Advent of Alpha Day 6: Kelly

John Larry Kelly Jr. probably created the most important equation related to the industrialisation of Information Theory, probability and wealth management in history.

Don’t believe me? Well, walk around Wall Street or the square mile, look around, and realise until Black, Scholes, Merton, the most important formula doing the rounds to build that place was Kelly’s 1956 work in showing how to optimally size a bet.

The simplest version of explaining Kelly is that the proportion of your bank as a percentage is your edge, expressed as a percentage, divided by your fractional odds. Got 2% edge at evens? Bet 2% of your bank. Got 0.5% edge at 7/2? Bet 0.5/3.5%, or 0.14% of your bank.

There are better formulas for more complex scenarios and to take into account existing positions, and some python libraries out there to help you, so go grab those.

But here’s the alpha, that I can’t understate enough:

What Kelly shows isn’t just how to maximise your profits from edge, but that even if you have edge, if you overbet, you will go bust.

I’ll say this again:

If you have a 1% edge at evens, and you bet 2% of your bank, you will eventually go bust.

If you have 0.5% edge at 7/2 and you bet 0.15% or more of your bank, you’re overheating to the point you will go bust.

You will go bust even if you have edge, if you overbet it.

Overbetting kills you even when you have edge.

Winning systems die from being overbite.

If you’re losing, you might be losing because you’re overbetting, not because you don’t have edge.

Got it yet?

Don’t think of Kelly as profit maximisation. Think of it as the upper limit, beyond which, if you’re betting even slightly over that upper limit, you will lose.

Even if you are confident you have edge, and you can size it accurately, consider betting under Kelly, just to be safe. Half-Kelly (taking the Kelly percentage and dividing it by 2), is popular, because it reduces variance by half, but still puts you at 75% of optimal growth. And it’s a long way from overbetting.

If there is nothing else you do this December than try to quantify edge and reduce your stakes, then just do this.

If you’re interested in a great book about the history of Kelly and the people involved and how the formula got a life of its own, I can recommend William Poundstone’s “Fortune’s Formula”. I read it every few years because I thoroughly enjoy it, and always seem to get something new from it.