Investors have to interpret a lot of numbers, and make sense of a lot of forecasts in order to come to well educated investment decisions. But many of us went through the math class that taught us how to do this asking the teacher, “When are we ever going to use this?” and spacing out.
Jordan Ellenberg does an excellent job giving you a crash course in some basic math principles that have great benefits for investing.
” Mathematics is the extension of common sense by other means”
I first heard of this book from Bill Gates’ 2016 summer reading list, but waited a while for the price to drop (currently, used copies are now around $5 on Amazon) before picking it up. The book was well worth the wait. If you are any bit of a math/numbers or history geek, you will likely get a kick out of the entire book (I read it in 3 sittings!). But Ellenberg has several chapters directly applicable to investing as well. Ellenberg does a great job telling stories and giving examples of absurd neglect of mathematical “common sense” in war fighting, brain cancer, political science and most importantly, investing. After reading this book, you will have no problem applying a healthy dose of skepticism to any “study”, forecast or prediction you hear – that’s a good thing!
3 Investing Lessons from How to Not Be Wrong – The Power of Mathematical Thinking
1) Linearity – Things do not continue in a straight line
Understanding linearity gives investors a great way to do a quick “BS check” whenever you hear a forecast or prediction – A quick way to find out if the forecast stands up to common sense.
Ellenberg cites a paper in the journal Obesity that comes to the conclusion that by 2048 100% of Americans will be obese. How did they come to that conclusion? By performing a linear regression (creating a “best fit” line) to fit today’s obesity data and extrapolating the current trend into the future. in the early 70’s, 50% of Americans were obese. In the early 90’s, 60% were obese. By 2008, 75% were obese. Connect the dots and assume the trend continues and like magic, 100% is hit in the year 2048 (and as Ellenberg points out, would also imply 110% obesity in year 2058!).
Of course it doesn’t work like that. 100% of the population will never become obese. Current growth trends can not continue, but performing a quick linear regression is easy. Interpreting the results, not as much.
“Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense – or deciding whether the method is right to do in the first place – requires a guiding human hand”
and I would add, requires a competent human hand at that. You don’t want to be like Ron Burgandy reading a teleprompter:
Linearity in Investing
So what can investors learn from this? Next time you hear a stock forecast, take a step back and determine what the forecast is based on. Is an analysts simply connecting a few dots on a graph and extrapolating?
Where do we see this today? Think growth estimates for Facebook, which already has two billion users, is one example. Can previous growth rates continue? Not unless the population of the earth starts growing very fast. That means Facebook’s business model needs to change to achieve previous revenue growth rates. It is going to get harder to get more eyeballs in front of adds, because we are getting to a point where Facebook simply can not get to any more eyeballs.
I’m not trying to seem overly bearish on Facebook. But if you see an analyst’s projections for future earnings on Facebook it is worth looking into how they come to that number. Facebook makes a lot of money, but it sits at a high P/E ratio of around 40, so investors are obviously expecting some serious growth out of Facebook well into the future. At current growth rates, in the next 5 years Facebook has more users than people in the world with internet access.
What is more likely? Facebook user growth slows. More people can not be on Facebook than have internet connections, just like more people can not be obese in America than the total number of people in America!
(To be fair, Facebook is working a some big projects to expand internet availability to the world. Additionally, Facebook may find other ways to monetize its traffic. All I am saying is that if your projections for Facebook’s earnings is based on user growth, make sure you are being realistic)
2) The Baltimore Stockbroker – You Too Can Have “Perfect” Record
Ellenberg gives us an example of a newsletter you probably get in your inbox every day, one containing a certain stock tip, or major stock market call. For week one, the newsletter may be predicting the stock market to rise. You take note, but probably delete the e-mail. But over the course of the next few weeks you keep getting newsletters, and it seems the newsletter is right in their predictions every time. After 10 weeks you see the newsletter as been right 10 weeks in a row – They must truly be talented! So you sign up and pay the stock picker some money because surely their process for picking investments in an excellent one.
But what you fail to see if what goes on behind the scenes. That same stock picker has been sending out emails to tens of thousands of people, each week splitting half the group with a “bullish” email and the other half with a “bearish” email.
Let’s assume this emailer started with 10,240 people on his email list. The first week, he sends 5,120 an email telling them to buy the stock market, and another 5,120 to sell the market. After week one, he is guaranteed to have made the right call to more than 5,000 people. Impressive, but many want to see more. Next week, he splits that 5,120 in half again, sending 2,560 people a bullish email and 2,560 a bearish email. This process continues for 8 more weeks, what do his numbers look like at the end?
No matter how dumb this “stock picker” is, 10 people from his original 10,240 will get a string of 10 consecutive newsletters that accurately predicted the stock market. To those lucky 10, this stock picker seems unstoppable and is probably worth whatever they are charging to read their newsletter.
But really, they were just duped by the large of large numbers. The stock picker was guaranteed to be right for 10 straight weeks to some of his readers, regardless of what the market did!
We see this play out every day. Not only in your e-mail inbox (which undoubtedly there are stock newsletter writers employing this tactic), but on TV and on investing website everywhere. We have all heard the talking head on TV, warning about an upcoming market crash or telling you that a certain stock is a screaming buy. They may even claim to be famous for “correctly” calling a previous stock market rise or fall. How much stock should you put in a correct call, or even a string of correct calls?
Take a minute to step back and calculate the odds and you realize, not much.
3) Mean Regression – What Goes Up Must Come Down
Ellenberg frames the topic on mean regression in prospective of a baseball player who starts the year out hot. Matt Kemp hit 9 home runs in his first 17 games of the season, leading ESPN to write an article stating, “Matt Kemp is off to a blazing start, hitting .460 and on pace for 86 home runs…”
The record for most home runs in a season is 73, so is Matt Kemp the best baseball player in history? No, because he is not going to keep on his current pace. (He didn’t, and ended the year with 39 home runs)
We see trends like this in investing all the time. A hot fund manager, or a sector of the stock market that outperforms and we immediately assume that their current performance will keep up.
I really like the quarterly report put out by J.P Morgan called ‘Guide to the Markets‘ and this page in particular:
What is regression to the mean? Just look at this chart that plots asset class returns over the years. No one asset class remains on top for very long.
in early 2000s it looked like emerging markets and commodities were destined to make investors rich! They were consistently in the top quartile of asset class returns. But, a return to normalcy soon struck. Emerging markets earned -53% in 2008, -18% in 2011 and commodities have been the worst performing asset class in 5 of the last 6 years!
Understanding regression to the mean will help you avoid getting sucked into the hype just as it is time for an investment to fade. We see investors chasing performance all the time. If the average investor took a look at this chart above, and applied its lessons to their investing, I think the average investor would improve greatly.
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I was pretty sure I could not go wrong reading one of Bill Gates’ ’10 favorite books’ of the summer and the book did not disappoint. Mathematical concepts are explained very well, and the examples he finds and includes in the book are great for basic math lessons and an occasional laugh. I’ll leave you to read the details in the entertaining chapters of “Can a dead fish read minds?” and “Does lung cancer cause smoking?”
And most importantly, it has some very real world applications to investors. In the end, I really enjoyed Ellenberg’s book and highly recommend it.