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There are two side to the Kelly Criterion which I think often get equated as the same when they really are not.
Traditional Kelly betting is about limiting your exposure to a risky bet. The bet in question is usually a "bet" in that when you lose, you lose everything you expose.
Traditional Kelly betting is about limiting your exposure to a risky bet. The bet in question is usually a "bet" in that when you lose, you lose everything you expose.
So you scale back and don't risk everything. Most casino games fit this description as do some financial instruments like options.
The optimal leverage here is less than 1. You want to hold cash on the side to buffer the future losses.
The optimal leverage here is less than 1. You want to hold cash on the side to buffer the future losses.
But standard investment assets, don't work this way.
I showed here, that individual stocks are effectively full Kelly bets.
Just buying one stock is the appropriate "size", as they have an optimal leverage of 1. https://breakingthemarket.com/stochastic-efficiency-is-real-and-its-spectacular/
I showed here, that individual stocks are effectively full Kelly bets.
Just buying one stock is the appropriate "size", as they have an optimal leverage of 1. https://breakingthemarket.com/stochastic-efficiency-is-real-and-its-spectacular/
You can go from there and see that the S&P500 has an optimal leverage of around 2. A 60/40 portfolio is closer to 4, and a risk parity portfolio is closer to 8.
In these cases the Kelly criterion says to increase exposure, not limit it.
In these cases the Kelly criterion says to increase exposure, not limit it.
Directionally, this is a pretty big difference. For one, the first example shrinks errors, and the second example expands them. This is not trivial, as an error with leverage can potentially cause you to owe money. https://breakingthemarket.com/error-drag-a-lesson-in-strategy-from-tiger-woods/
Secondly, limiting exposure is a single player decision. Its easy to do by just investing less.
Increasing exposure beyond what you own requires some else to lend you something. It requires other to be involved and other promises to be made.
Increasing exposure beyond what you own requires some else to lend you something. It requires other to be involved and other promises to be made.
Leading to the realization there is a bit of convexity built into the direction of the scaling factor.
Because of this, I feel that Kelly betting strategies that increase exposure are a slightly different animal than ones that limit exposure and need to be handled differently.
Because of this, I feel that Kelly betting strategies that increase exposure are a slightly different animal than ones that limit exposure and need to be handled differently.
