I want to start by saying this is not intended for specific circumstances that are highly sensitive to variance (close to retirement for example) – but I’d like to hear if anyone has considered the implications of the Kelly Criterion on their own portfolio.
A very brief and incomplete summary to anyone not familiar:
Consider a game where you flip a coin at even odds however the coin is weighted 60% heads, 40% tails. With a bankroll of $100, the optimal amount you should bet on this game is given by the kelly criterion as 20% of your bankroll.
The kelly criterion can be used to calculate optimal wagers on positive expected value (EV) games.
Investing in the S&P 500 is positive EV – historical returns are ~+7%.
In Kelly’s paper, the criterion can be simplified in a continuous return form as:
K = return / variance squared
So, for the S&P 500 historically if we use 7% as the rate of return and 17% as variance we get K = 2.42 suggesting leveraging ~2.4x is optimal.
In my own experience I have heard real advisor professionals suggest “quarter Kelly” or similar. Has anyone seriously applied this idea to how they think about their own portfolio? I’d love to know and hear your thoughts.
Edit: Kelly himself did not apply the criterion to continuous returns that was Ed Thorp later on. Apologies
Posted by thelman
9 Comments
No
St0nks go up. Until they don’t
I would probably think way harder about how you get that optimal leverage number, but there is an argument for levarage based more or less on the logic you lay out here. You probably already know about “lifecycle” investing. If in was just starting out at 18, I would use leverage. Im too old for it now.
Totally. Buy LEAPs on Monday at 60% of atm.
Yolo
/s
SPYU to the Moon!!!
Yes. And to anyone who says no, then you need to prove why a leverage of 1x is optimal.
https://www.ddnum.com/articles/leveragedETFs.php
The study concluded that just about 2x was optimal for the S&P500 after accounting for frictional costs.
Keep in mind the results of the study is based on historic data and only holds true if daily frictional costs are managed which for some 2x funds, they are severely over charging and will probably result in failure for those particular funds.
For return you’d need to use the excess over borrowing costs which would bring your lvg down a bit.
Kelly is also assuming you can “keep playing” over infinite turns. In reality – you might end up deleting your capital base so badly at one point that you’d need a 1000 years to get back ahead.
Let’s say we accept the premise of 2.42x leverage (or 1.5x, or whatever), the mechanism through which you get that leverage is imperfect. Leveraged ETFs kinda suck (look at performance of UPRO and SPY since Jan of ’22 as one data point). You could borrow against your portfolio to buy more SPY, and then you have to take interest (and liquidation risk) into account. Leverage isn’t free, and should be taken into account in any modeling you do.
Look up HedgeFundies Excellent Adventure (HFEA) and the Leverage for the Long Run pdf.