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?

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## 10 thoughts on “Mathematical Literacy And Trading”

1. I’m looking forward to it. For the record, I really enjoy the denser material. Keep writing for your younger self – I’m sure there’s one or two out there that will appreciate your work.

FYI – this reader has an advanced background in mathematics (MS, chemical engineering)

2. It’s true that most people won’t follow the math, but you can’t make everyone above average even if they do get it There are more than enough blogs that just take a few minutes to draw some candlesticks, islands, and christmas trees on charts and call it a deep analysis. I’m not a trader but I’m interested in seeing where this is going and if it holds up to a lot of testing. Trading seems hard enough, but trying to educate the uneducated seems like an impossible task (on the other hand entertaining them doesn’t take much).

3. I would encourage you to continue with the more advanced mathematics. It may fly over the head of many, and some of your readers will, at first, have no choice but to simply take it on faith, but that’s okay. We’re pretty emotion driven creatures, those who are inspired by your writings will put in the work to understand the nuances.

Incidentally, you’re writings on Kelly bring me back to the days when I used to count cards. This is a fine introductory paper discussing risk and potential draw downs for various fractions of Kelly:

I mention this as even the basic calculations in the paper made my eyes glaze over when I first read it years ago, but section 4.1 was of considerable value to me. Even I could understand the chart. Admittedly, I took the numbers on faith, but my faith had made worse gambles in the past. And the fact that the authors had put their calculations and methodology on display for their peers to judge lent a certain degree of credibility.

Ultimately, I think it’s the student’s responsibility to keep up with the material, please don’t dilute it.

4. I have to agree with the above comments. The reason I read this site periodically is to learn something that isn’t on every other investing/trading website. People will just have to suck it up and break out a calculus book.

I wouldn’t consider myself to be “advanced” in the math arena, but I would say I have a higher grasp than most (BS mechanical engineering). Unfortunately, I’ve been out of school long enough where I’ve noticed that I’m starting to forget things that I learned in the earlier classes in college.

5. More math please, but make sure it’s right. Your discussion of the kelley criterion left much to be desired, and your definition of alpha is completely wrong.

• If you don’t like the math in question, feel free to comment there with specifics.

Note that there are three (or possibly more) different definitions of “alpha” – no one has a monopoly on Greek letters. The ones relating to investment return are of no interest to anything we’re doing here – there’s not an investment in sight. Although if you do the math, you’ll find there’s a hidden symmetry – they’re actually all sort of the same thing.

• Ahh but it’s easier to make a snide driveby comment from my cellphone then, you know, be constructive…

I’ll continue the debate about alpha in that post

6. Late to the party, just started reading your blog a few days ago and I’m going backwards through the posts (maybe not the best approach, but that’s okay). I wanted to say that the Khan Academy is excellent. I started a masters in Applied Mathematics a few years ago with a long break from school and lacking the required background. I filled most of the gaps with the lectures from the Khan Academy until I became comfortable with the material again. That’s it, thanks for the posts.

7. FWIW, I’d love to see the additional Kelly material. I’ve tried expanding Kelly with multiple outcomes (for instance, a powerball-style lottery with multiple outcomes, pretending it had a positive EV and no chance of jackpot split) and quickly got into exponent hell.