A GrumpyTechBro joint

The bell curve is a lie

All of probability is based on the so called Normal Distribution, also known as the Bell Curve. That is what defines marbles falling in a pinboard. The nice thing about the Normal Distribution is that the math resolves cleanly. Mathematicians like clean math. Clean math is easier. Unclean math has icky infinities in it, and if they wanted to work with infinity, they would be black hole physicists.

The bad thing about the Normal Distribution is that it is impossible in real life. The pin board has boundaries. The marbles cannot go infinitely either way. Bad things happen more than they are supposed to. Same with good things. Real distributions show skew. Mathematicians gloss over this with the Central Limit Theorem, which says that if you add up a bunch of random numbers, you will still get a normal distribution, so you do not have to worry, you can use the clean simple math, and it will all be good.

This does not work. The probability distribution that does match the real world is the Stable Paretian, but mathematicians and Wall Street do not want to talk about the Stable Paretian, because it is not clean math. The tails do not converge to zero. Pesky infinities poke their head. But that is life. Crazy people fly airplanes into buildings. You can lose infinite money on a bad short, but you can only lose your buy price on a bad long.

But if we all pretend that the market can be modeled with the Normal Distribution, then we can all get jobs on Wall Street as quants at beaucoup dollars, we can win Nobel prizes for proving that the market is efficient, and we can skate closer to the edge than the old rules of thumb derived empirically: twelve times is solvency, more than twelve times is bankruptcy, and we can go to forty times, because we have computers now.

Sorry, but practice beats theory.