Kelly formula is just for gamblers

Discussion in 'Trading' started by ronblack, Jul 11, 2007.

  1. ronblack


    I see often references in books and websites to the Kelly formula as a revelation regarding optimal risk. Recall that the formula is :

    Kelly = P - [(1-P)/R]


    Kelly= fraction of capital to be put into a single trade
    P = Historical winning ratio of a trading system
    R = Historical Average Win/Loss ratio

    I'm not sure if the above formula works for gamblers but it should be avoided by traders. Example:

    P = 0.80 (80% success rate)

    R = 1

    and Kelly % turns out to be 0.60 or 60%. This means that according to this gambler's formula the optimal bet size is 60% of available equity.

    Obviously, no sane traders would use this formula. Yet, some authors and websites promote this suicidal technique. Any comments?

  2. empee


    I dont understand whats insane about this (If the #s are right, I dont use this ratio).
  3. Your risk of ruin (RoR) in using full kelly (60% in the example you gave) will be pretty high (5% or more). Professional card counters, for blackjack, use kelly at lot, but they will use half or quarter kelly to ensure that thier RoR probabilities are extremely low.

    And the numbers you are using are pretty unrealistic for a trading system. If you are getting those numbers off of a historical simulation I'd be ware of using them in the kelly calculation.
  4. ronblack


    If you think those numbers (P = 0.8, R = 1) are unrealistic you have been missing a lot. These are my actual numbers based on real trading for the past 10 years. I have been able to maintain such performance because I risk way below what is suggested by the Kelly formula,, 1/10 or less.

    At any rate, use your own numbers. Anything you use produces excessive risk figures. Maybe that's good for gamblers but it seems this Kelly formula has no place in trading.

  5. gbos


    Kelly formula maximizes the median of your capital. It’s just an optimality criterion. It doesn’t ensure the drawdowns of your capital or ROR will be below your acceptance levels.

    In simple terms. Suppose 999 traders starts using a system with Kelly formula, and 999 traders follow an arbitrary different betting fraction for the same system. After some time you rank the traders of the first group according to their ending capital from 1 …. 500 …. 999. You do the same for the second group 1 …. 500 …. 999. Kelly formula makes it more likely that the 500th trader of the first group will be wealthier than the 500th trader of the second group.
  6. Just go back and see how much you would have made and your draw downs if you risked more... Its obviously a trade off with risk and reward but the best solution is whatever your comfortable with.

    So your risking like less than 60/10 = 6% of capital? Your not interpreting the kelly number as how much of your capital your risking right? If it comes out to be 60%, then you allocate 60% of your total bankroll to the trade, and it's not having a stop loss that will wipe out 60% of your equity. Just wondering because everyone talks about that 2% rule..."Never risk more than 2% of your capital on one trade". But they are talking about having an exit point when 2% of your total equity is lost on a given trade. Kelly is different from that....
  7. Murray Ruggiero

    Murray Ruggiero ET Sponsor

  8. The simplest and sanest thing to do is go to the site and look at the position sizing of the big funds. Its tiny. Each position is probably 1/100 of the kelly criterion and no more than 1/10 on the most liquid, low volatility stocks.
  9. ronblack


    I agree. This is the only way they can do it without removing too much liquidity from the market and thus increasing price volatility. Good point.

  10. ronblack


    #10     Jul 12, 2007