<s> 05. - 07. October 2000
CAN TECHNICAL ANALYSISSTILL BEAT RANDOM SYSTEMS ?
Speaker: Rudolf Wittmer, WHS GmbH
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CONTENTS
Acknowledgements
The Problem
The Solution
Key System Performance Numbers
Monte Carlo SimulationSynthetic DataRandom Systems
Conclusion
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“Live (markets) can only understood backwards,but it (they) must be lived (traded) forwards.”SÖREN KIERKEGAARD, Danish Philosopher
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Acknowledgements
This manual could not have been written without the assistance of the following software:
Omega ResearchTrading Strategy Backtesting Software: TradeStationwww.omegaresearch.com
RINA SystemsDevelopment of Performance Analysis Software: Portfolio Evaluator, Money Managerwww.rinasystems.com
AnalyCorp (Dr. Savage)Business Analysis Software for Microsoft Excel: Insight.xlawww.analycorp.com
Tradeworks softwareRandom Number Generator by Dave de Lucahttp://mechtrading.com/tradestation/random.html
Inside Edge Systems, Inc.Portfolio Monte Carlo Simulation by Bill Browerwww.insideedgesystems.com
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1. The Problem
“Progress in knowledge results more from efforts to find faults with ourtheories, rather than prove them.”SIR KARL POPPER, Austrian Philosopher
Technical Analysts often find a system or technical method that seemsextremely profitable and convenient to follow - one that they think has beenoverlooked by the professionals. Sometimes they are right, but most often thatmethod doesn't work in practical trading or for a longer time.Technical analysis uses price and related data to decide when to buy and sell.The methods used can be interpretive as chart patterns and astrology, or asspecific as mathematical formulas and spectral analysis. All factors thatinfluence the markets are assumed to be netted out as the current price.
Figure 1: Random generated data with 200-Moving Average
On the other side it has been the position of many fundamental and economicanalysis advocates that there is no sequential correlation between the directionof price movement from one day to the next.Copyright 2000 © WHS GmbH
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Even if the markets were random, people fail to understand randomness. When along trend does occur in a random sequence, people assume that it is notrandom.They develop theories to suggest that it is something other than a long series in arandom sequence. This tendency comes from our natural inclination to treat theworld as if everything were predictable and understandable. As a result, peopleseek patterns where none exist and assume the existence of unjustifiedrelationships.
The following parts will show the results of some investigations done by theauthor regarding the random behaviour of price data and system results. Therewere three main topics:a. The fundamental issue of technical trading systems evaluation is to answerthe questions: How much did the result of the trading system differ from arandomly selected set of trading signals and how much did the results differfrom an available benchmark?b. Many technical based systems fail to meet expectations when used in tradingeven though they performed very well on historical data or in practicaltrading before. This can happen because of changing market conditions or in the case of backtesting only - because of insufficient testing.c. Measuring the risk /reward - profile of a system may sound somewhat trivial.At a closer inspection, however, various issues arise, affecting thecomparison between different systems or the probability for the futureoutcomes of a system.
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2. The Solution“I like the Japanese philosophie where you ask questions rather than look foranswers. The more questions you come up with the better. The answers willhappen.”SUNNY HARRIS, Trader
There are some different ways to get reliable numbers on the stability and themathematical expectation of a system:• Finding a profitable strategy in a historic backtest does not guarantee anymeasure of success in the future but at least there is a better chance that thestrategy will make money going forward than the strategy which hasconsistently demonstrated a propensity to fail. Still the profitable strategymust be assessed to see if it meets the investors risk/reward - profile. We cancompute probability risk/reward - profiles using a statistical method calledMonte Carlo Simulation (MCS).• One way to evaluate a system on a market is to test it on simulated orsynthetic data. Using synthetic data, a trader can test systems on price filesthat have been simulated from any underlying market. The need for extensivesystem testing on simulated (other names are synthetic, scrambled) data iswidely discussed in several books.• A given system can be compared with a system that was generated on thebasis of a random number generator. That means that the entry signals weregenerated by chance only.
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3. Key System Performance Numbers“It is not only fine feathers that make fine birds.”AESOP
A mechanical system should teach you proper principles of trading. In the caseof trendfollowing systems it teaches you to go in the direction of momentum. InFigure 2 you can see the equity-curves (in points) for a trendfollwing system onthe DAX in comparison with the underlying Cash-DAX. The system wasimplemented on the historical database over the last ten years.In Figure 3 you can see the same system implemented on the S&P 500 (againthe Cashindex is used for the study).While the system on the DAX shows a high correlation with the underlying, thesame trading logic failed on the S&P 500 nearly all the time.
Figure 2: DAX – Index vs. System (in points)
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Figure 3: S&P 500 – Index vs. System (in points)
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Some performance numbers are shown in table 1, statistical numbers are shownin table 2.
DAXTotal Net Profit (points)Return on Initial CapitalAnnual Rate of ReturnMax DrawdownNet Profit / Max DrawdownProfit Factor
S&P 500
Buy and Hold
System
Buy and Hold
System
5,386291.77%13.95%-35.00%10.29-
3,161170.87%10.07%-22.00%10.451.86
1,155329.96%15.00%-23.00%27.89-
-126-36.00%-4.19%-69.54%-1.170.88
Table 1: Performance Summary Report
DAXArithmetic Mean (% per day)Standard DeviationSkewnessKurtosisMaximumM inim u m
S&P 500
Buy and Hold
System
Buy and Hold
System
0.06%1.23%-0.324.987.54%-8.36%
0.04%0.90%-0.377.435.06%-8.36%
0.06%0.90%-0.255.105.04%-6.77%
0.00%1.47%-1.3826.8413.37%-20.13%
Table 2: Statistical Numbers
Notice:The underlyings and both systems are negativ skewed. This menas that wewould expect more high negative daily yields than the normal distribution wouldsuggest.No one of the systems were able to beat the “Buy and Hold” – strategy.
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Daily Yield DistributionFigure 4 shows the daily yield distributions.Result:The S&P 500 and the DAX has “fat tails” and lower peaks than thecorresponding systems, which means that they are more volatile.
Figure 4: Daily Yield Distribution
Problem:The above data shows the result of only one dataset. This shouldn’t give usreliable numbers for results in the future. To solve this problem we could useMonte Carlo Simulation (MCS).
4. Monte Carlo Simulation (MCS)Copyright 2000 © WHS GmbH
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“If a man will begin with certainties, he shall end in doubts, but if he will becontent to begin with doubts, he shall end in certainties.”FRANCIS BACON, English Philosopher
The idea of MCS is simple. One generates a large number (5.000 – 20.000) ofmarket scenarios that follow the same underlying distribution. For each scenariothe value of the parameter (e.g. Daily Yield, Max Drawdown, Profit-/Risk –Ratio etc.) is calculated and recorded. The calculated value form the probabilitydistribution of the parameter value, from which the probability for occurrencecan be derived.
Figure 5: Daily Yield Distribution using MCS
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The curves in Figure 5 shows two things:1. The system on the S&P 500 Future has the worst statistical values to make agood performance.2. It is evident that the curve on the S&P 500 and the curve on the DAX systemare nearly kongruent. This means that we were able to rebuild the statisticalcharacteristics of the S&P 500 with a system on the DAX. This system hasthe same technical logic as the (poor) system on the S&P 500.
Conclusion:The poor performance depends on the (random) curve of the S&P on the past.Imagine that this curve was arbitrarly chosen by a random generator. The onlythings we can say is the fact, that the statistical numbers didn’t change over thelast 40 years.
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5. Synthetic Data“I can’t believe that God plays dice with the universe.”ALBERT EINSTEIN
RINA Systems, Inc. has developed a model to generate synthetic data. The data– which can be downloaded in the case for the S&P 500 for free from theirwebsite www.rinasystems.com – has the same statistical characteristics as theoriginal file. This was accomplished through statistical analysis of the originalprice file distribution.Four synthetic data set were used as basis to implement the same trendfollowingsystem as on the original data. The results are shown on Table 3 for theS&P500. At this time there were only four synthetic data sets available. It isobvious that the more files trader uses for testing the closer results will be to theexpected performance.
Synthetic Data TestingTotal Net Profit (points)Return on Initial CapitalAnnual Rate of ReturnMax DrawdownNet Profit / Max DrawdownProfit Factor
Set 1
Set 2
Set 3
Set 4
92.3726.39%3.07%-47.34%1.211.19
17.034.87%0.63%-32.79%0.571.04
379.10108.31%9.89%-10.83%13.143.61
296.7784.79%8.21%-16.75%3.102.43
Table 3: System Results on the synthetic data basisResult:In comparison with the original system we get some respectable performnacenumbers on the synthetic data sets. Yet the “Buy and Hold” – strategy couldn’tbe beaten.In a next step we run a MCS with 5.000 iterations on the average equity of thefour systems on the synthetic data. The result is shown in Figure 6.Copyright 2000 © WHS GmbH
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Figure 6: S&P 500 Daily Yield Distribution using MCSThe curves in Figure 6 shows that the systems on the synthetic data are lessvolatile than the S&P 500 Index or the trading system on the original data.
To compare the perfomance numbers we run another MCS using the PortfolioMCS by Inside Edge systems, Inc.Figure 7 to 9 shows the computed probability of the “Maximum DradownRatio”.This ratio is computed by dividing the MaxDrawdown by the sum of thestarting equity and the net profit. On the ordinate we can see the number ofocurrences for a specific bins. We run 20.000 iterations for every data set.The result of the simulation confirmed the best performance characteristics forthe synthetic data sets.The extreme right data points on the graphs represents cases where the expecteddrawdown within the next year will reach its maximum.
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Figure 7: MCS on S&P 500 Buy and Hold
Figure 8: MCS on S&P 500 trendfollowing system
Figure 9: MCS on S&P 500 synthetic data trendfollowing system
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6. Random Systems“The biggest value is probably understanding the markets are highly irrational.They’re so full of random activity…”LARRY WILLIAMS, Trader
The following studies were inspired by the work of Charles LeBeau and DavidLucas. In their book “Technical Traders Guide to Computer Analyses of theFutures Market” they published the results of their studies on random entries.They used various types of entry signals to enter the market when doinghistorical testing. The only exit they used was at the close of business 5, 10, 15and 20 days later. Their primary interest in using this approach was to determinewhat percentage of their trades made money and if the percentage exceededwhat one would expect from entering the market at random. The result was thatmost of the indicators failed to perform any better than random.We tried to reproduce these results with our own investigations. Our aim wasnot only to look at the percentage of winning trades but also at the mathematicalexpectations.The results are shown in Table 4 and Table 5.
DAXStop Technique 3 * ATR(10)
Parabolic
5-Bar Exit
8,966 €17.57%33.76%-52,432 €0.171.13
-8,216 €-17.11%41.47%-50,021 €0.95
-14,815-29.84%46.61%-$51,2970.92
Total Net ProfitReturn on Initial Capital% ProfitableMax DrawdownNet Profit / Max DrawdownProfit Factor
Table 4: System Results for the random systems on the DAX
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S&P 500Stop Technique 3 * ATR(10)
Parabolic
5-Bar Exit
-72,751-145.47%33.26%-$118,1300.77
-38,464-76.93%40.03%-$93,1570.86
-15,845-31.69%48.10%-$86,6330.97
Total Net ProfitReturn on Initial Capital% ProfitableMax DrawdownNet Profit / Max DrawdownProfit Factor
Table 5: System Results for the random systems on the S&P 500
Test procedure:Ø The random signals on a ten year data basis were created on the TradeStationby Omega Research with the Random Generator by Tradeworks Software(Dave DeLuca). One can download this software for free onhttp://mechtrading.com/tradestation/random.html.Ø The results on 2.000 systems per exit-technique were recorded and averaged.The averaged values for some performance numbers are listed in Table 4 forthe DAX and in Table 5 for the S&P 500.
Conclusion:Though for some exit-techniques there are some respectable values for thepercentage of winning trades, the mathematical expectation on average isnegative.
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7. Conclusion
Ø Technical Analysis produce better results than random signals.Ø Using Technical Analysis has the advantage of consistent decisionmaking.Ø The performance of every trading system depends on the randomprice behaviour. This makes the usage of Technical Analysis as astand alone method not advisable.Ø To reduce the risk of your portfolio you should diversify not onlyover a broad spectrum of non correlated assets but also over timeand systems.Ø Further investigations should focus on the various yield distributionfunctions to get reliable numbers about market risk structures.
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AppendixSkewness…is the amount of distortion from a symmetric distribution shape.
Kurtosis…is the “peakedness” of a distribution, the analysis of central tendency.
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Central Limit Theorem…If enough independent samples of almost any distribution are averagedtogether, the resulting distribution is normal.
Profitfactor…broken down into three parts. The three segments of the equation are tradinglogic (when to buy and sell), money management (how much) and riskmanagement (when to exit a position).
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