“Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world.”
If I told you that there were two investment possibilities, one of which had a 100% gain and one of which had a 1% gain, you’d probably immediately think that you should invest in the 100% gain investment. It’s natural to think that – higher percentages are better, right?
Let’s add some more details to the description above. The first “investment” was made by me sitting down at a slot machine in Las Vegas. I put in a quarter into a slot machine, pulled the handle (or pushed the button…I hate those new-fangled machines that don’t have arms), and, voila! I got fifty cents back (I also miss the actual coins being dropped into the container; the paper tickets just don’t have the same appeal)! Woo-hoo! A 100% return on my investment! I saunter away, shaking my fist at the “house,” embellishing my dominance.
The second “investment” was made by Bill Gates, who owns about 440 million shares of Microsoft. On the day I’m writing this article, his company is up about 1%, or around $0.30. He has made $130 million, on paper, since he got up this morning. He probably didn’t even notice. I doubt he’s calling up his broker to sell his holdings to “lock in his profit.”
So, now, which position would you rather be in? The person who made 100% or the person who made 1%?
We are faced with mathematical problems which integrate magnitude and relative growth all of the time in our personal financial lives, but, it turns out, Monkey Brain isn’t really that good at math.
Author Tim Harford recently wrote about this dilemma. He wrote about a study which showed that doctors made similar mistakes in choosing what tests to perform for cancer screening. Doctors were drawn to activities which detected cancer earlier, but failed to choose the ones which actually helped reduce incidences of cancer.
What’s the difference?
You want to focus on outcomes, not on process. In this case, if you detect an incurable cancer earlier, you may increase the five year survival rate, but you haven’t affected the overall outcomes one iota. Sure, there is value in earlier detection – getting your affairs in order, doing the things you really wanted to do, etc. – but the actual goal is the defeat of cancer itself.
Monkey Brain messes up these calculations all of the time; you don’t have to be a MD to fall for mathematical illusions. Let’s take a common example of what has happened to many people in the recent past.
According to Freddie Mac, between 1985 and 1999, an average 61% of refinanced mortgages led to an increase in loan balance of at least 5% while the average refinanced interest rate was 86% of the previous interest rate. In other words, Monkey Brain saw a lower interest rate, and instead of using the opportunity to decrease the term of the mortgage or use it as an opportunity to pay less in interest, he doubled down on the risk, pulling cash out. Monkey Brain was willing to pay more money later for a little money now – confusing interest rate with total interest paid.
What is the lesson here?
Do not be fooled by rates. Yes, oftentimes, rates going in the direction you want them to go is a good thing, but you also need to look at magnitude of the impact. A high rate change with a small magnitude impact isn’t really that meaningful.
Look for large total moves, not large percentage moves. Remember, the goal in financial planning is the overall impact. If you’re willing to dicker all weekend with your car salesman about a half a percent decrease in your auto loan but not willing to shop mortgage loan officers for a quarter of a percent decrease because you think the paperwork is “too difficult,” then you’re probably missing out.
It’s never a good idea to let Monkey Brain do math. When you’re faced with rates compared to magnitude, stop for a minute and think about the total implications of your decision. Otherwise, Monkey Brain will think he’s getting more bananas than he might otherwise be getting.
If you want to read more about the importance of numeracy in your financial life, check out my U.S. News & World Report article about math.