The Tortoise & The Hare

Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.  Albert Einstein (1)

We like to think linearly. Our brains are wired that way: the shortest distance between two points is a straight line. It’s intuitive. If we invest $1,000 and make a 50% return, we have $1,500.

Compounding can make things a bit more complex, but it’s a good complexity. We have to shift our thinking from linear to exponential growth. No longer a straight line, but an accelerating line built on prior gains. When implemented correctly, compounding really can be the eighth wonder of the world.

With compounding, $1,000 invested for three years at a 20% rate of return becomes $1,728. Compare that to the linear interpretation: 20% each year for three years is 60%, so your $1,000 becomes $1,600. The extra $128 you earned ($1,728 - $1,600) is from compounding. At the end of the first year you have $1,200 ($1,000 x 20%). In the next year, you earn 20% on $1,200 (not the original $1,000), bringing you to $1,440. The third year takes you to $1,728 ($1,440 x 20%).

The longer you leave funds alone to compound, the better off you are. Had I chosen 30 years in the above example instead of three, your value using the compounding formula would have been $237,376 vs. $7,000 in the linear formula (2). That’s why one of our tenants at Allied is “never unnecessarily interrupt the power of compounding.”

But we’re splitting hairs here, right? The theory is still the same, whether linear or compound: higher returns are good, negative returns are bad. And the answer is yes . . . and no.

For example, we have a Tortoise investor earning 16% per year for 10 straight years: steady and predictable. This compares to the Hare investor who earns 20% per year for nine straight years, but in the 10^th year loses -15% (it doesn’t matter which year the Hare loses -15%, it can be any year of the 10). The Hare is fast, but a little unpredictable (3).

Our linear thinking leads us to believe the Hare has won the race. In most years (9 out of 10), the Hare outperforms by 4%, or a cumulative 36% (4% x 9). In one outlier year (1 out of 10) the Hare underperforms by 31% (16% -(-15%)). We’d expect the Hare to outperform the Tortoise by 5% (36% - 31%) based on these average returns. And that is what we see in the simple averages: the Hare has a mean 10-year return of 16.5% while the Tortoise averages 16.0%. 

When we compound the data, though, the Tortoise wins the race. Its $1,000 investment turns into $4,411 and a compound annual return of 16.0%. The Hare ends up with $4,386 on a compound return of 15.9%.

Just like in the fable, the Hare outperforms in most years, but stopping to take a nap on even one lap can change the dynamic. Even with a higher average return (16.5%), the volatility in the Hare’s returns (the -15% year) hinders its ability to accumulate gains on prior gains, making its compound return 15.9%. The Tortoise may have the lower average return (16.0%), but thanks to the steady approach, it is able to compound at that 16.0% rate.

This isn’t just a theoretical exercise. The real-life Tortoise of investing – the S&P 500 Low Volatility Index, which is an index of some of the more boring yet steady and dependable stocks – has outperformed the Hare, or the broad S&P 500. 

Since 1973 (51 years of data), the S&P 500 has posted a gain in 40 years, or 78% of the time. In those years, the S&P 500 was up an average of 19.4% per year. The Low Volatility Index often trails in those up years, averaging 16.9%. However, in the 11 calendar years that the S&P 500 has been down since 1973 (22% of the time), the S&P 500 falls an average of -14.5% while the Low Vol Index averages a drop of only -2.4%.

Just like in our example, the Tortoise wins the race thanks to compounding. The Low Volatility index, since 1973, has turned a $1,000 investment into $281,805. The S&P 500, while being flashier than the Low Vol index, has suffered the same fate as the Hare and lost the race, turning $1,000 into $169,612.

That’s why we focus on quality investments at Allied, many of which are low volatility names, dividend aristocrats, or value opportunities. We try to be the steady, dependable Tortoise, compounding your capital year in and year out.

If you have any questions about your account(s), if there has been a change in your financial situation or investment objectives, or if you’d like to schedule a complimentary consultation to learn more about how our team can help you navigate the market and achieve your long-term financial goals, please feel free to contact us at (406) 839-2037.

1. There’s no evidence Einstein actually said this, but for whatever reason, it’s been attributed to him.
2. Compounding = $1,000 x (1 + 0.20)^30 = $237,376.31. Linear = $1,000 x (1 + (30 x 0.20)) = $7,000.
3. This example comes from Margin of Safety by Seth Klarman (legendary Portfolio Manager of the Baupost Group).

Data Sources: S&P Global, Allied Calculations

The views expressed in this newsletter represent the opinion of Allied Investment Advisors, a Registered Investment Adviser. This material is for informational purposes only. It does not constitute investment advice and is not intended as an endorsement of any specific investment or services. The information provided herein is obtained from sources believed to be reliable, but no representation or warranty is made as to its accuracy or completeness. Investing in equity securities involves risks, including the potential loss of principal. While equities may offer the potential for greater long-term growth than most debt securities, they generally have higher volatility. International investments may involve risk of capital loss from unfavorable fluctuation in currency values, from differences in generally accepted accounting principles, or from economic or political instability in other nations. Past performance is not indicative of future results. Investments are not a deposit of or guaranteed by a bank or any bank affiliate. Please notify Allied Investment Advisors if there have been any changes to your financial situation or investment objectives or if you wish to impose or modify any reasonable restrictions on the management of your accounts through Allied Investment Advisors.