“You have total loans greater than your current balance. Under strict Kelly betting, you should not bet at all in this scenario because there is non-zero risk of ruin. This calculator allows some leeway in this, and will still recommend a bet as long as losing all your money does not actually occur in any of the (up to 50,000) scenarios it simulates.”
Does this take into account the fact that I could liquidate a position to generate more balance and avoid ruin?
It doesn’t account for that unfortunately, one of the simplifying assumptions it makes is that you will wait for all your positions to resolve rather than selling them.
It directly calculates the amount that will maximise expected log wealth, rather than using a fixed fraction. Basically it simulates the possible outcomes of all the other bets you have open. Then it adds in the new bet you are making and adjusts the size to maximise expected log wealth once all the bets have resolved.
If you have a very diversified portfolio of other bets this will be almost the same as betting the Kelly fraction (the f = p—q/b version) of your net asset value. If you have a risker portfolio, such as one massive bet, then it will be closer to the fraction of your balance. It should always be between these two numbers.
(Manifold also has loans which complicates things, the lower bound is actually on the Kelly fraction of (balance minus loans))
Sorry if it’s confusing that in the post I’m using “the Kelly criterion” to mean maximising expected log wealth, whereas some other places use it to mean literally betting according the formula f = p—q/b. I prefer to use the broader definition because “the Kelly criterion” has a certain ring to it 😌, this is also the definition people on Lesswrong tend to use.
It assumes the market probability is correct for all your other bets, which is an important caveat. This will make it more risk averse than it should be (you can afford to risk more if you expect your net worth to be higher in the future).
It also assumes all the probabilities are uncorrelated, which is another important caveat. This one will make it less risk averse than it should be.
I’m planning on making a version that does take all your estimates into account and rebalances your whole portfolio based on all your probabilities at once (hence mani–folio). This is a lot more complicated though, I decided not to run before I could walk. Also I think the simplicity of the current version is a big benefit, if you are betting over a fairly short time horizon and you don’t have any big correlated positions then the above two things will just be small corrections.
Maybe this is stupid of me, but should this be a fraction of your balance or a fraction of your net asset value?
I ask because of this message I got
“You have total loans greater than your current balance. Under strict Kelly betting, you should not bet at all in this scenario because there is non-zero risk of ruin. This calculator allows some leeway in this, and will still recommend a bet as long as losing all your money does not actually occur in any of the (up to 50,000) scenarios it simulates.”
Does this take into account the fact that I could liquidate a position to generate more balance and avoid ruin?
It doesn’t account for that unfortunately, one of the simplifying assumptions it makes is that you will wait for all your positions to resolve rather than selling them.
It directly calculates the amount that will maximise expected log wealth, rather than using a fixed fraction. Basically it simulates the possible outcomes of all the other bets you have open. Then it adds in the new bet you are making and adjusts the size to maximise expected log wealth once all the bets have resolved.
If you have a very diversified portfolio of other bets this will be almost the same as betting the Kelly fraction (the f = p—q/b version) of your net asset value. If you have a risker portfolio, such as one massive bet, then it will be closer to the fraction of your balance. It should always be between these two numbers.
(Manifold also has loans which complicates things, the lower bound is actually on the Kelly fraction of (balance minus loans))
Sorry if it’s confusing that in the post I’m using “the Kelly criterion” to mean maximising expected log wealth, whereas some other places use it to mean literally betting according the formula f = p—q/b. I prefer to use the broader definition because “the Kelly criterion” has a certain ring to it 😌, this is also the definition people on Lesswrong tend to use.
How can I do that without knowing my probabilities for all the other bets? (Or have I missed something on how it works?)
It assumes the market probability is correct for all your other bets, which is an important caveat. This will make it more risk averse than it should be (you can afford to risk more if you expect your net worth to be higher in the future).
It also assumes all the probabilities are uncorrelated, which is another important caveat. This one will make it less risk averse than it should be.
I’m planning on making a version that does take all your estimates into account and rebalances your whole portfolio based on all your probabilities at once (hence mani–folio). This is a lot more complicated though, I decided not to run before I could walk. Also I think the simplicity of the current version is a big benefit, if you are betting over a fairly short time horizon and you don’t have any big correlated positions then the above two things will just be small corrections.