This seems like a very handy calculator to have bookmarked.
I think I did find a bug: At the low end it’s making some insane recommendations. E.g. with wealth W and a 50% chance of loss W (50% chance of getting wiped out), the insurance recommendation is any premium up to W.
Wealth $10k, risk 50% on $9999 loss, recommends insure for $9900 premium.
That log(W-P) term is shooting off towards -infinity and presumably breaking something?
Edit: As papetoast points out, this is a faithful implementation of the Kelly criterion and is not a bug. Rather, Kelly assumes that taking a loss >= wealth is infinitely bad, which is not true in an environment where debts are dischargable in bankruptcy (and total wealth may even remain positive throughout).
There’s probably corrections that would improve the model by factoring in future earnings, the degree to which the loss must be replace immediately (or at all), and the degree to which some losses are capped.
Wealth $10k, risk 50% on $9999 loss, recommends insure for $9900 premium.
The math is correct if you’re trying to optimize log(Wealth). log(10000)=4 and log(1)=0 so the mean is log(100)=2. This model assumes going bankrupt is infinitely bad, which is not accurate of an assumption, but it is not a bug.
Hmm, I guess I see why other calculators have at least some additional heuristics and aren’t straight Kelly. Going bankrupt is not infinitely bad in the US. If the insured has low wealth, there’s likely a loan attached to any large asset that really complicates the math. Making W just be “household wealth” also doesn’t model “I can replace the loss next paycheck”. I’m not sure what exactly the correct notion of wealth is here, but if wealth is small compared to future earnings, and replacing the loss can be deferred, these assumptions are incorrect.
And obviously, paying $10k premium to insure a 50% chance of a $10k loss is always a mistake for all wealth levels. You’re choosing to be bankrupt in 100% of possible worlds instead of 50%.
This seems like a very handy calculator to have bookmarked.
I think I did find a bug:At the low end it’s making some insane recommendations. E.g. with wealth W and a 50% chance of loss W (50% chance of getting wiped out), the insurance recommendation is any premium up to W.Wealth $10k, risk 50% on $9999 loss, recommends insure for $9900 premium.
That log(W-P) term is shooting off towards -infinity and presumably breaking something?Edit: As papetoast points out, this is a faithful implementation of the Kelly criterion and is not a bug. Rather, Kelly assumes that taking a loss >= wealth is infinitely bad, which is not true in an environment where debts are dischargable in bankruptcy (and total wealth may even remain positive throughout).
There’s probably corrections that would improve the model by factoring in future earnings, the degree to which the loss must be replace immediately (or at all), and the degree to which some losses are capped.
The math is correct if you’re trying to optimize log(Wealth). log(10000)=4 and log(1)=0 so the mean is log(100)=2. This model assumes going bankrupt is infinitely bad, which is not accurate of an assumption, but it is not a bug.
Hmm, I guess I see why other calculators have at least some additional heuristics and aren’t straight Kelly. Going bankrupt is not infinitely bad in the US. If the insured has low wealth, there’s likely a loan attached to any large asset that really complicates the math. Making W just be “household wealth” also doesn’t model “I can replace the loss next paycheck”. I’m not sure what exactly the correct notion of wealth is here, but if wealth is small compared to future earnings, and replacing the loss can be deferred, these assumptions are incorrect.
And obviously, paying $10k premium to insure a 50% chance of a $10k loss is always a mistake for all wealth levels. You’re choosing to be bankrupt in 100% of possible worlds instead of 50%.