calendarsystems look phenomenal in historical analysis, but this type of systemdoes not take into consideration current market levels, recent marketaction, or any events leading up to the trade day. Would you buy theS&P 500 on every March 14, if history states that this action hasproven to be 75% accurate. We wouldn't, unless we knew what had happened in the market over the prior days leading up to the trade date.This type of pattern recognition is a beautiful study in how to curve fita system to historical data.The correct way to use pattern recognition is to incorporate it into asystem that utilizes other entry techniques. Certain visual patterns dooffer a small glimpse of the future and when used in concert with othertechniques can create profitable systems. The system that is shown herewas created by John Hill and demonstrates the success of pattern recognition when used us a filter fa calculation or pattern that determines if atrade should take place). This system was developed around the idea of apattern that consists of the last four days closing prices. A buy or sellsignal is not generated unless the range of the past four days closes isless than the 30-day average true range. This pattern indicates that themarket has reached a state of rest and any movement, up or down, fromthis state will most likely result in a significant move. The buy entry, ifit is allowed, is calculated by adding 62% of yesterday's true range to theopening price and conversely the sell entry, again if allowed, is calculatedby subtracting 62% of yesterday's true range from the opening. The protective stop for a long position is calculated by subtracting 62'S of yesterday's range from the open price and is recalculated on a daily basis. Thisstop is either a reversal stop if a trade entry is allowed or a liquidationstop if an entry is not allowed. On the other side, the protective stop for a
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short position is calculated by adding 62% of yesterday's true range tothe open price and is recalculated on a daily basis. Again, this stop iseither a reversal stop if a trade is allowed or a liquidation stop if one isnot. To demonstrate the importance of the four-day close pattern, we havetested the system with and without the pattern filter. Before we show theperformance, let's summarize this pattern system:• Calculate the average actual range for the past 30 days and define this as our volatility measure.
TABLE 9.18
Volatility Based Breakout with Pattern Recognition
ONE CONTRACT PER TRADETEST PERIOD 1/1/83-8/31/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
WHERE TO START
205
Calculate the highest and lowest close for the past 4 days.Determine if a trade can take place tomorrow. The distance fromthe highest close to the lowest close for the past 4 days must beless than the 30-day average true range.If a trade is possible, calculate the buy and sell stop. The buy stopis calculated by adding 62% of yesterday's true range to the opening and the sell stop is calculated by subtracting 62% of yesterday's true range from the opening.
TABLE 9.19
Volatility Based Breakout without Pattern Recognition
ONE CONTRACT PER TRADETEST PERIOD 1/l/83-8/31/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
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• If a long position is initiated then place a protective stop. Theprotective stop for a long position is calculated by subtracting62% of yesterday's true range from the open and is recalculatedon a daily basis. This protective stop is either a reversal stop or aliquidation stop based on the ability to initiate new trades.• If a short position is initiated then place a protective stop. Theprotective stop for a short position is calculated by adding 62% ofyesterday's true range to the open and is recalculated on a dailybasis. This protective stop is either a reversal stop or a liquidation stop based on the ability to initiate new trades.Table 9.18 on page 204 shows the system with the pattern filter, andTable 9.19 on page 205 shows the same system without the pattern.Did the pattern filter really help? We would have to definitely sayyes. The overall maximum draw down was cut in half, and coffee wentfrom being 36.3% of the total portfolio return to 26.8%.CONCLUSION
We covered a lot of ground in this chapter, so don't worry if everythingdidn't sink in. The most important points to remember are:• Get a computer, if you don't already have one.• Base your research and actual trading on clean historical data.• If you want your real time trades to mirror your hypotheticalones, then use the same data from the same vendor in the sameformat. Remember there are various data formats: actual, perpetual, and continuous. The different formats can be created in different manners; a back-adjusted continuous contract id differentthan a forward-adjusted continuous contract.• Most systems based purely on popular indicators usually fail.• Traders are always excited about leading edge technology, but inevitably fall back on the classical approaches. Most traders arenot rocket scientists, thank goodness, and will tinker aroundwith new age ideas, but most of them will trade only what theycan fully understand.• The most popular and successful approaches to trading themarkets are:— Donchian breakout— Moving average crossover
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— Short-term volatility open range breakout— S&P and stock day trading— Pattern recognitionExit techniques determine success of entry techniques andshould be given equal research time.
10HISTORICAL TESTING—ABLESSING OR A CURSE
Fast computers, historical data, and testing software are the greatesttools for system traders. With the use of these took any conceivablemathematically defined idea can be evaluated. Before the advent of thecomputer, traders had to spend hours testing a simple system over a fewmonths of historical data. Their tools consisted of a calculator; printoutsof daily open, high, low, close data; and pencil and paper. In today'sworld, 20 years of data on 50 different markets can be tested in a matterof seconds. This is real power. Unfortunately, power can be used orabused. Knowledgeable system traders use this power to determine viable trading ideas, develop systems with robust parameters, and selectportfolio composition. Naive beginning system traders abuse the powerto fool themselves and unscrupulous system vendors abuse the power tofool others by developing trading systems that only work in the past.Let's say you want to buy or develop a trading system. How can onedifferentiate between an honest and robust track record and one thathas been optimized to only work in history. The only measures of atrading system's viability and potential profitability are found in itshistorical performance results. Through due diligence and research, theanswer can he found. This chapter tries to point out the pitfalls andprovide answers to problems that arise out of historical back testing.SIMULATED ANALYSISWhen it conies to trading systems, the majority of historical performance data comes in the form of simulated analysis. Simulated analysishas several pitfalls, but the main two are insufficient slippage accounting due to hidden fast market conditions in historical daily data and
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analysis with the benefit of hindsight. Historical testing almost alwaysgets the price that you want to buy or sell at. Most hack testing softwarethen levies a commission and slippage charge for each and every trade.The industry standard for commission and slippage charge ranges from$75 to $100. In the past few years, especially in the S&P and coffee, wehave observed certain days that trades were slipped $500 or more. Slippage occurs when the market moves so fast that an order can't get filledbecause there are no buyers/sellers at the order price. Orders usually doget filled, but at a much less desirable price. Testing on daily bars, aperson or a computer would not see nor reflect such high slippageamounts. Testing with intraday tick data could help alleviate the errorsin slippage accounting, but unfortunately this type of data is very expensive, requires a lot of disk space, and is unreadable or impractical touse with today's testing software. A hypothetical simulated back test ondaily bars is a study in best ease scenarios. If you start your tradingsystem analysis with this in mind, you will be starting out on the rightfoot. In the next section, we discuss the dangers of curve fitting withthe benefit of hindsight.CURVE FITTINGAs we have mentioned before, a hypothetical track record is useless unless the underlying system is somewhat robust. With the benefit of hindsight, any historical track record can be manufactured; systemparameters can be adjusted until all of the best historical trades aretaken. Using hindsight and optimizing parameters and forcing a systemto only take the best historical trades is known as curve fitting. Over optimizing and curve fitting guarantees two things: unbelievable historicperformance and an extremely high probability of system meltdown inthe future. How can the public determine if a system is overly curve fitted or not. This is a dead end question unless the logic to the system isfully disclosed. Forget trying to determine robustness (the lack of a system's performance sensitivity to changes in its parameters) of a blackbox system. If you are buying a black box system, you better know andhave faith in the person you are buying from. And unfortunately thelogic of a white box system is usually not revealed until money haschanged hands. Many times a vendor will disclose the number of parameters before he sells a system. As a system purchaser, you would have toask whether the parameters are the same for all markets or are differentfor different markets. If the number of parameters is less than five andthey are the same for all markets then there is a good chance that thesystem was not curve fitted to historical data. The opposite is true ifthere is a high parameter count and the parameters are commodity dependent. This rule of thumb is the first step in the hunt for a robust
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system. The second step occurs after the white box system has been purchased and you have the system programmed into a piece of software.You may think that this is putting the carriage before the horse, but remember that a full test can't be carried out unless the logic is fully revealed. The cost of the system could be minuscule compared to thepotential losses that could be generated by an over-optimized system. Insome cases, you may get the system vendor to demonstrate the robustness of his system by running different parameter sets on his system onindividual markets. If the system vendor optimized the system originally, he may already have different runs with different parameter sets.After you have attained either the system in software form or theOptimization reports from the vendor, you can begin to determine robustness. Table 10.1 shows a typical optimization report. An optimization report will usually list the different parameters and the differentresults of those parameters tested over the same time period over thesame market. A robust parameter is one that when changed, (up ordown) in incremental values does not result in drastic differences inoverall performance.
TABLE 10.1
Typical Optimisation Report
ONE CONTRACT PER TRADE$75 ALLOWED FOR COMMISSION AND SLIPPAGE
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Figure 10.1 is a three-dimensional area graph that plots the profitthat is generated by different combinations of two parameters. There arepeaks, valleys and plateaus. It goes without saying that you don't want topick the combination of parameters that falls in the valleys. At the sametime, going against initial intuition, you don't want the combination thatfalls on the peaks either. The most robust parameter set is the one thatfalls on a high and level plateau. If you change this set of parameters upor down, the net result doesn't differ dramatically. You want this parameter set, because we all know that history does not repeat itself exactlyand that the optimal parameters today may not be the optimal parameters tomorrow. We optimized a simple open range breakout system on theBritish Pound from 1983 through 1991. The rules for the system are tobuy a certain percentage of the distance between the highest high andlowest low for the past three days off of the open. The sell side is just theopposite. In addition, we utilized a simple $1000 money managementstop. In our optimization test, we were striving to find the best combination of percentages. Figure 10.2 shows the three-dimensional area graph
FIGURE 10.1 Three-dimensional area graph of a British Pound optimization(1983-1991). The x-axis = parameter 1; y-axis = parameter 2; z-axis = $ profit.
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FIGURE 10.2
Same three-dimensional area graph as Figure 10.1.
of our optimization run. The x-axis represents parameter 1, the y-axisrepresents parameter 2 and the z-axis is net profit.In this illustration, we picked three combinations of parameters:two that we thought were unreliable and one that showed potential. Wechose the one good parameter set due to its placement on a high and levelplateau. The parameter sets that we felt would be unreliable were foundon peaks and in valleys. We walk-forward tested the three different setsof parameters on the British Pound from January 1992 through August1999. Table 10.2 shows the performance of these walk-forward testa.In this analysis, the valley parameters outperformed the peak andplateau parameters from a profit standpoint. The plateau parametersperformed the best from a draw down standpoint. Figure 10.3 showshow parameters can shift through time. This three-dimensional areagraph shows the profit generated by the same combination of parameters, but over the time period of January 1992 through August 1999. Itis interesting to see how some peaks turned into valleys and how the optimal parameters shifted from one set of values to another.The original "best" parameters were not optimal during the secondoptimisation run. No markets repeat history exactly and if you don't
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TABLE 10.2 Performance Using Three Different Sets of ParametersONE CONTRACT PER TRADETESTED FROM JANUARY 1992 THROUGH AUGUST 31, 1999S75 ALLOWED FOR COMMISSION AND SLIPPAGETotal NetMaxParameter SetProfit ($)DrawDn ($)ValleyPlateauPeak
-1,131-4,738-18,175
40,03119,58835.838
Best from profit stand pointBest from drawdown stand pointWorst overall
choose a parameter set that works in most market conditions, you willbe on the losing end of most trades. This analysis brings us to an intereating question: Does optimization really help?There is but one use for optimization and that is for locating ballpark parameters. When you begin to develop a trading system, you haveno idea of what your parameters should be. Through the use of optimization, you can rule out parameter ranges that don't make sense and
FIGURE 10.3 Three-dimensional area graph of a British Pound optimization(1992-1999), The x-axis = parameter 1; y-axis = parameter 2: z-axis = $ profit.
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get a general idea of a systems overall effectiveness. If you optimize asystem's parameters and nothing seems to work, then you know thatyou need to move onto another idea.PERIODIC REOPTIMIZATION—DOES IT WORK?Through our examples and studies, we have discovered that optimization is not always the best way to fine tune a trading system. Optimalparameters shift through lime and this shift is impossible to foresee.Many traders and system developers feel that because of ever-changingmarkets, parameters should be reoptimized on a periodic basis. Theyalso feel that the parameters need to be reoptimized over the most recent history. Reoptimization is not the answer. Markets evolve and maylook different today than they did 5 or 10 years ago. However, if a system is logical and based on sound market principles, it should be able tocope with any curve balls the market may throw it. It may get beat upfrom time to time, but it should come out ahead over the long term. I'mnot Baying that a system should never be changed; a $500 stop in theS&P 5 years ago is not the same as it is in today's market. If a marketdemonstrates a totally different personality than what is historicallyportrayed, then a system's fixed parameters may need to be changed.One way to prevent the need to change fixed parameters, is to make allparameters a function of the market (e.g., instead of a $500 stop use10% of the average range). We feel that reoptimization is a way to tryand fix something that is broken.We put our beliefs to the test and tested a simple Donchian systemthat is reoplimized on a rolling 2-year basis. (Remember Donchian typesystems buy when the highest high of x days is penetrated and sellwhen the lowest low of x days is penetrated.) We optimized the channelTABLE 10.3
Optimal Parameters over Several Markets and Time Periods
HISTORICAL TESTING—A BLESSING OR A CURSE
TABLE 10.4
Performance Results Using Reoptimizing Parameters
ONE CONTRACT PER TRADETEST PERIOD 1/1/86-4/30/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
TABLE 10.5
Performance Results Using Static Parameters
ONE CONTRACT PER TRADETEST PERIOD 1/1/86-4/30/99S75 ALLOWED FOR COMMISSION AND SLIPPAGE
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length to get into a long position and then into a short position. Everytwo years the parameters were reoptimized over the previous two yearsand the optimal parameters were selected and used for the followingtwo years. Table 10.3 on page 214 shows the time periods and optimalparameters for those periods for seven different markets.Table 10.4 on page 215 shows the overall performance of the sevenmarkets w i t h rolling the optimal parameters every two years. Table10.5 on page 215 is similar to Table 10.4, but instead of using optimizedor reoptimized parameters, the system uses a fixed parameter far allmarkets for all time periods.The fixed parameter set easily outperformed the reoptimzed parameters. These results basically state that overoptimization and reoptimizatinn simply does not work and you end up trying to out guessthe markets.ALTERNATIVE TO OPTIMIZATION—ADAPTIVE PARAMETERSWe have seen that optimization lone time or periodic) does not solve theproblem of parameter shift. An optimal parameter may start out at aparticular value, but through time that value may change; in 1983 theparameter may have the value of five and in 1987 the optimal parameter may have a value of ten. How can a trader keep up with the everchanging optimal parameters? You can either ignore the shift and hopethat your parameter selection and underlying system are robust enoughto handle changing market conditions or you can have your parametersadapt to the market conditions.Adaptive parameters are ones that change dynamically based onsome function of the market. In 1996, we developed the Dynamic Breakout system. We started with a simple channel breakout system and optimized the channel lengths over several years of data over severaldifferent markets. We used the power of optimization in the correctmanner; we wanted to eliminate the combinations of parameters thatsimply were out in left field and didn't apply. We found out that channellengths that fell between 20 and 60 worked for moat of the markets thatwe tested.For parameters to dynamically change, they must be a function ofthe market. Something about the market must dictate what the parameters should be and how they should change. Because we are dealing withmechanized trading systems, we had to come up with a mathematicalformula that in somehow reflected the state of the current market condition. The amount a market has moved up and down over the past fewdays usually gives a good indication of the market's current personality.This movement is known as volatility. If a market has had wide swingsover the past few days, its volatility is considered high. If a market is
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calm, it exhibits low volatility. In the Dynamic Breakout system, weused volatility as the indicator of current market conditions. We usedstandard deviation as the volatility measure. Standard deviation increases when the range of price swings are increasing, and decreaseswhen price variability slows.Deriving a formula that reflects a certain aspect of a market is thefirst step in making a parameter dynamic. The second step is the actualapplication of the formula that converts a static parameter into one thatchanges. Through observations and analysis, we discovered that channelbreakout systems were chopped to pieces during times of high volatility,whereas on the other hand, these systems traded well during times oflow volatility. We concluded that the channel length (the number of daysin the highest high and lowest low calculations) should he increasedduring times of high volatility and decreased during times of lowvolatility. The end result of the formula and its application is known asan adaptive engine. An adaptive engine can be modified and pluggedinto different types of trading systems.The Dynamic Breakout system starts out looking to buy/sell whenthe highest high/lowest low price for the past 20 days is penetrated. Thechannel lengths are changed based on market volatility. The volatilityTABLE 10.6 Performance Results of Nonadaptive System with Benefitof HindsightONE CONTRACT PER TRADETEST PERIOD 1/1/83-12/31/89$75 ALLOWED FOR COMMISSION AND SLIPPAGE
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TABLE 10.7 Performance Results of Nonadaptive System without the Benefitof HindsightONE CONTRACT PER TRADETEST PERIOD 1/1/90-8/31/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
measure is defined as the standard deviation for the past 30 days' closingprices. The channel lengths change in the same proportion as does thedaily volatility. If yesterday's channel length was 20 and today's volatility increases by 5%, then today's channel length becomes 21. If today'svolatility decreases, the channel lengths contract. Because dynamic parameters are a reflection of the markets, there are some instances whenthe markets go completely crazy and cause the parameters to get astronomically large or infinitesimally small. In these situations there mustbe some overriding rule to keep the parameters within an acceptablerange. We use a ceiling value of 60 days and a floor value of 20. The parameters cannot exceed 60 or fall below 20.To verify the validity of dynamic parameters, we tested a basket ofcommodities over nine plus years on the Dynamic Breakout system.We also tested the same commodities on a similar system with nonadaptive parameters over the same time period. We first optimized thenon-adaptive parameters from 1983 through 1989 and used the best inthe walk forward test that commenced on January 1990. Table 10.6 onpage 217 shows the optimized performance numbers for the non-adaptive system from January 1983 through December 1989.
HISTORICAL TESTING—A BLESSING OR A CURSE
TABLE 10.8
219
Performance Results of Adaptive System
ONE CONTRACT PER TRADETEST PERIOD 1/1/90-8/31/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
Table 10.7 on page 218 shows the walk-forward test of those optimized parameters from January 1990 through August of 1999. Table10.8 shows the performance of the Dynamic Breakout system with dynamic parameters on the same portfolio over the same time periodcovered by the walk-forward test of the system with optimized nonadaptive parameters. Adaptivity won this test hands down.YOU DESIGN THE TRADING SYSTEM, NOT YOUR COMPUTERWith all the data and testing software and super computers that areavailable today, we are seeing more and more systems designed by computers and not by humans. Trading ideas that should be placed in thetrash are being revitalized by computers and overoptimization. Just because a computer can infinitely optimize parameters until it finds different parameter sets that work on different markets, does not mean ithas uncovered a trading principle. Many system testers/traders startwith an idea that fits into their trading psychology, but after manynights of testing and optimizing and curve fitting, they usually end upwith something that, is completely alien to them.
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Everybody starts a trading system out with a core idea. They theninitially test the idea and if the results look somewhat promising, theyusually will cultivate the idea further. This cultivation usually comesin two distinct forms: addition of logic and optimization. Either formcan lead to the road of enlightenment or the road of destruction, ifthey are not universal to all markets and all market conditions. Wehaw already spoke about overoptimization and curve fitting, but thereare other dangers lurking out there when developing trading systems.For example, let's say you have developed and tested a multimarketsystem and through performance analysis you discovered that soybeans shouldn't be traded on Tuesdays and pork bellies shouldn't betraded on Fridays. The rest of the markets are okay throughout theweek. This is a form of curve fitting through the addition of logic thatis not universal through all markets and market conditions. Now. ifyou had discovered that trades should be eliminated across the hoard ifyesterday's volatility was too high, then that would be a valid additionof logic. It is universal to all markets and market conditions.HOW TO EVALUATE TRADING SYSTEM PERFORMANCE
Trading system evaluation goes well beyond just looking at the bottomline—profit. There are other key statistics one should look at when evaluating performance. In addition to profit, we like to look at these otherstatistics:• Maximum draw down: The highest point in equity to the subsequent lowest point in equity. The largest amount of money thesystem lost before it recovered.• Longest flat time: The amount of time the system went withoutmaking money. This could occur right off the bat or at the end ofa string of winners.• Average draw down: Maximum draw down is a one time occurrence, but average draw down takes all of the yearly draw downsinto consideration.• Profit to loss ratio: This statistic represents the magnitude ofwinning trade dollars to the magnitude of losing trade dollars.The higher the ratio the better. Beginning traders are alwaysstuck on the percentage of wins. This statistic is HO much more informative, because it tells you the ratio of wins to losses. Systemsthat have a high percentage of wins do not necessarily have ahigh profit to lose ratio. Quick profit taking systems can have upto 90% wins but average only a small profit per trade. Would you
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rather have a system with 90% wins and makes $50 on winningtrades and loses $25 on losing trades or would you prefer a systemthat had 33% wins and made $2000 on each win and lost $200 oneach loss?• Average trade: The amount of profit or loss you can expect on anygiven trade. This is another statistic that is more important thanpercent wins.• Profit in draw down ratio: Most traders are risk averse: they lookat the risk before they look at the reward. Risk in this statisticcomes in the form of draw down, whereas reward is in the form ofprofit. Of the following, which scenario would you choose? For$100 you have a 10% chance of making $1000 or for $1000 youhave a 10% chance of making $10.000. Most traders, due to theirlimited capital, choose the Scenario with the less risk. Even thoughthe risk to reward ratio is exactly the same.• Outlier adjusted profit: With any trading system, you are goingto have one or two monstrous wins and/or monstrous losses Theprobability of these trades reoccurring are extremely slim andshould not be included in on overall track record- We have seenprofitable S&P systems make all of their money on a small handful of trades and lose on almost all others.• Most consecutive losses: The total number of losses that occurredconsecutively. This statistic gives the user an idea of how manylosing trades one may have to go through before a winner occurs.• Sharpe ratio: Indicates the smoothness of the equity curve. Thehigher the ratio, the more smooth the equity growth or decline.This ratio is calculated by dividing the average monthly or yearlyreturn by the standard deviation of those returns.• Long and short net profit: In most markets, a robust systemwill split the profits between the long trades and the shorttrades. You probably wouldn't want to trade a system that madeall of its money on one side of the trades. There are exceptionsto this and markets that have had a bullish bias, such as theS&P futures and most stocks, usually have a propensity to longtrades.• Percent winning months: A system that averages only one winning month out of twelve is probably undesirable. You would wanta system that wins at least five months out of the year.• Visual representation of equity: A picture is worth a thousandwords. An equity curve expresses more to the eye than any tabular reports. We have seen systems that look decent in reports, butlook horrible as an equity curve. It is easier to interpret draw
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down, longest flat period, equity curve volatility, and equitygrowth in a visual medium.For demonstration purposes, let's analyze a system, from the lastchapter and apply the performance statistics that we just discussed.Let's take a look at the pattern system that we closed the last chapterout with. Table 10.9 includes the overall performance statistics of oursystem tested on the U.S. bonds from January 1983 through August1999. Seventy five dollars was levied against each round turn trade forcommission and slippage.The maximum draw down in this case was $13,330. A very respectable number and one that could probably work in to the budget ofmost traders. A lot of beginner traders see this amount and can't believethat on this one market this system lost $13.300 at one point. Typicaldraw down figures are a wake up call to most under capitalized traders.
TABLE 10.9 Performance Numbers of the Pattern System on U.S. BondsONE
CONTRACT
PER
TRADE
TEST PERIOD 1/1/90-8/31/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
HISTORICAL TESTING-A BLESSING Oft A CURSE
223
Over a sixteen plus year track record, this system on this market,went close to two years without making a penny. This could have occurred at the beginning, the middle or the end of the test period andtherefore this could happen again at any time after someone starts totrade it. Traders must understand the mentality of their system, so theycan prepare for such occurrences in the future. A flat time of thislength would not be that significant if it occurred after many years ofprofitability, but would be devastating if it occurred right off the batIn many cases, the average draw down figure is a better determiningfactor for minimum required capital than maximum draw down, due tothe fact that maximum draw down is a look at the worst case scenario.However, many traders like to be ultra conservative when allocatingmoney to trading and like to use the worst case scenario. The net profitsfor this system outnumbered the net losses by a 1.4 to 1 ratio and the average trade was $131. The profit to maximum draw down ratio was 7.71,a highly respectable showing. The overall equity is not affected greatlyby eliminating the best winning and worst losing trade, which indicatesan even distribution through out all the trades; a few large trades did notmake this system profitable. At one time, this system suffered through
FIGURE 10.4
Equity curve for the pattern system.
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seven consecutive losses. This is good information to know before actualtrading commences. A high Sharpe Ratio indicates smoothness, and thissystem had that with a 1