The Monty Hall Problem confused many academics with its counterintuitive solution. The essence of the problem is a game show host who knows which of three doors hides a car. You, the contestant, have guessed a door (A). The host opens a different door (B) to reveal a goat, and offers you the option of changing doors (from A to C). Because you have received partial information from a completely informed source, you are now a little bit smarter. Intuitively, all doors were created equal, so you would think there was a 50-50 probability split between the two remaining doors, but it is actually 1:2, in favor of changing your door. You are obliged to change doors so that you can make a decision after receiving your enhanced intelligence. Replaying the scenario, if you first guessed C, and the host revealed B, you would be obliged to change to A. It's not about the doors; it's about the inside information. Originally published in Reader's Digest, the problem was further popularized by Kevin Spacey in 21. There's a book about it.
I'm not taking you to quant land with "Monty Carlo Simulations" or "Fibonacci Patterns." I'm interested in why this math problem in particular baffles people. I'll get back to that in a moment. Let's talk about another mistake: trying to avoid incurring sunk costs.
Sunk costs are a bit more straightforward. We understand that the fact we paid $800,000 for a house in 2005 is not what gives the house its market value today. In theory, that house is only worth what someone will pay for it today, and you as a rational seller will take a good deal when you see one, which could very well be an offer below $800,000. But in 1976, it was shown that people often don't live up to the theory. People overweight their own responsibility in previous value determinations when making current value determinations. We seem to be obsessed with not losing, even after we have already lost. This is the behavioral paradox of sunk costs.
What Monty Hall and Sunk Costs have in common is the human tendency to overweight our own decision making, and underweight the intelligence of others. While Monty Hall is an example wherein a person should take new info into consideration, Sunk Costs is the idea that one should generally ignore the old info of how much was paid by oneself to enter a position. So even though these narratives both expose different mistakes, the underlying fallacy is a unified human narcissism.
Apple (AAPL) and Google (GOOG) have defied human common sense over the past decade (give or take) by overall meeting their astronomic growth expectations. The P/E for both, which was once at 100, is approaching 10. The bear case for Apple is that they had a phenomenal run with the iPod and the iPhone and the iPad, but this could come to an end soon, because "you never know." The bear case for Google is that its dominance exists as a search engine, and this is not in line with the next generation of the Internet, with HTML5 and fragmentation displacing Google from the gatekeeper/librarian position that it currently embodies.
There is this possibility that Apple and Google will not grow their earnings significantly. Let's pretend I'm the game show host, and I have absolute inside information (I don't). I'm telling you, Apple and Google are not done growing. I'm showing you what's behind that door, B. There's a goat there. You want to win the car. You can stay where you are, picking Door A, which is conservatively bullish, or you can up your bet, taking advantage of your enhanced intelligence. The truth is that game show host is part of your brain, already inside your head, screaming at you to buy in to the potential of these tech monopolies.
I'm also saying, many, including myself, underestimated the real growth that these companies have shown over the decade. This was costly. Overall, we missed out on an upward price movement. But now, it's a sunk cost. Even if you bought some shares, you probably didn't buy enough. So let's consider this decision, the decision of not buying more, to be a position in and of itself. This was a failed position. The question is, are you going to overvalue your previous failed position, committing the sunk costs fallacy? Or, are you going to take advantage of the current P/E affordability of Apple and Google?
You can't hear the game show host if you're listening to your ego complain about sunk costs.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I have liquidated my portfolio to provide capital for a business I am building.
