# Math Rules

Bruce Roberts

I STUDIED MATH AND statistics at university. When I mentioned my academic focus at parties, eyes would glaze over as fellow students looked for a way to extricate themselves from the conversation.

To lighten the mood, I’d say I was studying statistics to learn how to get rich in the stock market. In truth, I had no idea what I was talking about, but it sounded good and would often break the ice. Still, the notion of getting rich quickly was in the back of my mind as I learned more advanced math, including modeling and econometrics. (I sense—once again—that eyes are glazing over.) But I did wonder if there was a magic bullet that would help me conquer Wall Street.

When I left school and entered the working world, I continued to educate myself about investing. I read—a lot. Among the investment literature I read, Burton Malkiel’s A Random Walk Down Wall Street had a big impact on me. I decided that short of taking a job in the investment world—which I had no interest in doing—I wasn’t going to best the big boys at investing. But I continued my search for a way to build my personal fortune.

First, I thought about real estate as a road to wealth. At the time, many of the world’s richest people had made their money by owning property. But they were active investors, and I had neither the initial capital to be a landlord nor the necessary interest, so I dropped that idea.

I finally had an epiphany, and it sprang from my understanding of mathematics. It wasn’t complicated: compounding + time = wealth. This was the key—not getting rich quickly, but getting rich slowly. I was relatively young, and had time on my side. With the inexorable logic of math, this was a low-risk way to increase wealth, albeit over a longer period of time. I would just have to be patient.

Now, the question became: What investments should I put my money into? The more I read, it became clear that the stock market was the place to be. If I could ride out the rollercoaster ups and downs, I could reasonably expect 10% average annual returns over long periods. A secondary advantage of stocks: They’re relatively liquid, giving me access to cash when needed, something I wouldn’t get with hard assets like real estate and collectibles. With a young family, this ease of raising cash would prove useful as our needs changed over time.

I often hear others talk about non-stock market investments with explosive growth. The numbers often look compelling. But this is when I use some simple math and the rule of 72 to compare their return with investing in stocks. The rule of 72 says to divide a rate of return into 72, and that’ll tell you the number of years it’ll take to double your money. For instance, 72 divided by nine is eight, so a 9% return would double your money in eight years.

Real estate is often mentioned as a good alternative to stocks. One example: My folks bought their home in 1958 for \$23,000. It’s now worth \$925,000. Eye-popping, right? How could anything beat that return? I’ll use math to help answer this question.

The key assumption I make is that stocks return 10% a year, assuming dividends are reinvested. Using the rule of 72, we divide 72 by that 10%, and find that stocks double in value roughly every seven years. My folks owned their house for 65 years. How many seven-year doubling periods is that? If we divide 65 by seven, we get approximately nine doubling periods. So, a stock market investment would have doubled nine times. I multiply two by itself nine times, for the nine doublings, to get a growth factor of 512.

We can now use the 512-growth factor to calculate that a stock market investment of \$23,000 would have grown to around \$23,000 x 512 = \$11,776,000. Now, that’s eye-popping.

You may counter this by saying, “But they only put 20% down for the house, or \$4,600.” That’s a good point. They were able to leverage their money in real estate in a way they were unlikely to do with stock market investments. So, let’s look at that: \$4,600 invested in the stock market would have grown to \$4,600 x 512 = \$2,355,200, which handily beats the house value. Stocks win again.

Of course, these are all back-of-the-envelope calculations. I don’t take into account taxes, house upkeep, mortgage interest and other costs. In addition, I don’t factor in the imputed rent—the fact that my parents get to live in the place, rather than having to rent from someone else. Still, when I do these calculations, the differences are usually starkly in favor of stock market investing.

Let me be clear: I’m not saying you shouldn’t buy your own home. I’ve done that multiple times myself. But for investable cash, I’ve yet to find a passive investment that can compete with stocks over a lifetime.

I’ve been fortunate: Time has rewarded my fondness for the stock market. That’s no guarantee for the future, of course. Still, I talk about this to the next generation—my kids, nieces and nephews—in the hope they can learn from it and find their own path to financial security.

Bruce Roberts retired from IBM after a 35-year career as a software engineer. Degrees in math and computer science served him well during his career and when investing. In retirement, Bruce enjoys tennis, playing bridge and tutoring math. His previous articles were Getting Myself Ready and A Pretty Penny.