A little over a week ago I posted on the topic of the Kelly Criterion and its use in bet sizing. This post was notable for being the most mathematically sophisticated material I’ve covered thus far. On previous topics I’ve made some effort to hide the math – sort of like those cooking shows where they pull a fully baked cake from the oven immediately after putting the pan full of batter in. There are upsides and downsides to hiding the math this way, but I’m starting to think the downsides outweigh the upsides.
The upside of course is that limiting the math broadens the audience for my blog and makes it more fun to read. There’s nothing less fun that reading an exciting screed on how to make money, only to hit a big ol’ block of math. It’s like finding a fly in the punchbowl – you may keep reading/drinking, but it’s not quite the same. It’s also easier to write low-math posts because I don’t have to spend any time making sure the math is right.
The downside of limiting the math on ORF became apparent as I was writing yesterday’s post on contrarian thinking. In order to have the kind of unpopular/right ideas I’m saying you need to make money, you can’t let someone else do your thinking for you. That includes letting someone else do your math for you. If you want to follow where this blog is leading, you will have to check every single piece of trading math you encounter and make sure it’s right before you trust the result. By ‘right’ I mean not just that the calculations are numerically correct, but that the right concepts have been applied in the right way. This of course applies to my math as much as anyone else’s.
Truth be told, I’d like to be able to tackle much more advanced mathematical topics than what I’ve written on thus far. The intended follow-ons to the Kelly Criterion article are perfect examples:
- Kelly Criterion where there are more than two possible outcomes – the outcomes are spread on a distribution. Requires calculus and descriptive statistics.
- Kelly Criterion used to allocate capital between two or more bets with different properties that occur at the same time. This what Warren Buffett uses Kelly Criterion for as mentioned in the Wikipedia article. It requires vector calculus which is why Wikipedia punted and didn’t explain.
- Betting less than Kelly sizing to reduce variance. This require either hefty algebra and statistics if I want to do it analytically, or Monte Carlo simulation if I want to punt and take the easy route.
Here’s the problem: if I write this way, essentially no one can get anything from it. Maybe 1% of the US adult population has the full math background needed. Maybe another 1-2% could struggle through (which is incompatible with contrarianism – you’re still dependent on me being right). Now this blog has never been intended for the average Joe. At some level it’s really me writing to a younger me and explaining all the things I wish I’d known. The fact that I’ve found the audience I’ve got is really a little gratifying. But the dilemma remains – I have no idea how different my readers may be from the general population.
So first I’d like to encourage you to take math seriously if you ever want to trade. I don’t necessarily mean math classes. I mean taking math seriously the way many people take auto repair seriously. When the opportunity arises to do math , do it. Don’t punt or use someone else’s result. If you don’t know how, make use of resources on the internet an learn. Kahn Accademy is a good place to start. I’ve never taken any of their modules, but they seem to cover the right things. Their exponents and logarithms module would probably make the first Kelly Criterion article accessible for example. While I don’t have hard evidence, I’ve seen some intriguing hints that high level mathematics knowledge is strongly correlated with trading success. So this is worth you time.
Second, I’d like some reader feedback. Am I at the limits of people’s mathematical knowledge? Or would some articles that make use of more advanced statistics and calculus go over OK?