market becomes saturated and sustaining growth at the historical rate becomes impossible. *14* The direct parallel in financial markets is Berkshire Hathway, where Warren Buffett has openly acknowledged that the company’s historical share price performance is unlikely to ever be repeated because the company has now grown to be so large.

Transactions, and the taxes then incurred, represent another challenge to compounding. Each time an investment is sold, the taxes paid create a permanent decline in the value of the overall investment portfolio. This is essentially a step backward during the compounding process and future investments must have an even higher return to compensate for this. Given that the largest benefits of compounding don’t show up until very late in the process, the immediate cost of this step backward appears small but can become quite large over time, as shown in the chart below.

However, there are a few strategies for maintaining compounding that have proven successful. The first is to work to avoid the permanent loss of capital, either from transactions and taxes or simply from a bad investment. Such setbacks, as detailed above, have significant long-term ramifications for compounding.

Another strategy is to invest only in investments that you understand well. Doing so can reduce the psychological pressures that naturally arise from an investment and can also give you the confidence to double down and purchase more of an investment after it has declined in price. This strategy can be very effective, as compounding potential is not only maintained, but also enhanced by the incremental investment.

Lastly, it is important to structure your overall net worth in such a fashion that you are capable of ignoring the volatility in your assets. This avoids the permanent loss of capital that could result from liquidity needs or psychological pressures and provides the foundation for long-term compounding to occur. We will discuss this last strategy at greater length in the final column of this three-part series.

The highest-order goal for those seeking to protect and build wealth should be to compound their assets at the highest sustainable rate for as long as possible. Because compounding requires long, uninterrupted periods of time to work its magic, sustainability is the most important part of the effort. Achieving sustained compounding requires overcoming multiple challenges, both mental and mathematical, the foremost of which is managing all aspects of volatility. As hinted at above, asset allocation is both the answer to the volatility conundrum and the infrastructure upon which compounding happens. Appropriately then, our three-part series that began with volatility and continued with compounding will conclude with a detailed discussion of that very topic.

Thoughts? I would love to hear them. Email me at investmentinsights@zuckermaninvestmentgroup.com.

*Written By Keith R. Schicker, CFA*