I am trying to understand the implications of the kelly criterion for a real world portfolio. What I get as a result is that if I have free choice on any bet at any odds and chances I should, in total, invest more than I have. (Result by integrating over all probabilities/odds that allow positive expected value) In fact, I should invest infinitely much money. The wikipedia page states that taking out credit to buy a bet would be formalized by the loss formula so the infinity result is not exactly interpretable as taking out a loan, if I can.
One obvious fix is to limit the odds and probabilites to realistic values but that seems quite arbitrary. Intuitively I would expect the Kelly criterion to give a finite sum for all bets with positive expected value, at least it does so for any given odds b in wikipedias terminology.
What I get as a result is that if I have free choice on any bet at any odds and chances I should, in total, invest more than I have.
If you invoke infinities or indefinite sets of bets, it shouldn’t surprise you that regular results might not apply: if you decide to invest in a bet of n at 99% odds of doubling, wouldn’t it be even better to invest n at 99% odds of tripling? Or even better than that, invest n at 99.9% odds of tripling? Or no, invest n+1 at 99.9% odds of tripling! I’m not sure why you’d expect anything useful from a KC or a variant with such arbitrary inputs.
One obvious fix is to limit the odds and probabilites to realistic values but that seems quite arbitrary.
It does seem arbitrary because for sufficiently high intervals for p and b the integral will exceed 1, that is allocation of all my cash and I do not know how to interpret this result.
I am trying to understand the implications of the kelly criterion for a real world portfolio. What I get as a result is that if I have free choice on any bet at any odds and chances I should, in total, invest more than I have. (Result by integrating over all probabilities/odds that allow positive expected value) In fact, I should invest infinitely much money. The wikipedia page states that taking out credit to buy a bet would be formalized by the loss formula so the infinity result is not exactly interpretable as taking out a loan, if I can.
One obvious fix is to limit the odds and probabilites to realistic values but that seems quite arbitrary. Intuitively I would expect the Kelly criterion to give a finite sum for all bets with positive expected value, at least it does so for any given odds b in wikipedias terminology.
If you invoke infinities or indefinite sets of bets, it shouldn’t surprise you that regular results might not apply: if you decide to invest in a bet of n at 99% odds of doubling, wouldn’t it be even better to invest n at 99% odds of tripling? Or even better than that, invest n at 99.9% odds of tripling? Or no, invest n+1 at 99.9% odds of tripling! I’m not sure why you’d expect anything useful from a KC or a variant with such arbitrary inputs.
It does?
You are right.
It does seem arbitrary because for sufficiently high intervals for p and b the integral will exceed 1, that is allocation of all my cash and I do not know how to interpret this result.