There are two sides to the Kelly Criterion which often get equated as the same, when they really are quite different.
Using Cash to Create a “Kelly” Portfolio
Traditional Kelly betting is about limiting your exposure to a risky bet. The wager in question is usually a “bet”, in that when you lose, you lose everything on the table.
So Kelly betting scales down (holds cash) and doesn’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 keep cash on the side to maximize the geometric return and buffer the future losses.
To reach a full Kelly portfolio, you simply don’t invest all your money.
Using Leverage to Create a “Kelly” Portfolio
But standard investment assets don’t work this way. When you buy a stock, it certainly might go to zero. But unlike a “bet”, it’s very improbable in the near term.
Individual stocks are effectively full Kelly bets. Just buying one stock is the appropriate “size”, as they historically have an optimal leverage of 1. 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 maximum geometric return calls for increased exposure and scaling up (borrowing cash), not limiting exposure.
To reach a full maximum Kelly portfolio in the investing world, you must borrow money.
The Two Must be Evaluated Differently
Directionally, this is a pretty big difference. For one, limiting exposure is a single player decision. It’s easy to do by just investing less. But you can’t increase your exposure alone. You can’t lend money to yourself. It requires others to be involved and other promises to be made.
Secondly and more importantly, scaling down shrinks errors, and scaling up expands them. This is not trivial, as a levered error opens up the potential for bankruptcy. Holding cash does the opposite.
Kelly betting strategies that scale up (borrowing cash) are therefore slightly different animals than ones that scale down (holding cash) and they need to be thought of differently.
Keep this distinction in mind when creating your own portfolios.