The Kelly criterion - is it good...or bad?

Discussion in 'Risk Management' started by thenmmm, Nov 25, 2010.

  1. thenmmm


    Anyone trying to use it in sense? Actually, is it the optimal money management? I've read recently that using the square root of your capital and not the log will be optimal? I have some ideas as to "why" - but in any case...the KC needs the probability and the exact payoff to be known in advance and not to be changed over time - which is very hard.

  2. kc usually the last refuge of someone with no chance of making a profit
  3. It is kinda dumb. Its a bit like a cab driver asking if the speed limit will help him attract more customers...

    That being said:

    You would need statistical information for the distribution of your trades payoffs and losses. This would effect the optimal bet size that kelly C would return.

    You would need to consider the relationship of other bets (or signals) to each other if their is a mathematical relationship.

    and you would need to know your max pain - what is the max loss for the whole portfolio during a situation where the Market goes against you in an episode of risk aversion or some other highly correlated event....

    People like Ralph Vince are working on a more advanced version of something like KC called the leverage space model. It attempts to address the issues of the distribution of trade payoffs and their correlation in the portfolio. They also attempt to understand the optimal position size as the positions in the portfolio change continuously because price is changing continuously.... but for me its very theoretical and a work in progress for their model.
  4. thenmmm


    I guess what he tries to address is namely the margin - that can lose more than your initial "bet", something the kc has been criticized on.

    Anyway, some time year or 2 - I was KIND OF obsessed with the criterion, partly because it was advertised heavily by Ed Thorp and because when I decided to backtest the KC on a simple computer model of "monte carlo" games - it turned out to be indeed optimal. Basically, I don't want to sound as I am bragin' or something, so i won't post the computer code and mathematical formulas during my "kelly criterion hype", but you can see what I've written here in wilmott...some time ago:

    This gives (I dare to say...) a very good background on Kelly + 2 simple programs that I have written.

    Anyway...the issue remains the same:

    1. You need to know your maximum payoff - in other words when you buy a stock or an option the maximum is in theory...unlimited. Which is...NOT for kelly.

    2. You need to know the probability of winning:
    OK, here the KC behaves better, because let's face can't even enter a trade unless you have some pretty good idea of your chances of winning.

    3. The odds shouldn't change:
    Now this is a problem - for instance...suppose you buy a stock hoping to win with payoff win - and then you decide to buy again and estimate your payoff of 10% - according to the kelly criterion such situation can lead to ruin...why? See the so called 'Proebstring paradox' for explanation.

    Basically, in order for a money management system to be successfull a few things should be designed, which the KC lacks:

    1. Make the system multidimensional: In other words - the system must hold even if the odds change when you open and close positions over and over again...

    2. Is the log optimal? Again...according to some financial professor that I read online - the Log function (kelly criterion) is not optimal because it assumes that MOST of the time you will be richer - but if you bet less than kelly - then not most of the time...but at some point of time you will be much, much richer than a kelly investor and hence you can stop and remain richer - which is the right thing to do.

    3. Make the system deal with margin and hedging - in other words...the system must tell you how much you need to invest given a loss over your initial 'bet' and it must tell you how much to bet given hedging (e.q. - you have bought a put option or set a stop loss order).

    So these are just my 2 cents - the KC has many disadvantages. For (at least an attempt) on how to use the kc in the stock market, you can read this paper by Thorp: "The kelly criterion in coin tossing, blackjack and the stock market".
  5. u21c3f6


    Calling Kelly dumb is like calling a hammer dumb when you are trying to cut a board into two pieces. Yes you can take some whacks at the board and may in fact get the board into two pieces but probably not with the best results. The right tool for the right job.

    You cannot apply Kelly properly if your trading does not allow for you to quantify your inputs fairly accurately. If however you have a trading set-up that has a fairly accurate win% and you know your risk to reward, you can use Kelly fairly easily or as I would recommend, half-Kelly.

  6. Kelly is optimal in the geometric growth sense. Optimal is like "love". It means different things to different people.

    Square root of capital is optimal in some other sense, who knows? Maybe quadratic or something?

    This paper explains %Kelly for beginners:
  7. William Eckhardt: "Trading size is one aspect you don't want to optimize. The optimum comes just before the precipice."
  8. Ernie Chan has a post on his blog about how to calculate the Kelly Criterion for continuous payoffs like equity/commodity markets, as opposed to fixed-odds payoffs like betting (I'm not using the exact terms b/c I don't want to go look up the post, but it's there). Ernie's number ends up being a leverage number, rather than a percentage. A high Kelly percentage would equate to a high leverage number, so the relationship between the two calculations is very intuitively clear.

    From reading the replies, I sense that people believe there is 1 single Kelly number for your trading strategy and that's it. I recalculate Kelly after every trade and then use that number as the Kelly for the next trade. You could also do a "rolling Kelly" calculation and take the smaller of the two numbers (your Kelly for all trades vs. your Kelly for X-number of trades). If there is any correlation between your trade outcomes, that would enable you to bet more than the overall Kelly when your method is more in synch with the market and less at other times. Or, you could bet the average of all the calculations. You could figure out different Kelly numbers for different set-ups, etc. The possibilities are limited only by the amount of data you collect and your own imagination in how to use it.

    Once you get used to the volatility of trading with Kelly, I think it is a very good approximation of the right amount to put at-risk on each trade. In fact, if you automate your trading and money management, you'd never even have to see the volatility. Just figure out the appropriate amount of time to allow to elapse between checking in on your account balance and let the automation do its work in the meantime.
  9. Relatively slow day in the markets, so I went back and looked for the link.
  10. nitro


    #10     May 17, 2013