confidence bands for kelly ratio

filthy · Post by **filthy** » Thu Feb 20, 2014 8:35 pm

corey: "email in profile"

really?

Corey · Post by **Corey** » Thu Feb 20, 2014 11:22 pm

Ah ... yes. I am an idiot. Forgot to fill out the public e-mail.

Thanks.

Corey

pj · Post by pj » Sat Feb 22, 2014 2:10 pm

Most probably I don't understand something but

why

(11) [img]/User%20Files/126/Latex-Equation-11945.gif[/img]

and not

[img]/User%20Files/126/Latex-Equation-11946.gif[/img]

?

If I invest [img]/User%20Files/126/Latex-Equation-11947.gif[/img] of capital don't I need to take it from somewhere?

Of course (16) appears magically anyway and doesn't seem working

for the binomial case anyway. At least I am not able to reconcile

with (6).

And what happens with criterion (15) when one has the normal

distribution Φ and the random point x

hits a "black swan" value?

i.e. when

[img]/User%20Files/126/Latex-Equation-11948.gif[/img] ?

thus the Kelly criterion cannot be applied to normal distribution.

Because of the possibility of the unlimited liability.

Nonius · Post by **Nonius** » Sat Feb 22, 2014 10:48 pm

yes, this was discussed on another thread (with Nero and Silverside involved). In practise, your "bankroll" would include the ability to get financing, and you'd normally have other constraints from your broker in terms of leverage levels, measured in numerous ways. So, I think to do it in the real world the optimisation becomes a mildly constrained optimisation problem. I've also been thinking about how to incorporate costs as well as market impact, that latter of which in some typical assumptions renders a cost dependency that varies as the square of the size of your trade.

filthy · Post by **filthy** » Sun Feb 23, 2014 12:37 am

i'm hoping to address some of the issues raised in the next version, which should be out next week.

NeroTulip · Post by **NeroTulip** » Sun Feb 23, 2014 9:21 am

@pj:

Re: criterion (15), unless you are dealing with very pathological distributions (e.g. selling vol or doing carry trades), the risk of blowing up from a single extreme loss (g(x)<-1/f) is less of a concern than the drawdowns created by repeated small losses, or the vol of the optimal f strategy. So your choice of Kelly fraction will be driven by vol and drawdown considerations, rather than by tail risk considerations. Consider that if you have a Sharpe of 1, Kelly will tell you to leverage it to ~100% annual vol. From a psychological point of view, it would not be very clever to trade this way, because you (or your investors) are likely to throw in the towel at the wrong time. Quarter Kelly (~25% vol) is already quite punchy, no?

@filthy:

(13) seems incorrect, it should be ln(B_n/B_0)=Sum{ln(1+fg(X_i)}

It is interesting that in the binomial case, Kelly guarantees 0 probability of blowing up, but this does not hold in the continuous case. In the continuous case, we are maximizing the *expected* long term growth rate, so some paths may well blow up.

pj · Post by pj » Mon Feb 24, 2014 4:18 pm

I do agree I am an anal type but I don't like to

have an "intuitive grasp" before I understand what

the phuck it is about.

Let's not even get started about the delta formula

Cool I may have totally wrong ideas...

fantisst · Post by **fantisst** » Wed Feb 26, 2014 1:19 am

A little late to the party. May I ask for a copy? I'm very interested (and I read your books twice).

phy · Post by **phy** » Fri Feb 28, 2014 1:21 am

Could you be kind to send me a copy as well.

filthy · Post by **filthy** » Wed Mar 05, 2014 8:42 pm

i'm done with revisions so anyone who wants a new copy can email me.

the conclusions are largely the same. it is just typo'd and tidied.

i will also be happy to share photos of my dog and new motorbike...