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“The greatest shortcoming of the human race is the inability to understand the exponential function.” – Dr. Albert Bartlett

Do you understand the theory of exponential growth and its relationship to investing? Could you teach the concepts to a middle school class? Well, if not, you are in a large majority of investors. People tend to think linearly, so many of us have trouble grasping the effect of compounding, or exponential growth. For example, if you saved a penny on February 1 and then doubled that the next day to save 2 pennies on February 2, and doubled again to 4 pennies on the 3rd, then 8 on the 4th until the last day of February, the 28th, how much money do you think you would have? (Here’s a hint, at the end of the first week you would have \$1.27.) Make your best guess now, and we’ll reveal the correct answer later in this letter, after we explain the concept of exponential growth.

In 2016, the price value of the S&P 500 grew by 9.54%. It closed 2015 at 2,043.93 and closed out 2016 at 2,238.83. Since 1950, a portfolio made up of 50% equities and 50% bonds (50/50 portfolio) has had an average annual return of 8.9%. In other words, the annual rate of change from 1950 to the end of 2016 has been 8.9% per year. However, the amount of change over that time for even a modest portfolio would be quite substantial. The amount of change each year is dependent on the previous period’s value, and the amount of change will be a little bit larger each period, on average.

In investing, exponential growth has phenomenal power over the long term. Say you started investing at age 25 and for the next 40 years you put \$2,000 per year into a 50/50 portfolio averaging 8.9%, until you turned 65. The power is in the fact that you are receiving growth upon growth. Although each year you are receiving the same percentage change, 8.9%, the amount of change is growing larger at a faster rate.

To illustrate how the amount of growth of a \$2,000 annual contribution accelerates each year, let’s look at some key milestones along the way.

Unlike the rate of change, 8.9%, the amount of change is not constant in exponential growth. As shown above, \$100,000 milestones are met in much shorter time frames. In exponential growth, you can either think of the speeding up as (1) the accounts accelerate in size over each fixed time period or (2) you can think about how the amount of time shortens between each fixed amount added.

Exponential growth and the compounding of interest can be difficult for investors to understand and not understanding can have severe consequences. In a recent study using data from RAND American Life Panel and Understanding America Study data, researchers found that only 25% of respondents correctly perceived account balances to grow exponentially over time. There exists a significant “exponential growth bias” that limits investors’ expected return of saving and, thus, investors do not adequately fund their retirement accounts. Further, when an exponential growth bias of lower returns is coupled with a “present bias” to defer investing to sometime in the future, that unfortunate combination leads to smaller retirement account balances later in life.

In today’s world, with the decline of traditional pension plans and the possibility of smaller than expected Social Security benefits, future retirement income is the responsibility of the worker/investor primarily through company-sponsored 401(k) and IRAs. As a result, the individual skills, knowledge, abilities, habits and attitudes toward saving are incredibly consequential for their retirement security. Individuals who use commitment strategies such as auto-enrollment and auto-escalation in 401(k) accounts to counteract present bias, or who use tools and expert advice to address exponential growth bias, have a higher likelihood of experiencing a fully funded retirement.

If you know of someone who struggles with saving today for retirement income in the future due to an exponential growth bias or present bias, we would be happy to sit down with them. Please give us a call.

By the way, here’s the answer to the exponential growth problem in the opening paragraph: after 28 doublings starting with just one penny on day one, you would have \$2,684,354.55. And, if you began to double every day in March, which has 31 days, those extra three days’ worth of daily doublings would bring your total to a massive \$21,474,836.47.

We hope you’ve found this review to be educational and helpful. As we like to emphasize, it is our job to assist you. Thank you very much for the trust and confidence you’ve placed in our firm. We treasure our relationships with our clients, and seek to serve a few more people like you. If you know of someone who would benefit from our advice and services, we would welcome an introduction.

DISCLOSURES: The information provided in this letter is for general informational purposes only and should not be considered an individualized recommendation of any particular security, strategy or investment product, and should not be construed as investment, legal, or tax advice. The Nalls Sherbakoff Group, LLC makes no warranties with regard to the information or results obtained by third parties and its use and disclaim any liability arising out of, or reliance on the information. These indexes reflect investments for a limited period of time and do not reflect performance in different economic or market cycles and are not intended to reflect the actual outcomes of any client of The Nalls Sherbakoff Group, LLC. Past performance does not guarantee future results.