Question for Bruce Z
I stumbled upon an old thread discussing bankroll requirements and I was going through your formulas. I'm having trouble with a couple of them, and I was wondering if you could shed some light.
>>CORRECT RISK OF RUIN FORMULA:
bankroll = -(sigma^2/2u)ln(.05)
u = $30/hr, sigma = $650/hr gives bankroll of $21,095
>>GTAOT FORMULA FOR 5% RISK (combining equations, u = hourly rate):
bankroll = (1.64sigma)^2/4u
u = $30/hr, sigma = $650/hr gives bankroll of $9470
The above two formulas I understand and I can come up with the correct answer.
However the following formula is giving me some problems:
>>risk for GTAOT 5% bankroll of $9470 would be
r = exp(-2uB/sigma^2) = 26%
First of all what is exp? Is it 5%? If it is then I come up with .0672. If it is something else could you please explain?
In one of the threads you say:
>> I also agree that the 5% numbers should not be used since they really correspond to a 26% risk of ruin which I venture to say nobody wants.
I don't quite understand the premise. It appears you have two risk of ruins here. Namely, 5% and 26%. If your willing to take a 5% chance of going broke then what does the 26% mean? Does it mean that you actually have a 26% chance of going broke?
I'm just a bit confused. Thanks for any help.
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