confidence bands for kelly ratio

Nonius · Post by **Nonius** » Mon Feb 17, 2014 10:27 pm

The mu^2 term makes no sense as mu gets large. In the limit of (almost) arbitrage, it would dictate betting zero. But I see where it arises in the simplistic Taylor's argument.

goldorak · Post by **goldorak** » Tue Feb 18, 2014 9:20 am

mu/(mu^2+sigma^2) gives far better results than mu/sigma^2 in real applications. Maybe the mu^2 term helps taming slightly the Kelly ratio when IR expectation is high and it has a good influence in the overall trading result.

NeroTulip · Post by **NeroTulip** » Tue Feb 18, 2014 9:35 am

Or possibly it keeps you from betting the ranch in low vol situations... Sigma can be a pretty poor measure of risk.

pj · Post by pj » Tue Feb 18, 2014 9:40 am

Nonius is right.

Something fishy is going on with the formula. Confused

goldorak · Post by **goldorak** » Tue Feb 18, 2014 12:29 pm

OPTIMAL INVESTMENT STRATEGY FOR RISKY ASSETS

Nonius · Post by **Nonius** » Tue Feb 18, 2014 1:06 pm

Oh, but if mu increases, then higher order Taylor's terms come into play. Duh. Then the solution gets more complicated as it's a root of a higher degree polynomial.

Nero, if you believe thorp, vol and return are all that matters cuz of CLT.

filthy · Post by **filthy** » Tue Feb 18, 2014 7:35 pm

thanks for the responses. i've been busy at actual work so i've been unable

to respond.

the mu/var formulation is only an approximation and you can just extend the taylor expansion to include skew and kurtosis terms, but more interesting are the distributions

for which the expansion fails (undefined moments). i'm sort of working on this.

but i'm really just busy at my shitty day job.

dgn2 · Post by **dgn2** » Wed Feb 19, 2014 3:42 am

I would really like to contribute a bit on this, but I am also busy with my day job. I will do my best to find the time.

Corey · Post by **Corey** » Wed Feb 19, 2014 7:00 pm

I am interested in taking a read; can anyone share? E-mail in profile. Thanks.

yanko · Post by **yanko** » Thu Feb 20, 2014 4:40 pm

I'm also interested in having a peak, so would somebody please forward the paper?

Thanks,

yanko