0
$\begingroup$

I am trying to understand what the "correct"/optimal way of betting is using the Kelly Criterion but for bets that don't immediately give an outcome.

For example, I have 100 dollars. I get a buy signal, I run Kelly Criterion and it says optimal is 20% bet, so I put 20 dollars on that buy signal. Now, let's say in the next timestep, I get another buy signal on something else, but the first position hasn't been closed yet - so I have 80 dollars cash and 20 locked up in a position. The Kelly Criterion says 10% is optimal - would I bet 10 dollars on this new position (10% of my total portfolio value) or 8 (10% of remaining free cash)?

Any references or justification would be appreciated. Thank you!

$\endgroup$
3
  • 1
    $\begingroup$ The conceptual generalization you may be looking for is a "growth optimal portfolio" which can be obtained by maximizing the expected logarithm of terminal wealth: $\max \operatorname{E}[\log W]$. (My answer here might get you on the right track. In theory, you could solve a sequential problem with backwards induction: i.e. solve all possible cases of the last period $t$ problem then use that to solve all possible cases of $t-1$ problem etc.... $\endgroup$ Feb 23, 2023 at 1:34
  • 1
    $\begingroup$ In most any practical investment setting though, you can't solve for that kind of optimal solution because you don't have anything resembling enough information. So a practical way forward may look really quite different. $\endgroup$ Feb 23, 2023 at 1:36
  • $\begingroup$ Yes. It sounds to me like quite a challenging problem to formulate and solve. Much more complicated than what Mr. Kelly considered in his 1956 paper. $\endgroup$
    – nbbo2
    Feb 23, 2023 at 19:38

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.