Blog

Portfolio Splitting and the Kelly Criterion Suppose the Knicks play the Spurs tomorrow. A bookmaker believes $P(\text{Knicks win}) = p$. He sells two fractional contracts, each fairly priced under that belief: A $\$1$ Knicks contract that pays $\frac{1}{p}$ if the Knicks win. A $\$1$ Spurs contract that pays $\frac{1}{1-p}$ if the Spurs win. (Note: Zero vig $\implies$ fair value = $1) A gambler believes $P(\text{Knicks win}) = q > p$. He has just $1 but wants to grow it aggressively, so he spends: ...

I’ve read some inane discussions about the validity of the efficient market hypothesis (EMH). I’ve even participated in some. Proponents warn that cocky retail traders are naive, and detractors point to historical examples of inefficiencies. I claim this is a category mistake by both parties. The EMH is more like a philosophical razor: you should accept it for a given asset, unless you have some information to the contrary. We might as well call it the efficient market null hypothesis. ...

Elo Scoring Two players have Elo scores $A$ and $B$. With no info other than that, it’s generally accepted that $P(A\ beats\ B) = 1 / (1 + 10^{(B - A) / 400})$ If A indeed does beat B, here are the new Elo scores: $A' = A + K \cdot (1 - P(A\ beats\ B))$ $B' = B - K \cdot (1 - P(A\ beats\ B))$ Where $K$ is a hyperparameter, usually something between 10 and 40. ...

Hello, world! It’s me, blog!