How can Investors Use Kelly Bets in Practice?
In theory Kelly bets can supercharge your portfolio growth. Using it in practice is tricky.
For a single bet, if you know your probability of winning, and your expected payout, you can calculate how much of your bankroll to allocate to this bet. This calculation when done repeatedly over a large sequence of bets will theoretically minimize your risk of ruin, and maximize your portfolio growth.
The formula is
𝑓∗=(𝑏𝑝−𝑞)/𝑏
where f* is fraction to be allocated to the bet, b is the odds received on the bet and p is the probability of winning. q is the probability of loss, or q = (1 - p).
This is a mathematically rigorous result and works very well in many situations. If I was betting on a coin toss, or a horse in a race, this would be the correct way to decide how much to bet to maximize my winnings over time.
But investing is different for many reasons.
1. Do you know your probability of winning?
When you research a stock and decide to purchase it, you are making a judgement that the probability of you making a profit is higher that 50%. But what is it really? Can you put a number to it?
This is very hard to do. In fact, it is well neigh impossible to do on a stock by stock basis. What you can do is to review your past investments and calculate how many of the trades were the winning trades? If you go back 100 or more such trades, you have a reasonable approximation to the probability of winning that your system is expected to produce.
This requires you to have a system of stock selection that you consistently use.
2. Do you know your odds?
How much profit do you expect to make out of this trade?
For some, this can be as simple as saying I only enter positions that are expected to generate x% of profit per year. For others, specifically long term investors like me, the timing of when and how much of the profit is realized is undeterminable. But we can make estimates and set up a rule forcing us to exit a position if it has not performed within a certain period of time.
Again, you need to have a system that helps you make a profit estimate on the stock.
3. Do you really make single stock investments in a sequence?
You don’t. You have a portfolio of stocks (or ETFs or other investments).
If you did single investments, the volatility will be too much to stomach and you will not be able to stay the course. If you used fractional Kelly to mitigate volatility, as significant amount of your cash will remain unused. Not very ideal. You need a portfolio of stocks.
Let’s say you have successfully solved the problems #1 and #2. You are now ready to start investing in a growth optimal way. You know what your bankroll is and you have found a list of 5 stocks you would like to allocate your capital to. (It could be 10, or any other number, that is not important here).
You can easily calculate the portion to allocate to Stock #1. Use fractional Kelly if you wish.
Once you have made this allocation, what is your bank roll for Stock #2? Is it the total portfolio value or is it the cash that remains after investing in Stock #1? What about the remaining stocks?
Does it matter?
Yes, it does matter. You can easily reason this out yourself.
For now, I will make the point that you should not calculate the fraction for any stock in isolation from the other stocks in the portfolio. Different stocks are correlated with each other to different degrees. Do you think if you own Home Depot stock, buying Lowe’s stock will give you as much risk reduction versus, say, buying Microsoft stock?
You need to consider all the stocks in your portfolio holistically, compute their correlations and expected returns and standard deviations and then figure out the relative weights.
I solve this problem of applying Kelly Criterion to our portfolio of stocks. I use various tools to find correlations, generate return expectations with my proprietary research and calculate optimal position sizes for each stock using the Kelly Criterion
One curious outcome of this process is that not every promising stock with high expected returns will make it to the portfolio. The correlations have to fit with the rest of the portfolio. Best bet is to find great stocks that are uncorrelated or inversely correlated with what we currently have in the portfolio.
In short, the process forces you to build a diverse portfolio in a precise manner.
Which is great, because now we can also apply another technique to amplify returns even more. I will explain more in an upcoming article on Shannon’s Demon.