Article / 14 September 2016 at 13:00 GMT

Applying zero-sum games to a trading strategy

Hypothesis Testing
United Kingdom
  • Using zero-sum games can help a trading strategy
  • A price breakout strategy relies on a single directional trade

  • Casinos use zero-sum strategies to skew odds in their favour

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Zero-sum games can enhance a trading strategy. Photo: iStock


By fxtime*

First let's consider a very simplistic trade model.

Using the 9-10am trading range of the spot cable market (GBPUSD) we can trade the price break out seeking 5+ pips net.

The ticket spread will determine how far the spot mid price must move before your trade opens. A spread of 1.8 pips implies you open a trade 2.3 pips above/below the trade range before entering a trade. The success rate is 90%.

Before you rush off and commit to the trade we must also consider stops...plus deal costs etc.

Cable, EURUSD and USDCAD are interesting FX pairings as they all have the same optimum stop. There is a level of price movement that, should the market move by 45 pips in one direction, then there is a greater probability value that the market will indeed continue further in that direction where as below 45 is what is known as ''noise'' — an area of natural vibration/oscillation that is statistically directionless.

Thus lets go back to the original strategy above.

A 90% success rate sounds great for net 5+ pips profit each day. But using the optimum stop value gives an interesting conundrum. If we measure 10 consecutive trades on a 90% success rate we get the following:

Nine successful trades totalling 9 x 5 pips = 45 pips profit and the optimum stop should of course be 45 pips.

Now we have a zero-sum trade scenario. We know over time that every point/pip profit we make will be totally lost.

Maybe we can consider a means of taking advantage of this zero-sum balance. We know that a break beyond 45 pips implies a continued move in that direction. Therefore a 46-pip move follows that trade direction. Probability implies a further 12-pip minimum move using the same stop value.

Also we know the 9-10am trading range strategy is a price breakout strategy so if the trading range you are measuring is in excess of 45 pips, do not enter that trade as empirically the trade is against you. Conversely a trade range below 45 pips is far more favourable.
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Cause and effect. Photo: iStock

For example, if the trade range was say 30 pips then make your stop that amount. After all a price breakout strategy relies on a single directional trade. Consequently your risk is reduced but the probability of success remains.

Using the original example:

  • 90% success on 10 trades is really 9 trades x 5 pips = 45-pip profit
  • One bad trade with a 30 pip stop means we are still 15+ pips in profit
  • Should the market continue moving beyond the stop and the 45-pip value, then you would expect to earn a further 12 pips
  • The result is a 27 pips net profit overall

As a poor student when studying for my degree, I worked in a casino and came across zero-sum strategies as used by casinos. If you look at the roulette table, you can wager on red or black numbers and would expect a 50/50 chance but in truth it isn't because the zero number is green.

American roulette tables are slightly different as they have two green number slots. This is because it introduces skew to a game of chance. They are taking advantage of a mathematical fundamental called The Law of Large Numbers.

Equally card players playing Black Jack etc were often using statistics and counting high value cards used by other players and the ''House'' to establish what other cards were available. However casinos started to use two decks of cards always having in play a 52 rolling supply of playing cards at any given time to eliminate conditional probability card players and introduce a skew in favour of the casino. The element of chance remained static for the player but the element of risk dropped for the casino. This is a zero-sum advantageous game play.

There is a plethora of permutations you can play in forex and mainstream indices using these theorems which consider a three-month timeframe as a reference value and determine how many trades are required to break even only, then introduce skew (really known as a Kurtosis Skew) to the trade to be more beneficial/profitable whilst seeking the worst-case parameter such as a stop maximum level as a reversal point and an individual trade structure in its own right.

As I have no reliable broadband and charting at present due to maintenance work in my area I will post real-time charts later in the week to show the workings of the above. Hopefully, however, this makes some sense?
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Glitz and glamour are not the only tricks used by casinos. Photo: iStock


— Edited by Martin O'Rourke

*fxtime is an alias
14 September
fxtime fxtime
as promised...a screen grab of the cable for today and yesterday....both worked easilly enough and I had the opportunity of using a tighter stop as the triggering range is below the optimum zero sum value which makes the trade more efficient.
14 September
fxtime fxtime
Now the eurusd...same time frame and again the stops were tighter which makes the trade more efficient. Three trades done all successful.
14 September
fxtime fxtime
Now the usdcad....I have posted the time frame many times before. We trade from the 11 - 12noon BST trading range. Again we seek at least +5 based on the zero sum game and once again the trade is more efficient as the stops were less than half the optimum stop/zero sum level.
14 September
Qi2 Qi2
Different time stamp on GBPUSD than USDCAD in the set up?
14 September
fxtime fxtime
Yeah the usdcad is illiquid when the others are traded so I await the ideal time frame. Each 1hr and 30min candles are backtested using python models that backtest bid/ask prices over the last olling 7yrs to see which gives the highest confidence level statistically and that happens to be the loons ideal time stamp. After which I look for reasons why it should occur and the best reason that consistently appears is that there is a price fixing point at that time frame for re-valuing usdcad.
14 September
fxtime fxtime
Qi2....note that the usdcad is literally a zero sum as per the others....the stop amendment is what introduces a skew that benefits the trade scenario.
14 September
fxtime fxtime
Typo above....olling 7 yrs = rolling 7 yrs
14 September
Michael O'Neill Michael O'Neill
I know for a fact that FXtimesUSDCAD strategy works
15 September
Qi2 Qi2
I have employed fxtime's EURGBP strategy manually, works well, currently having it coded for automation :). I will have to tryout the USDCAD strategy, always nice to add to the earnings!
15 September
kom75 kom75
So far this week, I've got 28,1 pips for all 3 USDCAD strategies, would be better but on Monday I lost around 40 pips. Bottom point strategies earn:)
15 September
kom75 kom75
Qi2 what stamp point do you use for EURGBP? Although it's illiquite time strategy for some reason I found it better working with 6-7 BST stamp point. I trade it from about 2 months, so it's not a rolling 7 years data LOL
15 September
fxtime fxtime
kom...your comment on the time stamp is true but that is a recent aberration. The six month data supports your findings but the longer term is slightly out (as you say). Bad news with the losses but these are underlying strategies that post over a period of time an underlying profit trend :-)
15 September
kom75 kom75
fxtime, I'm used to losses and don't cry over them LOL. Thanks for all your contribution, which helped me improve my trading
15 September
fxtime fxtime
Eurusd and cable both worked today....usdcad didn't and incurred a 16pip loss but as mentioned above a failed zero sum implies 12 pip minimum on the contrarian trade which did occur.
15 September
fxtime fxtime
I have just checked my accts and I need to correct the comment on the cable as a stop of 26pips was hit and the opposing stop order regained +12....apologies for the error.
15 September
Qi2 Qi2
kom75, as I live on the west coast of Canada, its hard to find a timeframe to trade currencies, non the less I set up my EURGBP model to start at 3:00 PM BST and trade until 5:00PM BST. It executes a trade between 3:30 BST and 4:30BST. Today however I have decided to try a 2:30 BST time stamp as that is US market open and it will trade in European market close.
15 September
Qi2 Qi2
Todays EURGBP trade, timestamp for range was 2:30 to 3:30 BST, trade set up was long EURGBP at 0.8515 target was 10 pips, but trade closed at 0.8520, due to M5 candle close. The trade system calculate ROC of pips per second, calculating them every 5 seconds, staying with the entry trade rule, that was executed (based on the 6 lines or rules) for 5 minutes and in this case the ROC on the 3:55 BST candle dropped from a high of 0.8525 to 0.8520 during 5 second ROC calculations.
15 September
kom75 kom75
Fxtime, is your 12 pips contrarian trade valid only for cad, euro and cable or for audusd (10am), usdjpy and usdchf (both 12pm stamp point) as well?
15 September
fxtime fxtime
A failed zero sum trade always seeks 12pips min on the contrarian trade
15 September
kom75 kom75
But are audusd, usdchf and usdjpy zero sum trade? With same sl 45 pips?
15 September
fxtime fxtime
Not if the trading range is below 45pips then adjust your stop to be equal to the trading range plus your trade ticket spread.....I am not near my main computer systems so can't send a chart however to skew the zero sum trades into your advantage of a period of time then tighten the stops if the trade range is below he 45 pips.
15 September
fxtime fxtime
Qi2 I am impressed with your results....it isn't a time frame I normally employ but certainly effective :-)
15 September
kom75 kom75
Thanks a lot:)
16 September
Qi2 Qi2
fxtime, there seems to be one trade available in this time frame, which is a bit risky, as it's going into London fix. However, that is also what allows the faster ROC to play out, as GBP generally moves faster than EUR, so the pips typically are earned in 2 or 3 M5 bars :) hence the 5 second calculation rate..
16 September
fxtime fxtime
I see what you are getting at and am currently testing that idea now ....will get back to you asap.
16 September
Qi2 Qi2
Same EURGBP set up as yesterday, range is set 1:30PM GMT to 2:30 PM GMT, trade trigger long at 1:45 0.85272 and ran up to 0.85393, so a 10 pip TP would have been hit, but the way my algo calculates, I closed on the pull back at 0.85361.
18 September
zefy zefy
After working a bit more with the example given in the article, I can say it is a brilliant example how to affect to skew in your trading system and can be utilized really to different kind of trading system implementations!
18 September
Qi2 Qi2
@fxtime, sent you a theorem of sorts :)
19 September
fxtime fxtime
Qi2 the email didn't work as I have a lot of computer symbols only showing where as other emails are fine....can you resend mate? Highly recommend retirement mate....you trade for yourself with no client pressures LOL
19 September
fxtime fxtime
Zefy thanks for your commentary and I assume you made on the cable move today ? :-)
19 September
fxtime fxtime
Zefy chart attached ref reversed zero sum game on cable
19 September
zefy zefy
Yeah, got it. I will start run it live today afternoon. Good stuff!
19 September
Qi2 Qi2
fxtime, I sent the email, attached a pdf
19 September
fxtime fxtime
Yeah have received and responded with a few queries on settings....I liked the process however as I am in the City of Bath at present and in a Betty Lunns tea shop writing an alternative stochastic on a napkin to test out as a control for you !! The trouble being the napkins are small and my lousy writing isn't LOL. I am intrigued to know your outcomes and will typeset the ''control'' later and forward for you to consider if you so wish :-)
19 September
Qi2 Qi2
Wonderful, I look forward to seeing the write up. I am striving to work out the timestamp details on my EURGBP set up, still having issues with trading to often due to ROC changes, which are not tied to the time stamp.
20 September
fxtime fxtime
Qi2...I am on the road home now but what you forwarded could be done with a markov Chain using fast stochs and it would give similar outcomes but I still prefer an adjusted std dev on the orginal permutation of yours. A normal distrib pattern is 68% for 1st std dev and 98% for the second obviously but if you traded an adaptive such as kurtosis skew the shallow slope side of the curve intersects usually at the 27% value eg 0.27 and completes fractionally earlier at 0.48 value. All straightforward I know BUT you can applly as a band formation too eg similar to your theorem and the skew will then work to your advantage faster imho.
20 September
fxtime fxtime
Zefy...again on cable :-) For the price break out (above) and the 45pip scenario etc
20 September
Qi2 Qi2
Thanks fxtime, I have read about Markov, but never run a model, will put it on the "to do" list :)
22 September
zefy zefy
Yeah, cable 12 pips banked. Good stuff!
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