Kelly sizing...

Discussion in 'Trading' started by Eight, Sep 6, 2010.

  1. "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.""

    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
     
    #101     Nov 19, 2010
  2. ben111

    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
     
    #102     Nov 24, 2010
  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.
     
    #103     Nov 24, 2010
  4. ben111

    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 :)
     
    #104     Nov 24, 2010
  5. 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.
     
    #105     Nov 24, 2010
  6. bustermu

    bustermu

    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
     
    #106     Dec 7, 2010
  7. 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.
     
    #107     Dec 7, 2010
  8. #108     Dec 30, 2010
  9. +1 Best post on ET this year!
    (Or was it of last year??? Or even of the year before the year before that???)
     
    #109     Apr 12, 2013