Kelly betting for normal distributions

aptenodyte · May 8th, 2006, 4:37 pm

AM trying to determine kelly bet size when returns come from a normal distribution;Searches on Wilmott and on Google suggest that kelly fraction is mu/sigma^2 but this makes no sense:if I have a annual Information ratio of 1.5 with a mean of 6% and stdev of 4% the fraction comes outto be 37.50 well above the upper limit and a guarantee of probable ruin -- even if I subtract risk free rate of 5% from mu fraction is 6.25 - does anyone know what I am missing?Thanks..

Lepperbe · May 8th, 2006, 6:20 pm

you should indeed substract riskfree rate, and given assumption of normal distribution in Kelly criterion the 6,25 leverage factor is about right. it would take more than a 4 sigma event to bankrupt you. highly unlikely in a normal distribution. not so unlikely however in real life (optimal f leads to slightly over 10% chance of bankrupty along the way anyway so you would probably not want to use optimal f anyway)

aptenodyte · May 9th, 2006, 6:49 am

Thanks. Does subtracting the risk-free rate make sense if the portfolio generating the returnis self-financing? Seems like kelly theory may break down in this case and argue for limitlessleverage since its effectively a free bet with high expectation.