Thread by @breakingthemark

Let’s tweak the game a tiny bit: Flip a coin. Heads, Double money. Tails, lose 51%

Arithmetic return=24.5%

Geometric return= -1%

100 coin flips through time. Now the values trend downward toward 0.

Arithmetic mean, the dark blue straight line, leaves the picture early on.

Here is the average wealth of the 100 coin flips. It climbs, and climbs quite aggressively due to the positive arithmetic return. But the wealth ends up peaking, and then falling back down to where it started. The portfolio can’t escape the negative geometric return.

Three more random trials. These coins are a great examples of news traveling slowly between the coins. Early on some coins don’t realize others are landing heads. Once they do, they shoot up. Then later the coins hesitate to realize they are supposed to start losing money.

Here are 3 more. These charts wonderfully show how the coins display herding behavior. These coins do well, and they continue to do well (because herding), before the coin herding stops and they universally decide to all lose money reverting toward the mean (more herding).

The final set is rife with market inefficiencies. These coins have no idea how to behave themselves rationally. Clearly building up irrational coin bubbles before crashing backwards. By understanding these coin biases we can profit from this behavior.

I joke, but in all seriousness, I’m not trying to say the beliefs about the causes of stock momentum are necessarily wrong, but they are overstated.

SOME aspect of the price movement seen in momentum studies is due to random multiplicative compounding.

breakingthemarket.com/randomness-in-…

We all know purely positive random compounding curves up. The curve is expected.

When the arith return is positive and the geometric negative, the curve begins up and then turns down. This curve is also expected.

You don't need behavior to explain it.

breakingthemarket.com/what-is-the-ex…