Kelly sizing...

[fundjunkie]

"Frankly, I know nothing about Kelly's size and I have no interest in finding out.

As for you guys with all of your numeric specificity, you might do well to consider Sebastian Mallaby's words on page 231 of his book, More Money Than God: "The real lesson of LTCM's failure was not that its approach to risk was too simple. It was that all attempts to be precise about risk are unavoidably brittle.""

Quote from u21c3f6:

I disagree, here's why:

The fact of the matter is that LTCM's approach to risk was too simple because it did not account for all possibilities.

I''m fascinated by this reply to the above point. In it's earnest naivety it unwittingly reinforces rather than diminishes what is being said.


Thx
D

 

[ben111]

Hello,

I have a question about the Kelly formula and it's application.

Kelly% = P - [(1-P)/Ratio]

Now, if you have a trading system with the following measures:
Ratio (average win to average loss) = 1:3 = 0.33
Probability of win = 95%
Probability of a loss = 5%

=> Kelly% = 0.95 - 0.15 = 80%

But that doesn't mean that you can invest 80%! What's the Kelly fraction in this case that should be invested? (0.80/3??)

Thanks and regards

 

[jimbojim]

Quote from ben111:

But that doesn't mean that you can invest 80%! What's the Kelly fraction in this case that should be invested? (0.80/3??)

Yes, it means that if you want geometric equity growth you must risk 80% of your capital. For example, if you have 100K and you trade crude for 1 point stop per contract, you must open a position with 80 contracts. Obviouskly, with 100K you cannot do that so you have to settle with the amount you can afford and you grow proportionally.

If a stock trades at $200 and your stop is $10 per share then you must get 8000 shares. Obviously, this will cost you 1.6 Million so you have to get whatever you can, with 100K you can get 500 shares (no margin). You just risk 500 x $10 = $5000 this way or 5% rather than 80%.

I think this paper explains it well.

 

[ben111]

@jimbojim

Thanks for your reply.
I thought that perhaps the formula is only applicable for ratios of avg win to avg loss greater 1, cause all examples I found in the web were with rations >= 1.

Thanks for the paper. The example in the paper is also with a ratio >1

 

[intradaybill]

Quote from ben111:

I thought that perhaps the formula is only applicable for ratios of avg win to avg loss greater 1, cause all examples I found in the web were with rations >= 1.

Just look at the formula. As R grows big, %K approaches P, the win rate. Thus, R < 1 always gives fractions less than P. If R =1 then %K = 2P - 1 = 0.9 or 90%, even more.

 

[bustermu]

Quote from ben111:

I thought that perhaps the formula is only applicable for ratios of avg win to avg loss greater 1, cause all examples I found in the web were with ratios >= 1.

Thanks for the paper.

ben111,

The formula you presented,

Kelly% = P - (1-P)/Ratio,

is applicable only if:
i) there is only one value for a win,
ii) there is only one value for a loss and it is 1, and
iii) the formula yields a nonnegative value.

In order for the numerical example you gave to be a correct application, the only win value is 1/3 and the only loss value is 1. The proportion of equity (wealth) to invest (purchase stock) is 0.8.

The paper referenced is an example of an incorrect application of the formula.

The inequality:

Kelly# <= [P - (1-P)/Ratio]/L

holds where:

P = probability of win
Ratio = (average win)/(average loss)
L = average loss

The win and loss values are in proportions of the purchase price. For example, if the purchase price is $100 and the result is a $5 profit, the win value is 0.05.

Thanks,
Jim Murphy

 

[intradaybill]

Quote from bustermu:

The win and loss values are in proportions of the purchase price. For example, if the purchase price is $100 and the result is a $5 profit, the win value is 0.05.

No, that is incorrect. The average win should reflect the expected value of a winning trade in real terms. Gamblers call it the odds.

It is not the percentage of purchase price. Purchase price is irrelevant. Also, Kelly deals with expected values. Trades can have different values.

It is easy to check that the Kelly betting system results in gemometric growth.

 

[warrenmurdoch]

Has anyone read Thorp's new papers (2010) on Kelly? See www.edwardothorp.com.

 

[abattia]

Quote from Gabfly1:
... I confess that I don't know either the [...] or [...] formulas, nor do I care to find out. Each one invariably assumes an immediately stable probability distribution when, in fact, no legitimate probability distribution actually exists for the financial markets in real time. An ever changing frequency distribution of past behavior is a poor substitute if your intention is to get numerically specific. For my own limited purposes, I only rely on "the balance of probability," which invalidates overly precise fine-tuning and requires a sizable margin for error. That is the difference between true probability and uncertainty.

+1 Best post on ET this year!
(Or was it of last year??? Or even of the year before the year before that???)