Kelly-betting for FX trading

  • matt21

    Kelly-betting for FX trading

    I have a question regarding position sizing for trading the FX markets. If the moderators think it’s more appropriate for this to be posted in another section, please do move the thread.

    In my AP play I have been using the Kelly principle in determining how much to bet with various levels of edge and payoff. I have been using the formula of Edge%/Paypoff to determine the ratio of my BR that I should wager. Given warnings from established full-time gambling pros that AP’s tend to overestimate their edge and to avoid the rollercoaster rides of full-Kelly betting I generally aim for half-Kelly bets.

    As well as being an AP, I also speculate/trade in the FX markets, and am now trying to apply the Kelly theory to determine how much I should risk per trade. Many serious retail traders opt for risking no more than 1% of their BR per trade. I have one trading strategy which has been working quite well, in fact so well that I am heavily discounting the win rates in order to address the position size issue.

    Assume therefore (conservatively) that there is a trading strategy – that creates 45% winners, 10% break-even and 45% losers. Losing trades result in a $1 loss. Winning trades result in a $1.30 gain [after all transaction costs]. This creates an EV of 13.5% per trade. This should be a very respectable edge for any AP. The other beauty here is that I have this edge every time that I have a setup that meets my requirements. When I dont have the setup then I dont trade. This is one major difference to my AP playing – I dont have any waiting bets in my FX trading. Though I might only have a half a dozen such opportunities per month.

    Putting that into the Kelly formula we get 13.5%/1.3 = 10.38% implying that a full-size Kelly bet should be 10.38% of the BR. Half-Kelly would be 5.19% and quarter-Kelly would be 2.6%. At the moment I am only risking 1% per trade.

    One argument that traders use for restricting themselves to 1% per trade is that it is psychologically difficult to see your BR decrease if you have several consecutive losing trades. However, I am quite used to psychologically deal with wins and losses from my AP experiences, so it seems that this reason shouldn’t apply to me?

    I am wondering whether anyone can comment as to whether it seems I should be increasing the amount I risk per trade? Is it wrong to apply the Kelly approach in this context? Also whether I have made any errors in my calculations?

  • MangoJ

     

    Quote: matt21 said:
    Assume therefore (conservatively) that there is a trading strategy – that creates 45% winners, 10% break-even and 45% losers. Losing trades result in a $1 loss. Winning trades result in a $1.30 gain [after all transaction costs]. This creates an EV of 13.5% per trade.

    If you want to Kelly bet, you better know your edge, not assume something how the market will react. I’m sure you’re doing well in normal days, but the single crisis is what will kill you.

    Advantage play is something different, where you do know exactly what you’re doing (at least you are supposed to). APs don’t play games with unknown rules, or rules that are subject to change without notice (as in the crisis).

  • Midwestern

     

    matt,

    please remember that kelly sizing for trades represents a profit-maximizing strategy. this says nothing about the portfolio’s volatility in regards to its size (you’ll see VaR, or Value at Risk, as well as the Sharpe Ratio, as the main statistics in this regard). Many traders size their trades much smaller than Kelly because they want their portfolio to have a lower volatility of returns.

    if your particular trading strategy consistently yields these profit statistics, i wouldnt change a thing. Why? because this is your portfolio and the only person you are growing it for is yourself. i.e. no one will sweat the swings but you. HEDGE FUNDS out there have to worry about the public’s perception about their performance and volatility. obviously they don’t want their returns swinging +/- on a daily basis , so they under-size their trades relative to the size of their portfolio to give the portfolio an air of consistency.

    its up to you and your risk tolerance, but if i found something with a 13% edge, id be betting the max kelly amount on my portfolio every darn time.

  • zengrifter

     

    Cannot accurately apply Kelly UNLESS you know your advantage BEFORE you bet. zg

  • matt21

     

    MangoJ I think you make a good point. Though my trading strategy is very short term – the strategy in question has trade durations from 30min to several hours and the European and US markets are sleeping (well mostly) at the time that I apply the strategy. A crisis would be even less likely to occur during this time, but yes it still could.

    Midwestern – agreed. Large hedge funds could not ‘afford’ to have high volatility in their returns, as they would then probably struggle to attract investors. I think this is one of the advantages that small traders have over deep-pocketed players.

    Yes the trouble is that with the markets you can only use empirical and testing results as guidance for potential results, whereas with most AP strategies one should be able to precisely calculate the theoretical return and associated volatility.

    Having thought about it, I have decided to gradually increase my risk per position (on established strategies) from 1% to 2.5%. Yes this will increase the volatility but if my win rates and Win:Loss ratio hold, then over 6-12 months I will also increase my net return by a factor of 2.5. Even with 2.5% risk I should theoretically still be way underbetting/undertrading my BR. The only reason why I questioned the 1% rule of thumb is thanks to the AP experiences that I ahve collected. Maybe that’s where being AP provides additional insight to being a trader in the financial markets.

  • blackriver

     

    i think 2.5 is ok, but very aggro. i would deff not go further. people cite buffet as an excuse when they want to approach their kellys but day traing is almost always different than long term value investing where you arent really concerned about public opinion in making you decisions, but day traders should mostly focus on public opinion.

    also i assume you get that everyone is referring to black swans. yours and most strategies dont take into account the 1-1000 chance of losing 50% on some bet because of a maket frenzy of some sort. i suggest reading a lot of iscouraging stroies then betting around 2%.

    does your strategy somehow not show any differences between trades? if you can estimate stronger certainty with some trades than others maybe you can bet 2.5% on you best trade per month, 2% on the next 2, 1.5% on the next 2, and 1% on your least certain trades. then keep a record of how your tades do over a year. maybe you will not even make your least certain trades but can bet 3-4%on your best trades, etc

  • blackjack avenger

    I Agree

    Quote: zengrifter said:
    Cannot accurately apply Kelly UNLESS you know your advantage BEFORE you bet. zg

    As one is less certain of their advantage they should be more conservative, as is the case with market trading.

    example:
    half kelly blackjack bank
    3rd or 4th kelly market trading bank

    For certainty of growth 4th through 8th kelly is very strong.

    Also, should be considered one bank for all games/investments.

  • blackjack avenger

    Like it

    Quote: blackriver said:
    does your strategy somehow not show any differences between trades? if you can estimate stronger certainty with some trades than others maybe you can bet 2.5% on you best trade per month, 2% on the next 2, 1.5% on the next 2, and 1% on your least certain trades. then keep a record of how your tades do over a year. maybe you will not even make your least certain trades but can bet 3-4%on your best trades, etc

    I like this, I think you would have to use models vs real results because in the real world one would have a limited number of trades for comparisons.

  • matt21

     

    Quote: blackjack avenger said:
    As one is less certain of their advantage they should be more conservative, as is the case with market trading.

    example:
    half kelly blackjack bank
    3rd or 4th kelly market trading bank

    For certainty of growth 4th through 8th kelly is very strong.

    Also, should be considered one bank for all games/investments.

    Can you clarify what you mean by “3rd or 4th Kelly” and “4th through 8th Kelly”?

    I think your other point is dead on – I consider myself to have one single BR that is used for AP and trading simultaneously.

  • MangoJ

     

    I guess he means 1/3 or 1/4 of kelly.

    A martingale player claims he has an edge of 1% from his strategy, based on past performance (several hundred “trades”). How much should he bet for kelly betting ?

  • blackjack avenger

    Lost in Translation?

    Quote: matt21 said:
    Can you clarify what you mean by “3rd or 4th Kelly” and “4th through 8th Kelly”?

    I think your other point is dead on – I consider myself to have one single BR that is used for AP and trading simultaneously.

    3rd kelly = .33 kelly = 1/3 kelly
    4th kelly = .25 kelly = 1/4 kelly

    5th = 1/5 kelly
    6th = 1/6 kelly
    7th = 1/7 kelly
    8th = 1/8 kelly

    or is my terminology wrong?

  • matt21

     

    bump.

    I have a follow-up question here. I started this thread off with reference to the Kelly formula that states that the amount to be wagered on a bet or trade should be calculated by: Edge% / Odds. In this case odds refer to the amount of a winning payoff. Thus the higher the payoff (and thus the higher the variance) the lower the fraction of the BR that should be wagered.

    What happens in the situation where the win result is less than a loss result? For example, a FX trading strategy that results mostly in winning trades of $10 and few losing trades of $50. The win rate is 90%, thus the edge per trade is $4 (90% x $10 + 10% x -$50) or 8% ($4/$50).

    The win pay-off is equal to 0.2 of a loser – surely it would be wrong to divide 8% by 0.2, and then bet 40% of the bankroll?

    It would be great if somebody could shed some light on this for me.
    I am currently dealing with an FX strategy where I encounter this situation a lot, and am not sure how much to risk per trade using a fractional Kelly approach.

  • DDutton

     

    Quote: matt21 said:
    I have a question regarding position sizing for trading the FX markets. If the moderators think it’s more appropriate for this to be posted in another section, please do move the thread.

    In my AP play I have been using the Kelly principle in determining how much to bet with various levels of edge and payoff. I have been using the formula of Edge%/Paypoff to determine the ratio of my BR that I should wager. Given warnings from established full-time gambling pros that AP’s tend to overestimate their edge and to avoid the rollercoaster rides of full-Kelly betting I generally aim for half-Kelly bets.

    As well as being an AP, I also speculate/trade in the FX markets, and am now trying to apply the Kelly theory to determine how much I should risk per trade. Many serious retail traders opt for risking no more than 1% of their BR per trade. I have one trading strategy which has been working quite well, in fact so well that I am heavily discounting the win rates in order to address the position size issue.

    Assume therefore (conservatively) that there is a trading strategy – that creates 45% winners, 10% break-even and 45% losers. Losing trades result in a $1 loss. Winning trades result in a $1.30 gain [after all transaction costs]. This creates an EV of 13.5% per trade. This should be a very respectable edge for any AP. The other beauty here is that I have this edge every time that I have a setup that meets my requirements. When I dont have the setup then I dont trade. This is one major difference to my AP playing – I dont have any waiting bets in my FX trading. Though I might only have a half a dozen such opportunities per month.

    Putting that into the Kelly formula we get 13.5%/1.3 = 10.38% implying that a full-size Kelly bet should be 10.38% of the BR. Half-Kelly would be 5.19% and quarter-Kelly would be 2.6%. At the moment I am only risking 1% per trade.

    How can one apply Kelly without a reasonable degree of confidence in what the +EV is?

  • matt21

     

    Quote: DDutton said:
    How can one apply Kelly without a reasonable degree of confidence in what the +EV is?

    Hey DDutton, I am assuming that I know what the +EV is. I need to do that in order to ask the question. You are of course right in pointing out that with the FX markets the probabilities are not certain as they are in casino games.

  • blackjack avenger

    conservative

    Bj bank 1/4 Kelly
    Fx bank 1/6 Kelly, because of uncertainty
    The above may balance the 2 investments.

    How important is it to know exact advantage when being this conservative? I would think not much. It’s one of the reasons we bet a fraction of Kelly, because of uncertainty.

    Consider this:
    An investment/game with an advantage of 1%.
    Player A thinks its a .5% advantage
    Player B thinks its a 2.25% advantage
    They both bet 1/6 Kelly based on their perceived advantage.
    Throw in a lot of variance. Both will be fine because they were conservative.

    If player B had bet full Kelly, he would experience bank decline.

    Also, being conservative allows one to have a low N0 because they don’t have to resize bank down on losses as frequently.

    Never be afraid of being conservative.

  • Thunder

     

    Quote: blackjack avenger said:
    Bj bank 1/4 Kelly
    Fx bank 1/6 Kelly, because of uncertainty
    The above may balance the 2 investments.

    How important is it to know exact advantage when being this conservative? I would think not much. It’s one of the reasons we bet a fraction of Kelly, because of uncertainty.

    Consider this:
    An investment/game with an advantage of 1%.
    Player A thinks its a .5% advantage
    Player B thinks its a 2.25% advantage
    They both bet 1/6 Kelly based on their perceived advantage.
    Throw in a lot of variance. Both will be fine because they were conservative.

    If player B had bet full Kelly, he would experience bank decline.

    Also, being conservative allows one to have a low N0 because they don’t have to resize bank down on losses as frequently.

    Never be afraid of being conservative.

    I’d go with 1/3 but this is just me. How many trades have you had so far to lead you to thinking that you win 90% of them and lose 10%?

  • matt21

     

    Quote: Thunder said:
    I’d go with 1/3 but this is just me. How many trades have you had so far to lead you to thinking that you win 90% of them and lose 10%?

    Hey Thunder. Again I wanted to proceed on the assumption that the win rate, and the EV, is known. What I was perplexed about is how to apply the Kelly formula – I have tried to explain my confusion in the post above.

    Any thoughts?

  • Thunder

     

    Well if you have $1000 let’s say, in that scenario, you’d want to risk 40% of your bankroll so that the maximum loss you’d have is $400 while the max gain would be $80. This would be full Kelly. Your bankroll will grow at a rate of 1.82% per trade. The difference between this and having a trading system where you win 70% of the time and lose 30% of the time (but the loss amount equals the win amounts) is that in the 70/30 trading system, you don’t have these huge drawdowns which essentially kill any growth in your bankroll.

    This page might further help.. http://www.1stmillionat33.com/2006/04/kelly-criterion-for-stock-trading-size/

  • blackjack avenger

    overcomimg variance

    One should be able to overcome (edit MANAGE) variance in a tough game/trade if they bet conservatively. In Thunders $400 bet example, make it $100 or $40.

  • zengrifter

     

    Quote: blackjack avenger said:
    As one is less certain of their advantage they should be more conservative, as is the case with market trading.

    But how certain can you be? zg

  • zengrifter

     

    Quote: Thunder said:
    Well if you have $1000 let’s say, in that scenario, you’d want to risk 40% of your bankroll so that the maximum loss you’d have is $400 while the max gain would be $80. This would be full Kelly. Your bankroll will grow at a rate of 1.82% per trade. The difference between this and having a trading system where you win 70% of the time and lose 30% of the time (but the loss amount equals the win amounts) is that in the 70/30 trading system, you don’t have these huge drawdowns which essentially kill any growth in your bankroll.

    Say what? zg

  • zengrifter

     

    Quote: blackjack avenger said:
    One should be able to overcome variance in a tough game/trade if they bet conservatively. In Thunders $400 bet example, make it $100 or $40.

    Huh? Come again??

  • Thunder

     

    Quote: blackjack avenger said:
    One should be able to overcome variance in a tough game/trade if they bet conservatively. In Thunders $400 bet example, make it $100 or $40.

    With all due respect, betting more conservatively won’t overcome variance. What it will do is lower the risk of ruin at a cost to the growth of your bankroll.

  • Thunder

     

    Quote: zengrifter said:
    Say what? zg

    Which part didn’t you understand?

  • blackjack avenger

    overstayef

    Quote: Thunder said:
    With all due respect, betting more conservatively won’t overcome variance. What it will do is lower the risk of ruin at a cost to the growth of your bankroll.

    Agree “overcome variance” was to strong a term, perhaps manage is better. I also agree with your statement.
    However,
    Bank growth “Kelly” should not be the only consideration. You, yourself recommended 1/3 Kelly. In this example of high variance & uncertain edge (as Zengrifter keeps needing lol) betting conservatively can greatly increase the probability of growth, even if we overestimate our edge.

    In bj Kelly long run numbers are staggering! As I am sure you know

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