From 34c847c2a00c2319b36d317d9b98502e0d45ed7e Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 3 Oct 2023 03:29:23 -0400 Subject: [PATCH] make footnotes shorter so they don't go off the side of the page --- _blog/2023-10-03.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/_blog/2023-10-03.md b/_blog/2023-10-03.md index 3d3a722..19a87b0 100644 --- a/_blog/2023-10-03.md +++ b/_blog/2023-10-03.md @@ -34,7 +34,7 @@ This lead me to the conclusion that, as an example, one should take as much debt However, one hiccup with such a strategy is that a margin call could blow up your entire portfolio. This starts hinting at a gambler's ruin aspect to the problem: > [...] A persistent gambler with finite wealth, playing a fair game [...] will eventually and inevitably go broke against an opponent with infinite wealth. [^1] -[^1]: https://en.wikipedia.org/wiki/Gambler%27s_ruin +[^1]: [Gambler's Ruin](https://en.wikipedia.org/wiki/Gambler%27s_ruin) As it turns out, this applies not only to leveraging oneself, but to ordinary bets as well. In the simplest case, the *Kelly Criterion* defines the optimal bet size to maximize long-term growth rate of wealth. It states, roughly, that **for a bet with expected return $$b$$ and probability of success $$p$$, the optimal bet size as a percentage of your portfolio can be computed as $$f^* = p - \frac{1-p}{b}$$.** @@ -43,7 +43,7 @@ As it turns out, this applies not only to leveraging oneself, but to ordinary be Quoting from Wikipedia[^2]: > In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. -[^2]: https://en.wikipedia.org/wiki/Kelly_criterion +[^2]: [Kelly criterion](https://en.wikipedia.org/wiki/Kelly_criterion) Notice (if you read the Wikipedia article) that the Kelly Criterion relies on the fact that the utility of money increases with the *log* of money. Although this seems like a pretty arbitrary and strong assumption, realize that: 1. This is actually another way of saying we want to maximize the growth *rate* of our money, since $$\log Pe^{rt} = rt \log P$$ which is proportional to the growth rate $$r$$.