The Kelly Criterion - The Smart Investor's Tool to Bet Sizing
How to decide on the optimal size of the investment and make sure you avoid losing your capital
When I was making investment decisions, I thought of two questions:
The first was: should I invest in this asset or opportunity? This is the most difficult question, which involves considering the risk profile, the type of asset, etc..
And the second - if I invest - how much should I invest?
While the first question will always be asked, the second had me stumped for a while. Until I recently came across the concept of Kelly Criterion - a formula that calculates the betting site based on the probability of winning and the size of your potential payout. And it does so in a way that pretty much guarantees you won't go broke.
Why is this important?
In just about any real investment system, you're dealing with a Non-Ergodic system. This means that the probability of your success doesn't work the same way as a probability based on the statistics of that investment good.
Suppose you've ten sequential bets to make. If any of those bets can result in the loss of your entire stack (if you bet all or most of it) and you can't keep playing (you're in a non-ergodic system) - you won't be able to achieve the probability of success of that bet in that short time. And so it's with almost every investment.
About a year ago, I published an article about Angel Investing decisions. And the conclusion from it was similar - you need at least 30 investments in your portfolio to expect a return that's close to the industry standard.
So while the statistical return of angel investing on a large scale could be 2 to 4 times, you can't even hope to get something like that with 1-2 investments.
That's the case with pretty much any risky form of investing.
Kelly Criterion
One way to deal with this risk is to use the Kelly Criterion, a formula that helps you determine the optimal size of a bet to maximize the expected value of your investment. The Kelly Criterion takes into account the probability of winning, losing, and the potential payoffs of each bet to determine the optimal proportion of your portfolio for each bet. This approach can be helpful for investors who want to maximize their returns while minimizing their risk of loss.
Kelly fraction (proportion of bankroll to be allocated) = W-(1-W)/O
Where:
- W is the probability of winning the bet (value from 0 to 1)
- O is the ratio between the potential payout and the amount bet (also known as odds). Basically, it's your expected multiplier on the outcome
Quick Example
If you invest in an early-stage startup, let's make the following assumptions:
- The probability that this startup is successful is 2%
- If it's successful, you earn 100 times your money, so your odds are 100/1=100
- According to the formula Kelly fraction = 0.02 - (1-0.02)/100 = 0.0102 = 1.02%
- This means that you've to invest up to 1.02% of your stake in this chance
I've created a quick example of this formula in Google Sheets. Feel free to use it for your investment decisions
Keep in mind that the Kelly criterion is only valid when the probabilities of outcomes are known, which isn't always the case with investments. While it can be a helpful tool, it's not a guarantee of success.