diversi®cation, how much money to invest or risk in anymarket, the use of stops, reward±risk ratios, what to do after a period ofsuccess or adversity, and whether to trade conservatively or aggressively.We undertake money management by elaborating market portfolios (assetallocations between dierent strategies), a general portfolio (asset allocationbetween the dierent market portfolios) and determining the most ecientuse of investment capital.14.4.1 DiversificationDiversi®cation is a way to achieve higher returns with the same or lessamount of risk, and is clearly an important aspect of money management.Dierent ways to diversify include using dierent markets, time frames andmethods.Asset-allocation policy is determined for every market and implementedstrategy, in order to keep the global level of exposure (leverage) unchanged. Itbegins by elaborating portfolios of each selected market and then bycombining these portfolios. A combination of strategies and markets oering
Notionnal
Realized + unrealizedRealized profit
Figure 14.3 A short-term system
Notionnal
Realized + unrealized profit
Realized profit
Figure 14.4 A long-term system
BAREP futures funds
401
FUNDa1
Market 2
Market 1b1Strategy 1
b2Strategy 2
a2
a3
Market 3
b3Strategy 3with a1 + a2 + a3 = 1b1 + b2 + b3 = 1Figure 14.5 Asset allocation
low correlation with the others, good Sharpe ratio and low drawdowngenerates a portfolio which oers a high, regular and also steady performance(Figure 14.5).The managers bene®t from a quick intervention, thanks to the developmentof computerized valuation instruments in real time. The managers re-studythe various strategies integrated in the fund constantly.A market portfolioIn the portfolio, all strategies are managed independently. Indeed, it ispossible to follow, at the same time and on a same market, complementarybut dierent approaches.Our global exposure on a market depends on each asset evolution and onits relative weighting inside this market.Using several strategies in a same market is one way to catch dierent kindsof movements, dierent trading horizons and timings to enter the markets.Some trading methods perform well in trendy markets (small variations orlong movements), others in chartist or contrarian situations.The choice and the weighting of these assets, in each market, depend on:(1) a good historical return on investment (the return on investment is theamount made or lost in a certain period of time divided by the amountinvested and represents one of the best measures of return)(2) a decrease in the risk (risk is evaluated by the standard deviation ofreturns and the maximum drawdown ± the largest drawdown during aperiod of time and, therefore, the worse case scenario)(3) a large diversi®cation and a low correlation between assets (diversi®cation is a way to achieve return and reduce risk; successful diversi®cation is achieved by choosing models with the lowest correlationpossible).
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Advanced Trading Rules
An example of market diversification (Figure 14.6)It is possible to achieve a diversi®cation with one trend-following strategyusing moving averages.The moving average is one of the most versatile and widely used of alltechnical indicators. Because of the way it is constructed and the fact that itcan be so easily quanti®ed and tested, it is a good basis for trend-followingsystems.Its purposes are to identify or signal that a new trend has begun or that anold one has ended or reversed, and so to track the progress of the trend.With a strategy using moving averages, the selection of couples ofparameters gives several assets and at the same time dierent timing andtrading horizons.f Market: Notionnalf 40 days moving averagef 150 days moving average.
The portfolio, with this two equi-weighted assets, is long in a bullish trendymarket, neutral if a correction happens in a trend, and short in a bearishtrendy market.We can generalize about this diversi®cation with other dierent assets ofthis strategy and with other approaches we have created.The multi-market portfolioTrading dierent markets should tend to reduce risk and is probably the mostfamiliar and widely used way of diversifying. Trading markets with lowcorrelation coecients is a good start in proper diversi®cation.As we are completely systematic, the number of contracts can beimportant. The problem lies in the liquidity of each market. Trading marketswhich are not really liquid can reduce, because of the slippage, any of thebene®ts of increased diversi®cation. That's why we only trade on liquidmarkets.In order to minimize global risk and increase pro®t opportunities, the logicof each market's diversi®cation is extrapolated to a diversi®cation of marketsall together. This study creates the multi-market portfolio.The choice and the weighting of these dierent markets depend on:(1) a good historical return on investment(2) a decrease of the global risk(3) a signi®cant diversi®cation and a low correlation between markets.The end result is a multi-markets and a multi-strategies portfolio, with amultitude of methods, concepts and trading horizons.We actually trade dierent assets and strategies on the same market,
SELLlong-term strategy
SELLmedium-term strategyBUYlong-term strategy
BUYmedium-term strategy
Figure 14.6 Example of medium-term and long-term diversi®cation
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Advanced Trading Rules
according to the trading horizons (short-, medium-, long-term). In our funds,more than 300 assets are managed in real time on 25 dierent markets.The global purpose of diversi®cation is to generate a regular performanceon a medium-term investment maturity, given the fact that at any time duringthe investment period, the portfolio must contain at least one market with atrend, and the appropriate model to extract a performance from this trend.14.4.2 LeverageThe leverage is de®ned as the ratio between the sum of nominal values ofevery contract in position adjusted by their market price and the net assetamount of the fund.The portfolio created gives the weighting of each market and each asset.The number of contracts traded depends on the fund's size and on the degreeof risk sought. This degree determines the global leverage.The assets' allocation has determined a trading portfolio which givesindication concerning historical rewards and drawdowns. The maximumdrawdown is used to calculate the general leverage of the fund.Finally, the level of a non-guaranteed fund leverage is de®ned in order tosupport eight times the historical maximum drawdown of our simulatedportfolio.BAREP reinvests the trading pro®ts of the fund when pro®t-makingrepresents half a drawdown. In the same way, we lower the leverage whenthe losses represent half a drawdown.In certain situations, we can hedge a part of the portfolio, with thepurchase of options. This hedge is done to conserve a part of the portfolio'sreturn after a strong bullish or bearish movement, to cover the risk of amarket consolidation. But we never modify the orders given by the strategieson futures markets.14.5 EPSILON FUTURES FUNDEpsilon futures fund is a FCIMT without any capital guaranteed. A FCIMT(Fonds Communs d'Intervention sur les MarcheÂs aÁ Terme) is a Frenchfutures fund registered under French law and accepted by the `Commissiondes OpeÂrations de Bourse' (COB), with daily valuation, FFR denominated.Total invested funds in a FCIMT is limited to 50 per cent of total capital.The balance is placed in Treasury bills.The trading of our funds began in August, 1994, on three markets(Notionnal, CAC, Bund), about ®fteen assets and with one million dollars.After less than two years, we manage 200 million dollars on 28 markets and600 assets.
BAREP futures funds
405
Net asset value is actually above 1,200 million francs (200 million dollars)or 18.900 francs per share (Figure 14.7).14.5.1 Characteristicsf Legal status: futures fund (FCIMT under French law), authorized by COBf Currency: French francf Valuation: dailyf Management fee: 2.5 per cent of the net asset valuef Performance fee: 30 per cent of the pro®ts net of brokerage and management fees gained on the futures markets, on a half-yearly basisf Front fee: up to FRF 5 000 000: 3.5 per centabove FRF 5 000 000: 2.5 per centf Redemption fee: 0.5 per cent maximum in case of 7 days prior notice, 10per cent otherwisef Investment maturity: open, one year minimum advisedf Tax: depending on the law of the country of residence of the investorf Document available: investors can obtain each business day in Paris thelatest net asset value of the fund, the leverage component, the deposit, andall legal documents.
(Futures funds constitute a volatile type of investment, with the possibility ofloss of all the capital invested. It is strongly advised that investors who don'thave a sucient knowledge about the futures markets and the risks involvedshould not invest in this kind of fund. It is the investor's responsibility toobtain the necessary information on the futures market. BAREP will not beheld responsible for any lack of information on these markets.)14.5.2 Actual markets'allocation (for 20 million dollars)The futures markets' weights of our multi-markets portfolio allocation isrepresented in Table 14.2 for an amount of 20 million dollars and a leveragecalculated in order to support eight times the historical maximum drawdown.In our portfolios' allocation long-term bonds represent above 40 per cent ofthe funds' allocations, short-term bonds 10 per cent, currencies 30 per centand equities 20 per cent (Figure 14.8).14.5.3 PerformanceHistoric volatility of Epsilon, our non-guaranteed fund, has decreased as thenet asset value (represented by the shares' number) has risen strongly. Thishas been possible by an increasingly signi®cant diversi®cation in terms ofassets and markets. We did not have problems with the increase in our funds'size (Figure 14.9).
Since emissionFlat yieldAnnual yieldStandard deviationMax drawdownSharpe ratio
60.24%18.50%13.08%12.85%1.41
Since 1 yearFlat yieldAnnual yieldStandard deviationMax drawdownSharpe ratio
25.24%25.40%8.36%6.02%3.04
Number of positive monthsNumber of negative monthsMaximum monthly pro®tMaximum monthly loss
Figure 14.7 Epsilon futures fund performance between 25 June, 1994, and 15 November, 1996
24108.84%6.15%
BAREP futures fundsTable 14.2 Futures market's weights
Contracts
Numbers
Daily volatilitiesfor a contract (in dollars)*
1400840280350105350490490350
52082556561957785981040423981
700700700700
388173289166
350350700700105105
6845719451156520560
490350420140280
11061926185720801300
Long-term bondsNotionnalBundGiltTNote 10 yearsJGBBonosBTPTNote 5 yearsT-BondShort-term bondsPiborEuro-DMShort sterlingEuro-DollarCurrenciesUSD/DMUSD/GBPUSD/CHFUSD/JPYUSD/AUDUSD/CADEquitiesCACDaxNikkeiS&PFTSE
*The volatility in dollars is the average amount in dollars of daily movements on a contract.
LONG-TERM BONDS40%
SHORT-TERM BONDS 10%
Figure 14.8 Portfolio allocations
407
Figure 14.9 Evolution of shares' numbers and historic volatilities of Epsilon futures
BAREP futures funds
409
14.5.4 ComparisonWeekly performance between Epsilon and two benchmarksThe two benchmarks chosen are `The JP Morgan Global Bond' for bonds'performance and `The Morgan Stanley Global Equity' for stocks' performance (see Tables 14.3 and 14.4). Epsilon futures performance is taken afterthe deduction of management and performance fees while stocks and bondindices don't include fees.Epsilon outperformed by over 60 per cent in three years as in the same timethe two benchmarks increase by 24 per cent and 50 per cent. The learningphase at the beginning of Epsilon saw a quite high volatility. Nevertheless, thevolatility on the period is decreasing as we saw it (Figure 14.10) and it isactually around 9 per cent.
Table 14.3 Rewards and risks since the beginning of Epsilon (1 August, 1994 to 5 July, 1997)
Epsilon
JPMorganGlobalBond
MorganStanleyGlobalEquity
50%Epsilon +50%Bond JP
50%Epsilon +50%Equity MS
Flat yieldAnnual yieldVolatilityMax drawdownSharpe ratio
60.24%18.50%13.08%12.85%1.41
23.74%7.97%4.91%3.98%1.62
50.26%15.79%9.46%6.11%1.67
41.97%13.45%7.32%4.95%1.84
55.27%17.16%8.10%3.99%2.12
Number of positive monthsNumber of negative monthsMaximum monthly pro®tMaximum monthly loss
24108.84%6.15%
19155.20%2.15%
2686.80%4.61%
2595.30%3.29%
2596.80%3.06%
*The volatility is calculated with weekly returns.
Table 14.4 Rewards and risks since one year (16 November, 1995 to 5 July, 1997)
Flat yieldAnnual yieldVolatilityMax drawdownSharpe ratio
Epsilon
JPMorganGlobalBond
MorganStanleyGlobalEquity
50%Epsilon +50%Bond JP
50%Epsilon +50%Equity MS
25.24%25.40%8.36%6.02%3.04
5.62%5.65%4.07%2.52%1.39
22.55%22.69%10.94%4.83%2.07
15.86%15.95%5.14%3.63%3.10
23.93%24.08%7.75%3.99%3.11
Performances are calculated for 100 dollar investment on 1 August 1994
Figure 14.10 Compared performance between 19 September, 1994 and 3 July, 1997
BAREP futures funds
411
Table 14.5 Correlation between dierent weekly returns
EpsilonJP Morgan Global BondMorgan Stanley Global Equity
Epsilon
JP MorganGlobal Bond
Morgan StanleyGlobal Equity
100.00%10.28%9.79%
10.28%100.00%44.24%
9.79%44.24%100.00%
The second year of trading shows a management more secure with ahigher diversi®cation in terms of markets and more approaches andstrategies.The global yield kept very high (about 25 per cent ¯at) while JP MorganGlobal Bonds increase only by 22 per cent. The maximum drawdown isweaker and represents only one-quarter of the ¯at return. Table 14.5 shows avery low correlation between Epsilon and the two benchmarks with 10.28 percent with the ®rst one and 9.79 per cent with the other one. On theopposite, the correlation between the two benchmarks is quite high withnearly 50 per cent. To conclude, Epsilon outperformed both benchmarks witha higher, but falling, volatility and is a very good instrument of assetdiversi®cation.Figure 14.11 proves that Epsilon is a very good instrument of assetdiversi®cation. If you allocate a portfolio with 50 per cent of Epsilon and50 per cent of Morgan Stanley Global Equity instead of Morgan StanleyGlobal Equity alone, the yield is higher with a better Sharpe ratio (from 1.67to 2.12) and a lower maximum drawdown (from 6.11 per cent to 3.99 percent).14.5.5 Probability curvesOur management methods being totally systematic, we can simulate a proxiportfolio on market historical prices and check the daily gain. We havestudied the empirical distribution of this daily gain and compared it to aGaussian process. We do obtain the results in Figure 14.12. Several tests ofnormality (test of  2 , kurtosis and skewness) show a signi®cant level ofcon®dence to make the assumption that the daily gain of the proxi portfoliofollows a Gaussian process which mean and standard deviation are estimatedempirically (m; ).Daily gain  m  uiui ! N 0; i 
*Performances are calculated for 100 dollar investment .Figure 14.11 Compared evolutions between 19 September, 1994 and 3 July, 1997
Figure 14.12 Empirical distribution of the daily gain of a proxi portfolio5.73 ]]7.2
8.67 ]
5.44;6.91;8.375;
9.845; 10.14 ]
[[[[
17.485 ]18.955 ]20.425 ]
[ 17.19;[ 18.66;[ 20.13;
[ 15.725; 16.015 ]
[ 14.255; 14.55 ]
[ 12.785; 13.08 ]
[ 11.315; 11.61 ]
4.265 ]
3.97;
1.325 ]
[
0.15 ]
0.445;[
2.795 ]
1.62 ]
1.91;[
1.03;
3.09 ]
3.38;[
2.5;
4.555 ]
4.85;
[
[
6.025 ]
6.32;
[
[
7.495 ]
7.79;
[
11.905]
[ 12.195;
8.965 ]
13.37 ]
[ 13.665;
10.435]
14.84 ]
[ 15.135;
9.26;
16.31 ]
[ 16.605;
[
17.78 ]
[ 18.075;
[ 10.73;
19.25 ]
< 20.72
[ 19.545;
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Advanced Trading Rules
We suppose that the perturbations are homoskedastics: Vui  8i. TheDurbin±Watson test shows that the perturbations are not autocorrelated:cov ui ; uj   0
8i 6 j
Under all these assumptions, we can conclude that the cumulative gain ofthe proxi portfolio follows a Gaussian process whose distribution is perfectlyknown.pCumulative gain i ! N im; i
We are able to compute the distribution of the return of Epsilon fund overany period of time and de®ne brackets in which Epsilon valorization has goodprobability to evolve.If we draw the real valorization of Epsilon since the beginning of the fund,we can note that it ®ts quite well with the anticipations that had been made atthe beginning (see Figure 14.13).The 30 per cent curve means that the fund has a probability of 30 per centto do less than the level indicated by the curve.Since the inception, we almost realized our objective (target at 50 per cent)with a realization between 40±50 per cent.Epsilon futures fund is today an indispensable instrument as its presence ina classic portfolio reduces the average risk while improving global return.Given the market diversi®cation which is used (short- and long-term interestrates, currencies, stocks and commodities) and speci®c strategies, the FCIMTcan be considered as a new autonomous asset class with no correlation withclassic investments.
14.6 PERFORMANCE FUTURES FUND AND BAREPCOMMODITIES FUTURES FUND14.6.1 Performance futures fundPerformance futures fund is a FCIMT with a capital guaranteed. Eachinvestor bene®ts from a principal guarantee at maturity date which is givenby BAREP on 100 per cent of the invested principal on the advisedinvestment period, which runs from 17 November, 1994, to 17 November,1997.Net asset value is actually above 200 million francs (50 million dollars), or142.000 francs per share. The trading concepts and the markets traded are thesame as for Epsilon futures fund. Only the global leverage of the fundchanges, because of the capital guarantee (see Figure 14.14).The other curb represents the linear-performance of a 3 years ratecalculated on 17 November, 1994.
NAV per share
Figure 14.13 Epsilon futures ± anticipation and actual
Money market rate of 7.32%
Actuarial yield: 14.29%Flat yield: 42.10%
Figure 14.14 Performance futures ± fund performance between 17 November, 1994 and 4 July, 1997
Flat yield
21.75%
Return of BAREP Commodities Futures (basis 100)
Figure 14.15 BAREP commodities futures fund performance between 22 July, 1996 and 5 November, 1997
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Advanced Trading Rules
14.6.2 BAREP commodities futures fundBAREP commodities futures fund is a new BAREP's product invested onlyin futures commodities. It started in July 1996 and the return is about 22 percent (Figure 14.15).We intervene simultaneously on the principal commodity futures marketsin the world: crude oil, natural gas, heating oil, NY harbour gasoline, sugar,coee, cacao, gold, silver, copper, corn, wheat, soybean, soybean oil, soybeanmeal, live cattle.
14.7 CONCLUSIONSSince 1994, BAREP has developed original, high value-added managementstrategies in the futures markets, based principally on trend-following tradingtechniques. Since the beginning, we conducted extensive research intotechniques for reducing the natural volatility of futures funds, which led tonew trading methods and greater diversi®cation of the contracts handled. Forexample, the Epsilon futures fund is now spread over 28 markets with 20management strategies per market. All in all, it requires nearly 600 strategiesto be followed in real time.
Chapter 15The need for performance evaluation intechnical analysisFELIX GASSER
15.1 INTRODUCTION15.1.1 Why I chose this subjectThe last ten years I have worked in the ®eld of computer-supported technicalanalysis, for a large commodity trading advisor (CTA), as a product managerfor technical analysis software and as trading system developer in the bankingindustry, including the 3 years in my current position at Credit Suisse PrivateBanking. During the course of developing and testing hundreds of tradingstrategies, my objective in these positions has always been the development ofbetter-performing trading strategies. This has increasingly led me to moreinvolved performance testing and to the development of proprietary performance-evaluation tools. Today, I feel con®dent that I can make a contribution to the ®eld and dedicate this chapter to the subject.15.1.2 The importance of performance evaluationTechnical analysis (TA) is de®ned as the analysis of pure market pricemovement as time series called charts. Although this is a clear de®nition,anyone who has read a book on TA knows it's not necessarily straightforward. If we include all the tools and theories labelled technical ± from thehighly scienti®c to the rather esoteric ± the subject can become controversialand confusing.The ¯ood of technical instruments has turned TA into an alchemist'smelting pot, resulting in scepticism especially among the academic community. On the other hand, the in¯ux from other disciplines, most of all statisticsand the computer sciences, has added powerful analytical tools, strengtheningthe position of TA as a valid discipline in the investment community andincreasingly in academia as well.
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Advanced Trading Rules
The question of who can now be the objective judge of what is valid andwhat is not can only have one answer. Consequently, it must be determinedby the resulting investment performance measured in dollars and cents. Validare those strategies which give us in the long run a ®nancial edge in themarket. It is the aim of this chapter to explain and highlight the importance ofperformance results as an instrument to evaluate indicators, strategies andmarket behaviour. I will discuss the pros and cons of standard performance®gures and add some of the tools I have developed.
15.2 TOOLS AND DEFINITIONS15.2.1 Trading report performance summaryThere is an increasing number of technical analysis tools on the market, suchas Trade Station and Metastock, which are two of the high-end packages.Most charting packages ± especially those included by data-service providers± are limited to visual display, without the option of a statistical performanceevaluation. The main handicap of visual charting is the deception of thenaked eye, when it subjectively tries to recognize pattern. On the other hand,a strategy de®ned as an algorithm in the form of a trading system producesclear-cut buy and sell levels, resulting in a detailed performance report indollars and cents. Regardless of what is used for analysis, whether a simplespreadsheet or complex proprietary software, one has to be concerned withthe same questions regarding performance ®gures. Accordingly, this chapteris not only aimed at the classical, visual chartist, but also at users of high-endanalytical tools, which provide ready-made performance statistics. While thesecond group especially runs the risk of drawing wrong and overly optimisticconclusions from their ready-made performance reports, the chartist may notknow the performance statistics of his or her trading approach at all.In the remainder of this section I present the reader with de®nitions ofperformance statistics and also some technical terms to describe marketconditions.15.2.2 Definitions of performance dataf Net pro®t: The total amount of dollars made or lost by a trading strategyduring an observed test period (see details in Section 15.3.1).f Max drawdown: The drawdown is the equity decrease from a previousequity high. The max drawdown is the dollar amount (or better, thepercentage) of the largest equity drop. Remember the drawdown inpercentage is not symmetric, a 50 per cent drop needs a 100 per cent
The need for performance evaluation
421
recovery to equal the same net equity. The unrealized largest drawdown ofa single trade is called the maximum adverse excursion (see details inSection 15.3.2).f Runup: The opposite of the drawdown, the max runup is a strategy'smaximum pro®t gain during the course of trading. The runup during asingle trade is the maximum pro®t potential called the maximum favourable excursion of a trade.f Trade eciency:Long trades  (exit price entry price)/(highest ± lowest price)Short trades  (entry price exit price)/(highest ± lowest price)Trade eciency measures the eciency as a percentage of how close to thetop and bottom within a trade the entry and exit was placed. Unrealizedrunups, for example, are accounted with a loss of eciency. Unfortunatelythe price moves before the entry and after the trade exit are not accountedfor, which severely limits the value of the eciency numbers. This excludesopportunity losses before a potential trade and after an actual trade.Stopped-out trades, on the other hand, are considered to exit at the lowestand worst level of a trade and are not credited for avoiding what couldhave been a possibly ruinous equity drop. This results in consistent lowerratings for the exit-eciency versus the entry-eciency and severely limitsthe use of trade eciency ratings as a whole.f Largest loser: This is the largest losing trade and can be directly controlledwith the stop-loss.f Average pro®t per trade: The average pro®t or loss of all winning andlosing trades. This ®gure is especially crucial for short-term and intra-daytrading and must be large enough to account for all trading costs (seeSection 15.3.3).f Per cent pro®table: The percentage of winning trades produced by atrading strategy. Trend-following strategies have a winning percentage of35±45 per cent. Although they have more losing trades, these strategies arepro®table because winners are larger than the more frequent, but smaller,losers. These strategies are much less focused on predicting the next marketmove, but more on letting their pro®ts run. A percentage under 30 per centis dangerous and carries a high probability of ®nancial ruin. There are fewstrategies with over 50 per cent winning trades because they need the rarelysuccessful element of predicting the next market direction after trade entry.Strategies with over 50 per cent should be carefully performance tested.They are usually a result of over-optimization (curve ®tting), or too tightlyset stop-losses, resulting in many winners, which are critically smallercompared to losers.f Average winner to loser: This is the counterpart performance ®gure of per
422
Advanced Trading Rules
cent pro®table and measures the ratio of the size of winners to losers. Anaverage winner to loser of 2.5 would mean that winners are, on average,2.5 times bigger than losing trades. For all strategies with 35±50 per centwinning trades, we look for a ratio over 2. Anything under 1.5 can again beruinous.f Number of trades: The number of trades is crucial for statistical relevance.In a random environment, we would need at least 30 trades for a soundstatistical sample. Since we often carry out testing in a non-randomenvironment (hopefully so) of unknown distribution, we look for as manytrades as possible before we draw conclusions regarding the robustness andpro®tability of a strategy. Since