The Kelly Criterion is a tool you can use to help decide how much weight you should give each position in a portfolio.
Invented by John Kelly, who was originally employed at Bell Labs, the formula enables you to calculate how much of your bankroll you should bet on an opportunity depending on the odds of winning. This is the simple version of the formula:
“The simple rule goes like this. Suppose that with probability p you will make a profit of b times what you bet, and otherwise you lose the bet. Then the optimal amount to bet is (bp−(1−p))/b. (Note that p is a number from 0 to 1. So 50% probability means that p is 05.) Gamblers call pb−(1−p) their edge, and b their odds leading to the simple rule bet edge over odds.”
If you are offered a coin toss where heads means you get $2 and tails costs you $1, according to the Kelly formula, the edge is 0.5 [(0.5*$2)+(0.5*-$1)] suggesting that you should bet 25% of your bankroll each time (0.5/$2). Employing the same technique in investing is not as straightforward, but it achieves the same results.
To use this in investing you have to work out the probabilities first, which is not an exact science, but this is why the margin of safety principle was invented.
For example, let’s say company ABC is trading at $10 and book value is $20. The company is selling one business division that will realise $10 per share in cash, and management has promised to return this to investors. If this deal completes, the firm will have $10 per share in cash, and if the stock remains at $10, there will be zero value ascribed to the rest of the business — an undeniable value proposition.
Let’s also say that this deal has been agreed in principle, it’s a cash deal, so there’s no financing risk, but as of yet, no formal agreement has been signed, and the underlying business is in no danger of going under.
Looking at the data available, we can say that there’s a strong 70% chance that this deal will complete and the money will be returned to investors. There’s a 5% chance the business will fold (margin of safety, there’s always a risk) and 25% chance that the deal won’t go ahead. Based on these odds, according to the Kelly Criterion, it’s sensible to bet 55% of your capital on this opportunity, which has a 70% chance of you being able to double your money.
As with any strategy, this isn’t a definitive guide, it’s only part of the investment process, and there’s no requirement to follow its guidance. However, the Kelly formula is useful for trying to work out the best way to deploy your capital into opportunities.