I suspect there's a Pons Asinorum of probability between the bettor who thinks that you make money on horse races by betting on the horse you think will win, and the bettor who realizes that you can only make money on horse races if you find horses whose odds seem poorly calibrated relative to superior probabilistic guesses.

There is, I think, a second Pons Asinorum associated with more advanced finance, and it is the concept that markets are an anti-inductive environment.

Let's say you see me flipping a coin. It is not necessarily a fair coin. It's a biased coin, and you don't know the bias. I flip the coin nine times, and the coin comes up "heads" each time. I flip the coin a tenth time. What is the probability that it comes up heads?

If you answered "ten-elevenths, by Laplace's Rule of Succession", you are a fine scientist in ordinary environments, but you will lose money in finance.

In finance the correct reply is, "Well... if everyone else also saw the coin coming up heads... then by now the odds are probably back to fifty-fifty."

Recently on Hacker News I saw a commenter insisting that stock prices had nowhere to go but down, because the economy was in such awful shape. If stock prices have nowhere to go but down, and everyone knows it, then trades won't clear - remember, for every seller there must be a buyer - until prices have gone down far enough that there is once again a possibility of prices going up.

So you can see the bizarreness of someone saying, "Real estate prices have gone up by 10% a year for the last N years, and we've never seen a drop." This treats the market like it was the mass of an electron or something. Markets are anti-inductive. If, historically, real estate prices have always gone up, they will keep rising until they can go down.

To get an excess return - a return that pays premium interest over the going rate for that level of riskiness - you need to know something that other market participants don't, or they will rush in and bid up whatever you're buying (or bid down whatever you're selling) until the returns match prevailing rates.

If the economy is awful and everyone knows it, no one's going to buy at a price that doesn't take into account that knowledge.

If there's an obviou...

Eric6

Eric6

Eric6

Eric6