Z-Score to improve strategies
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I am posting my version of the code to calculate Z-Score and manage it, in order to embed it into your strategies. It also comes with a simple test strategy.
What is Z-score?
Z-score measures the distance between the mean of some set of the statistical results and the given observation.
A trader might suspect a dependency if he or she experiences a run of several consecutive profitable trades, or a run of several consecutive unprofitable trades. “Obviously, there was some kind of dependency or serial correlation among your trades [in this case], where winners were followed by winners and losers were followed by more losers,” Thomas Stridsman wrote in the April 1998 issue of Futures. “If this happens again, you’ll want to exploit the good times and perhaps avoid trading altogether in bad times.”
In Forex systems, traders are interested in Z-score not of a trade’s return (profit/loss size) but rather in a Z-score of the outcome — was it a profitable one or a losing one?
Z-score, calculated using winning and losing streaks, measures the dependence between the outcome of the previous position and the outcome of the next position.
If we consider profitable positions as positive results and losing positions as negative statistical results, counting the total number of all wins, losses, overall trades, as well as the number of win and loss streaks, we can calculate a Z-score for a given
trading strategy.
Usually, Z-score fluctuates between -3 to +3, but sometimes, can go above and below these “limits”. A Z-score value of 0 means that we are dealing with completely random results.
Each Z-score value has also a probability of dependence (P) associated with it, which informs us of how probable dependence between the trades is. P values below -2 and above +2 have high (>95%) probability of dependence between trades:
- a positive Z-score means that:
– a profitable position is likely to be followed by a losing one
– a losing position should probably be followed by a winning one.
Basically, it means that the probability of long winning and losing - a negative Z-score means that:
– profitable positions are likely to be followed by more profitable positions
– losing positions are to be followed by more losing positions.
Basically, it means that winning or losing streaks are probable.
It should also be noted that Z-score calculation makes sense only for sufficiently
large samples. Math literature suggests a sample size of no less than 51 (some talk about 30) to get a reliable Z-score value.
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////Z-Score (code)////The results can be INCORRECT when, on the SAME bar, the following 3 conditions are met://// 1) a trade is closed// 2) a new trade is opened (usually due to a Stop & Reverse)// 3) the new trade hits TP////Furthermore, optimization should be avoided when accumulating positions, unless it's//possible to consider all of them as one.////(streaks)-https://www.forextraders.com/forex-education/forex-money-management/using-the-z-score-to-determine-trade-size///(streaks)-https://www.earnforex.com/guides/z-score-optimization-in-forex-trading/////(runs) -https://www.mypivots.com/dictionary/definition/233/z-score//(runs) -https://www.referenceforbusiness.com/encyclopedia/Val-Z/Z-Score.html//// Counting STREAKS (+ are Winning trades - are Losing trades)////trades: +-++--++-----+---+++- (21 trades)//tally: 1 2 3 4 5 6 (6 streaks) a STREAK is a TWIN pair followed// by a different sign////// Counting RUNS (+ are Winning trades - are Losing trades)////trades: +-++--++-----+---+++- (21 trades)//tally: 12 3 4 5 67 8 9 (9 runs) a RUN is any sign followed// by a different sign//// --- start of Z-Score codeONCE Periods = 0ONCE Streaks = 0ONCE CurTrade = 0ONCE TotalWin = 0ONCE TotalLose = 0Periods = Periods + 1MyProfit = StrategyProfit// tally Total winning + losing streaks (streak = consecutive winning or losing trades)IF MyProfit <> MyProfit[1] AND (BarIndex > 0) THENIF MyProfit > MyProfit[1] THENCurTrade = 1ELSIF MyProfit < MyProfit[1] THENCurTrade = -1ENDIF//---------------------------------------------------------------------------------// code using STREAKS (it seems to be returning only negative values)// (a sign change preceded by a twin, i.e. a couple of the same sign)////Twins = (CurTrade = CurTrade[1]) //TWO identical trades to make a STREAK//Streaks = Streaks + ((CurTrade <> CurTrade[1]) AND Twins[1])//now Different trade +// prior candle's TWINS////---------------------------------------------------------------------------------// code using RUNS (like PRT seem to be doing)// (a run is each sign change, no matter twins)Streaks = Streaks + (CurTrade <> CurTrade[1]) //now Different trade//---------------------------------------------------------------------------------//// tally Winning & Losing tradesTotalWin = TotalWin + (CurTrade = 1)TotalLose = TotalLose + (CurTrade = -1)N = TotalWin + TotalLoseENDIFIF Streaks > 0 THENP = 2 * TotalWin * TotalLoseR = StreaksZscore = ((N*(R-0.5))-P) / sqrt((P*(P-N)) / (N-1))Zscore = round(Zscore * 100) / 100ELSEZscore = 0ENDIFZpos = Zscore > 0 //or whatever else > 0Zneg = Zscore < 0 //or whatever else < 0// --- end of Z-Score code////*********************************************************************************// Z-Score managementONCE SkipOneTrade = 0ONCE MinTrades = 30 //30 or 51 trades minimum to consider Z-Score Reliable// as suggested on some websitesIF Zpos THEN//Positive Z-ScoreIF (CurTrade = 1) AND (Curtrade[1] = -1) THEN //Winning trade following a Losing oneIF N >= MinTrades THEN //use Z-Score only when MinTrades+ have been talliedSkipOneTrade = 1ENDIFENDIFELSIF Zneg THEN//Negative Z-ScoreIF (CurTrade = -1) AND (CurTrade[1]= 1) THEN //Losing trade following a Winning oneIF N >= MinTrades THEN //use Z-Score only when MinTrades+ have been talliedSkipOneTrade = 1ENDIFENDIFENDIF//*********************************************************************************//// S T R A T E G Y//ONCE MA = 100 //100ONCE T = 1 //1=emaIF close CROSSES OVER average[MA,T] AND Not OnMarket THENIF SkipOneTrade THEN //Do not open any trade when SkipOneTrade is TRUESkipOneTrade = 0 //clear it for the next tradeELSEBUY AT MarketENDIFELSIF close CROSSES UNDER average[MA,T] AND Not OnMarket THENIF SkipOneTrade THEN //Do not open any trade when SkipOneTrade is TRUESkipOneTrade = 0 //clear it for the next tradeELSESELLSHORT AT MarketENDIFENDIFset stop ploss 250 //250set target pprofit 2500 //2500////*********************************************************************************// Nicolas' trailing stop functiontrailingstart = 25 //25 trailing will start @trailinstart points profittrailingstep = 5 //5 trailing step to move the "stoploss"//reset the stoploss valueIF NOT ONMARKET THENnewSL=0ENDIF//manage long positionsIF LONGONMARKET THEN//first move (breakeven)IF newSL=0 AND close-tradeprice(1)>=trailingstart*pipsize THENnewSL = tradeprice(1)+trailingstep*pipsizeENDIF//next movesIF newSL>0 AND close-newSL>=trailingstep*pipsize THENnewSL = newSL+trailingstep*pipsizeENDIFENDIF//manage short positionsIF SHORTONMARKET THEN//first move (breakeven)IF newSL=0 AND tradeprice(1)-close>=trailingstart*pipsize THENnewSL = tradeprice(1)-trailingstep*pipsizeENDIF//next movesIF newSL>0 AND newSL-close>=trailingstep*pipsize THENnewSL = newSL-trailingstep*pipsizeENDIFENDIF//stop order to exit the positionsIF newSL>0 THENSELL AT newSL STOPEXITSHORT AT newSL STOPENDIF//*********************************************************************************//graph Zscore coloured(255,0,0,255)graph TotalWingraph TotalLoseOne of the attached pics shows correspondance between these calculations and PRT’s.
I tested it on DAX, h1, 200K units.
In the attached PIC about the formula, PRT stands for “the above formula in PRT Language”, not “PRT Formula”.
Link to above added as Log 295 here …
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I think I found the culprit.
1IF MyProfit <> MyProfit[1] AND (BarIndex > 0) THENIt goes wrong at that line (or because of that line used as a trigger);
The first attachment shows a small drain of money at the entry (this happens at each entry). The difference you see reported as -60.
The second attachment shows the used BrokerFee (this is IB). It is 60 … (counts for entry and counts for exit again – this latter does not bother regarding the issue).
And so each entry is seen as a “Streak” and counts as such. Also, it will count as a loss and it confuses everything.
When I eliminate the BrokerFee, all is fine (fourth attachment) – I’ll grant PRT the small difference (Reverse Orders is inactive though measurement is over 157 trades so maybe rounding errors are in place somewhere.Remedy : Let trigger the Z-Score code by a means which does not incorporate the entry. It is not easy (for me) to see how to do that, knowing that we’d want general code for that (like Roberto’s example which nicely has it all at the top of the program code). I myself probably would dare to code something like :
12345678910111213// Untested :BrokerFeeAmount = 60 // Set to what's in the Editor/Backtest startup screen.DontIncreaseStreaks = 0If MyProfit < MyProfit[1] then // We lose some ?// Is it the entry which charges the BrokerFee (Commission) ?If MyProfit - MyProfit[1] = -BrokerFeeAmount then // This compares at 5 decimals.DontIncreaseStreaks = 1endifendif[...]I hope this addition helps someone (BackTesting with PRT-IB or other brokers who charge commission).
1 user thanked author for this post.
P = 2 * TotalWin * TotalLose
Do you see a problem changing line 67 to “P = max(1, 2 * TotalWin * TotalLose)” ?
There’s a Division by zero error after the first trade since only win or lose has a 1 and the other is 0. Figured this way was more appropriate than “IF Streaks > 0 AND TotalWin > 0 AND TotalLose > 0 THEN”.
1 user thanked author for this post.
- a positive Z-score means that:
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