Kelly formula

[joesan]

Well, I must say when I posted the question about whether optimal f is about the percentage of the total amount of an account to be put into one trade, or is about the percentage of the total amount of an account to be risked in one trade, I did not know the exact answer. But if according to some posters above, it is the percentage of the total account to be put into one trade, then I roughly calculated the optimal f of my strategy and found I should only put 12% of the account into one trade, that is less than my current operation, in which I usually put 20-30% money in the account into the trade. Have I been embracing an ridiculously high level of risk and am I too agressive in my trading? Well, according to my MDD level, it is unlikely the case.

So to figure out the doubt, I pulled out the book "Portfolio Managment Formulars" by Ralph Vince, and on page 80, I found the following words in the second paragraph :

" Most people think that the optimal fixed fraction is the percentage of your total stake to bet. This is absolutely false. There is an interim stop involved. Optimal f is not in itself the percentage of our total stake to bet, it is the divisor of our biggest loss, the result of which we divide our total stake by to know how many bets to make or contracts to have on."

Then it all makes sense to me. So I am still a conservative trader and risking much less than the optimal f suggests (12% as mentioned above ) in my trading.

 

[dont]

search google for thorp , ziemba together with kelly.

 

[trading1]

I believe the correct answer is (b). Kelly was derived with stakes where the entire amount would be won or lost. Also, the amount to expose in itself does not mean anything unless it's connected to an amount at risk, as in answer (b).

Quote from joesan:

I also have a question about kellys formula. Regarding the optimal fraction in kelly's formula, is this the percentage of the total account to be risked , or is this the percentage of the total amount that can be used to trade ?

For example, suppose you have a USD100,000 acount for trading stocks, kelly ratio is 20%, current price for ABC is 100 PER share,stop loss for stock ABC is USD10 away from the current price,. so how many shares you will buy for ABC, as follows

a)
USD100,000*20%/100=200 shares

b)
USD100,000*20%=USD20,000 as the total amount to be risked
USD20,000/10=2,000 shares

min(100000/100,2000)£½1000 shares


According to kelly's formula , a) or b) is correct ?

 

[trading1]

Yes, a baseline is needed. Apart from this, I believe trades have to be grouped until a trend emerges where each group tends to have a regular sort of amount at risk, eg 6% at risk for an entire bundle of trades. One way or another, I believe Kelly requires the user to specify how much is at risk (not merely how much to expose).

Quote from kut2k2:

You've pinpointed a key issue with Kelly sizing. You need to establish a trade distribution baseline. Once you have the baseline, you can test the Kelly sizing with the remainder of the trades in your backtest. There's no hard and fast rule on how long the baseline should be, but anything less than 20 trades is probably asking for trouble.

 

[joesan]

Yes, now I also believe the correct answer is b),according to the definition given by Ralph Vince.

Quote from trading1:

I believe the correct answer is (b). Kelly was derived with stakes where the entire amount would be won or lost. Also, the amount to expose in itself does not mean anything unless it's connected to an amount at risk, as in answer (b).

 

[ronblack]

Simplistic thinking.

I think you totally missed the point. Nobody spoke about "total risk control" but you. Obviously you mean something different by that than most of us here. I spoke of the normal risk control every trader exercises through position sizing. Kelly does fine if your system does fine. If you get an unexpected streak of losers, Kelly breaks down and risk is out of control. Your account is wiped out in that case, period.

Ron

Quote from kut2k2:

This is a common misconception with the Kelly fraction. Is there total risk control? No, total risk control would be to not trade at all. But if the Kelly fraction did not mitigate a lot of risk, there would be no maximization of returns. That's just a basic outcome of the mathematics. Despite ignorant claims by some, there is zero risk of ruin with the Kelly formula, and the remaining risk that is reduced by, say, half-Kelly sizing comes at a cost of taking twice as long to reach your same goal if you were full-Kelly sizing. A quarter-Kelly sizing would take four times as long.

TANSTAAFL

 

[kut2k2]

Quote from ronblack:

Simplistic thinking.

I think you totally missed the point. Nobody spoke about "total risk control" but you. Obviously you mean something different by that than most of us here. I spoke of the normal risk control every trader exercises through position sizing. Kelly does fine if your system does fine. If you get an unexpected streak of losers, Kelly breaks down and risk is out of control. Your account is wiped out in that case, period.

Ron

Yes, that is incredibly simplistic thinking on your part. If one gets a string of losers, the Kelly fraction (which is ridiculously easy to update) shrinks accordingly. That is, if you're smart enough to make it adaptive in the first place. Some people, on the other hand, never think ahead.