Do Investors Need to be Good at Mathematics?
In the book “Money for Nothing and Your Stocks for Free,” author Derek Foster asks why we force kids to spend so much time “calculating the hypotenuse of a triangle,” something he can no longer remember how to do, when skills like this “are never used by most people in the real world.” He advocates spending more time teaching kids financial literacy.
I agree that schools could do more to teach financial skills. However, I’m not sure how to keep vested interests from influencing the curriculum. We may end up teaching our children to buy expensive mutual funds, hire expensive real estate agents, and pay transaction fees on all purchases.
The first part of Foster’s argument is that much of the math he was taught wasn’t very important. A curious thing about discussions like this is that people who lack a certain skill are often the ones who assert that the skill isn’t important. For example, I might say that knowledge of Russian literature isn’t important in investing. In reality, I don’t know if this is true or not because I know little about Russian literature.
The reason that few people ever calculate the hypotenuse of a triangle in their daily lives is mainly because they can’t. Further, they wouldn’t recognize a situation where it might be useful. For example, measuring out a 3-4-5 triangle is a way to get a square corner when laying out a football field.
If you have to lay out bases on a baseball diamond, it can be useful to figure out that second base is 127 feet, 3 inches from home plate by calculating the hypotenuse. I once helped a volunteer who had no measuring tape figure out where to put a new pitcher’s plate by figuring out that it should be about 3 feet in front of the line from first to third base. Opportunities to make use of a skill are often impossible to recognize unless you have the skill.
Getting back to investing, I’m not arguing that you need to know calculus to succeed. In fact, people who delve too far into mathematical topics like efficient market theory and modern portfolio theory often get caught up in details and can’t see the forest for the trees. When a writer comes up with incorrect conclusions and baffles his readers with math, don’t blame the math; blame the author.
Any skill is potentially useful when investing. Some are clearly more useful than others. Basic math is obviously important for investing, and I think that more advanced math can be helpful. Common sense, curiosity, and the ability to stay calm are beneficial as well.
I agree that schools could do more to teach financial skills. However, I’m not sure how to keep vested interests from influencing the curriculum. We may end up teaching our children to buy expensive mutual funds, hire expensive real estate agents, and pay transaction fees on all purchases.
The first part of Foster’s argument is that much of the math he was taught wasn’t very important. A curious thing about discussions like this is that people who lack a certain skill are often the ones who assert that the skill isn’t important. For example, I might say that knowledge of Russian literature isn’t important in investing. In reality, I don’t know if this is true or not because I know little about Russian literature.
The reason that few people ever calculate the hypotenuse of a triangle in their daily lives is mainly because they can’t. Further, they wouldn’t recognize a situation where it might be useful. For example, measuring out a 3-4-5 triangle is a way to get a square corner when laying out a football field.
If you have to lay out bases on a baseball diamond, it can be useful to figure out that second base is 127 feet, 3 inches from home plate by calculating the hypotenuse. I once helped a volunteer who had no measuring tape figure out where to put a new pitcher’s plate by figuring out that it should be about 3 feet in front of the line from first to third base. Opportunities to make use of a skill are often impossible to recognize unless you have the skill.
Getting back to investing, I’m not arguing that you need to know calculus to succeed. In fact, people who delve too far into mathematical topics like efficient market theory and modern portfolio theory often get caught up in details and can’t see the forest for the trees. When a writer comes up with incorrect conclusions and baffles his readers with math, don’t blame the math; blame the author.
Any skill is potentially useful when investing. Some are clearly more useful than others. Basic math is obviously important for investing, and I think that more advanced math can be helpful. Common sense, curiosity, and the ability to stay calm are beneficial as well.
For those who REALLY want to understand money, I would strongly suggest the Actuarial Science courses at the University of Waterloo (available by correspondence), the two first year courses will teach you more about how to calculate the value of money than you will ever need, mot likely.
ReplyDeleteThe best and most useful math I ever learned was my Finite Mathematics course in college. I have found it useful with investing and well, playing Keno (lottery). Sometimes the market is just that, a game..
ReplyDeleteGreg
Greg: I'm curious about the Keno. Any Keno game I've looked at was a losing proposition. Did you find an edge somewhere or did you figure out that playing was a bad idea?
ReplyDeleteEverything you say is true about mathematics (I always figure out which pizza is the best value by comparing the ratio of the squares of the radii), but it's imperative that children be taught about money and finance.
ReplyDeleteAnd to reduce your concerns about learning the 'wrong' lessons, we must be certain that there are no sponsors and that no (for example) mutual fund company can provide 'educational' materials.
I don't disagree that it is important to teach money skills at school but even if it is, I'm not convinced that most people will (a) learn it well enough and (b) apply it rigorously when they are adults. Ultimately, blaming the school system is a cop out. If someone desperately wants to learn, there are enough resources out there.
ReplyDeleteCC: You made me think (which I like). I partially agree and partially disagree with each of your statements.
ReplyDelete"I'm not convinced that most people will (a) learn it well enough and (b) apply it rigorously when they are adults."
This is likely true of just about everything taught in school. Maybe we should go for a very small victory. Students could look at case studies of typical (but fictitious) people who mess up their lives by overspending for years. Maybe then slightly fewer young people will grow up and abuse consumer debt.
"Ultimately, blaming the school system is a cop out."
If a person messes up his financial life and then blames school, I agree 100% that this is a cop out. I don't blame schools for financial illiteracy, but I do see a modest opportunity to help the next generation with some basic financial education.
"If someone desperately wants to learn, there are enough resources out there."
There is so much bad information out there that figuring out what is right and what is wrong is a very slow process. It took me several years.
Neither children nor adults are desperate to learn. After all, they simply don't know what it is they don't know.
ReplyDeletePeople borrow and live well beyond their means because that's what they learned at home. The few voices trying to prevent people from developing (or continuing) these habits are few and far between.
If some effort were made to add this topic to an economics class, it's possible that some students will see the light.
Mark: I agree that trying to teach basic information about avoiding debt in school could be helpful. However, I think that overspending isn't always caused by examples set by parents. It is natural to try to get what you want immediately, especially when consequences aren't obvious or seem remote. To teach the consequences of overspending requires a certain amount of battling against human nature. Having a good example set at home helps, but is no guarantee of future good choices.
ReplyDeletemichael: This was a few years back but I used math to narrow down which set to play that had the best odds, how many tickets to buy and the numbers spread. With that I ran a simulation over a month to see if I ended out ahead and I did not... oh well. I think what got me started was a report on some guy in Montreal who had broken the casino Keno game and they went after him.
ReplyDeleteGreg
Greg: If I'm thinking of the same story you are, it was a problem with the random number generator. It was so bad that someone was able to predict what numbers would be drawn next by looking at the past draws.
ReplyDeleteTo me, human nature is not spending what you don't have.
ReplyDeleteI don't overspend. Sure I want what I want when I want it - but I don't go out and buy it. Not unless I can pay the credit card bill IN FULL when it's due.
Good discussion
Mark: That's a great philosophy: don't spend what you don't have. This should mean avoiding debt. However, the often used phrase "borrowing power" undermines this philosophy. It transforms debt into something you have. And if you have it then you can spend it. I run into this kind of thinking when I suggest that people should save up and pay cash for cars. Young people often don't even think of this as a possibility.
ReplyDeletemichael: yeah, that was it. They stated they fixed the problem but I know a thing or two about RNG and didn't believe them. I set out to see if there was some form of a pattern. I think I was tracking the winning numbers for a month in a spreadsheet.. this was a while ago. You could get the past three months of numbers off the web so I had my sample.
ReplyDeleteSo, (if memory serves)even though the numbers are actually random, there could be a pattern developed from their (not so) random beginnings. If you played enough numbers and had the right spread, after looking at the first three weeks of winning numbers you should be able to play the last week of the month and come out ahead.
In the end I tried it and did not come out ahead. I wasn't actually buying tickets, just pretend of course!
I think it was buying 20 x 6 number tickets for 7 days... I'll have to find that spreadsheet and devote some more time to it as the market is not playing fair now ;-)
Greg
I actually calculate the hypotenuse of triangles at work on a regular basis. Who knew? I look at a lot of construction drawings.
ReplyDeleteMyself & my husband lived in an extremely wealthy old-money town in the US for a while. They had very well-run, and to my mind quite advanced, personal finance classes for the kids in the ($75million) library there on a regular basis while we lived there. I thought this was quite interesting. All the hedge fund running daddies were certainly setting their kids up with the right information.
Lots of comments today.
ReplyDeleteI actually used the Pythagorean theorem today, interestingly enough. Haven't used it in a long time, but still, I certainly remember it.
I was figuring out the surface area of my 19" CRT monitor to compare it to a brand new 22" LCD widescreen monitor. Turns out, if my calculations are correct that the 22" monitor is about 20% larger, by area.
Reminds me of taking baffling engineering math classes and thinking "When am I ever going to use this?" Since I dropped out, I really haven't used it, but I can conceive that even the process of learning advanced math might improve one's thinking in seemingly unrelated areas, and possibly improve intelligence and problem solving.
Guinness416 and Gene: It's good to see more people who find math useful in their lives come forward. It has become too fashionable to declare that math is unimportant.
ReplyDelete