Kelly Criterion with Time

Discussion in 'Risk Management' started by LivingInVol, Feb 17, 2012.

  1. If you don't know what Kelly Criterion is:

    Essentially my question is: How do you convert kelly between bets that have different time frames?

    Let's say somehow you have figured out an edge in all the casino games...blackjack, roulette, sports betting, etc. Some games have a higher kelly bet than others. Given that these games take different amounts of time to pay off, meaning you can't do anything else with the money you've wagered, which do you choose?

    For example, let's say blackjack hands are dealt at 1 per minute and sports bets take one full day. If the kelly you've calculated is 10% for sports betting and only 1% for blackjack which would you rather play given that you can only do one. You've got a higher edge in sports betting, but you can only do it once while in blackjack you have a lower edge but can bet ever minute for a full 24 hours.

    Extrapolate to the financial markets... Day trading (small kelly, short timeframe) or long-term investing (large kelly, long time frame)? And yes, I know trading/investing is not that simplistic and so kelly won't really apply which is why I went with the casino example above.

    Thanks for your input.
  2. gmst


    for casino example, answer is obvious. Just calculate your end of day, week, month, year take using proper kelly on each game and play the game which maximizes your return at the end of time period.

    For real world trading, where you can't assume kelly - if you have to choose between multiple strategies, above approach will still work. Just that your objective function needs to have return as well as drawdown, recovery period etc. Question becomes much harder when you are trying to do multiple strategies that don't necessarily overlap but sometimes overlap.

    Say strat1 and strat2 - lets say trade signals overlap 30% of the time - Other than monte carlo, there is not much that you can do here - just run the simulations and decide on capital allocation to both strategies based on a proper objective function. Maybe linear programming can be applied, but I would rather do it in excel or some other software - basically i would focus more on empirical rather than maths here.

    When you are running 10 different strategies on same set of symbols, problem becomes exceedingly complex. I don't know what I would do in this case.
  3. It's good advice you have provided but I am looking for something formulaic. Maybe some numbers would help. I'm offering you two bets for a max of $1000 :

    A) You have calculated kelly on this to be 60%. But I only offer it once per year and it takes a year to know if you've won and get paid. You have to put up the $1000 immediately.

    B) You have calculated kelly to be 10%. I offer this 1000 times per year and payout is immediate if you win.

    I think Choice B provides for much better growth assuming all random processes are independent from one another.
  4. gmst


    ofcourse B would be better in almost all imaginable cases.

    Only negative case would be if your average win in 2nd case is much much smaller - say 0.01%. In that case maybe first case would be preferable.

    Again, getting to a formula would be tedious and I am not sure possible. A much more straightforward approach would be to start excel and run the numbers. Numbers will be for you to watch and see.

    For a theoretical/formulaic discussion, go through ralph vince work.
  5. Appreciate your help gmst. Quickly simulating it in excel does show some patterns. I'll have to figure it out over the weekend and follow up later. This ralph vince guy looks like he has some interesting stuff on his website too which I"ll have to check out. Thanks.
  6. In trading i call this subject, Position Time Managment.

    Means how to get the most out of your setups in a given time.


    You can do one trade a week on a higher timeframe.
    Or you can do three trades on a lower timeframes, a week.

    So lets say the risk for the one trade a week is 30%.
    Then i would say the risk of one of the tree shorter timeframe trades must be 10%.

    In other words, what you can achieve on average should be basically the same in your riskmanagment.

    What you do then in the end is up to your personal feeling.
    So much for this.

    NOW it becomes complicated, if you want to push it.....

    Position Switching Managment:

    Lets say you have found a shorter timeframe setup and it is ready to trade, while you also have a longer timeframe setup on the watch list, but the entry will likely be in one or two days.
    So you enter the shorter timeframe trade.

    Next day, your longer timeframe setup shows entry signals, while your current shorter timeframe trade is in good profits.

    So now, you can close the trade and switch to the longer timeframe trade.

    Next two days, the trade works and you are in good profits, around your minimum target. At the same time you have another shorter timeframe trade entry.

    Now, you can close the current trade and switch to the shorter timeframe trade.

    If you be always correct and if you always use the risk% from your intitial plan, you will make more, than if you just would do the one thing.

    If you increase the leverage after every winning trade you will maximize your profits, as much as possible.

    On the other side, you must allow the trades to reach a certain profit level, before you can switch to another setup, so that the risk/reward ratio of the trade is acceptable for the risk you have taken on.........
    But easy said: If you win, increase risk. If you lose, decrease risk.
    And if you lost, dont increase risk, until you have made back your lost money. If you keep losing, decrease it further.

    So your risk % managment is totally depending on your results....

    :p :p :p
  7. rvince99


    I cover this at length in "Risk-Opportunity Analysis," specifically Chapter 3.

    I'm not here to hustle the book -- I don't care how many copies sell or don't sell, and there's no publisher I am answerable to on it. I did it because I love working on things of this sort. -Ralph Vince
  8. We appreciate that but if you do not care how many copies you sell it would be better giving a link to a scanned copy of the chapter or you providing a summary of your method.

    I am sure other ET members will agree with me on this one. Even those I dissagree with on other issues.
  9. This is an allocation problem. You can solve it with the mean-variance method. You first calculate the expectancy and then multiply by the frequency to get the expected profit. Then optimize the allocation.

    What you have neglected is the covariance of the two methods.
  10. rvince99


    Why don't I put it up as a pdf for free? if thirty bucks is more than nothing, they really don't need to be reading what I have written.

    That sounds like the kind of lament the guys at the bar drinking the water, eating the popcorn say about "the girls at that table," being "too stuck up."

    -Ralph Vince
    #10     Feb 19, 2012