Ever since I first read about it, I’ve found the Monty Hall problem to be absolutely fascinating. It’s a math question that almost everybody gets wrong–even very smart people who have careers in math. Here’s the riddle:
Suppose you’re on a game show and you’re given the choice of three doors. Behind one door is a car; behind the others, goats.
The rules of the game show are as follows: After you have chosen a door,the door remains closed for the time being. The game show host, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly.
After the host opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you “Do you want to switch to Door Number 2?” Is it to your advantage to change your choice?
When they read the question, most people (myself included) answer that changing doors wouldn’t affect the chances of winning. And most people are wrong. If you switch doors, your chances of winning the car increase from 33% to 66%. It seems like a simple question, though, doesn’t it?
Fooled by common sense
In a similar vein, Nassim Nicholas Taleb, in his book Fooled by Randomness asks:
What is the greatest factor in determining how many fund managers outperform the market in a given year?
Here’s what came to mind for me as possible answers:
- Average expense ratio among mutual funds
- How well the market did that year (with the dodgy assumption that actively managed funds would outperform in down years due to their significant cash holdings)
The real answer? The total number of fund managers attempting to outperform the market is the biggest factor in determining how many fund managers do outperform the market.
Oh yeah. Duh. It’s so obvious, and yet I hadn’t thought of it.
What’s the lesson here?
It seems to me that the takeaway is that, when it comes to investing, the most obvious answer isn’t always the correct one. For example, common sense tells us that:
- A growing company should be a growing stock. (Wrong.)
- Professional management should beat no management. (Wrong.)
- A fund manager who has outperformed the market for the last 7 years in a row must be good at what he does. (Wrong.)
In the world of investing, terrible practices can be supported with common-sense-sounding arguments.
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{ 8 comments… read them below or add one }
Agree. Lots of ‘obvious’ statements are not true.
Passive investing outperforms managed investing. The evidence tells us that’s true.
Oblivious investing is another matter. I get the point of not worrying and investing for the long term. But my over-riding question remains: Why ignore risk?
Best regards,
I was watching the “Un-Broke” TV program the other night which I thought was rather helpful and timely program on Personal Finance for the general public. One of their statements was that “the stock market was an indication of the health of a company or the economy”. I didn’t like the way they worded that, and I felt that it could have been said better: “The stock market and share prices are an indication of how people generally think a company is doing, or that everybody is panicking or going nuts.”
Throw in misleading accounting, analysts with an agenda, and irrational investors and you get … what? Not always an accurate picture of how a company is doing, maybe?
I think that the point being made in this blog entry is a very important one.
I don’t think that investing is all that hard to understand. But it is in several respects extremely counter-intuitive. That throws people.
So, no, you cannot just go by common sense. I believe that the best investing minds are minds that can handle paradox.
Rob
“A growing company should be a growing stock. (Wrong.)”
I wonder how many are fooled by this poor rationale. I’ve heard this one numerous times in the past from friends who are, er, maybe a bit naive when it comes to investing; ‘Company X should go up because summer is coming and that’s when they do their best business’. D’oh!
Mark: When did I say to ignore risk?
If anything, I’d say I bring up the topic of risk more often than most investment writers.
(I just checked: According to Google Webmaster Tools, “risk” is in fact the 3rd most-used word on this site–excluding prepositions, articles, etc.)
I’ve never heard of the “Monty Hall” problem – I had a hard time understanding it but then I figured out that they are right (after 20 minutes!)
Yeah, I had to read the explanation several times when I first encountered it. Once you understand what it’s saying though, it seems so obvious. Love that kind of thing.
The normally constrained Monty Hall problem is pretty easy… Basically with the constraints that you KNOW the guy is going to show a goat then it transforms into… if I pick a goat first then switching gives me a car.
I like the weird versions that are almost exactly the same but w/ small amounts of cheating. I think the case in which the guy randomly shows you a door and somehow ends up w/ a goat is fun to look at… and even tho it sounds to be the same, it’s different!