a competitive trading environmentcharacterized by diminishing pro®t margins, in hand with growing computingpower, we cannot forfeit the analytic advantage available to anyone with acomputer. This is an appeal to test everything you use in technical analysis,the observed market, the trading strategy or indicators and the evaluationtool itself. One should understand not only the indicators and trading systemsthat are applied, but also the analytical data used for evaluation. The moretransparent everything is ± from strategies to evaluations ± the greater thechance that future performance will be in line with expectations.Although I have tried to address all the relevant performance measurement®gures of trading in this chapter, it cannot be regarded as conclusive to thesubject. Performance evaluation is an ongoing process that is changing alongwith the evolution of markets and the trading tools. Everyone who needs tomaintain an edge in the market cannot stop developing and testing on acontinuing basis.GLOSSARYAlgorithm The naked formula of a strategy. This can be the basis for atrading strategy or an indicator (i.e. a moving average, average(price,length)).Degrees of freedom Every rule uses a degree of freedom with the eect that
The need for performance evaluation
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strategies with a lot of variables and rules use up a great deal of freedom andbecome less general and robust in changing market behaviour.Indicator Visual display of an algorithm or trading strategy in the form oflines.Methodology Trading method.Money management How much money we risk on a trade. MM de®nes thesize of the trade and, with it, the risk we assume with respect to our totaltrading capital.Optimization The search for the best-performing parameter.Parameter The number entered as input in indicators or strategies.Robustness The reliability of a trading strategy to perform steadily indierent market conditions and in the future. We look for robustness oruniversality in trading strategies.Slippage The dierence between the actual traded price and the trade signalprice calculated by the computer.Stationarity A time series is stationary if the underlying rules that generateit do not change over time. Non-stationary distributions change theirprobability distributions over time. This is the case in trading. An exampleof a stable probability distribution would be a casino game like roulette.Trading system Algorithm or trading strategy that results in trading signalsplacing orders in the market.Variables All elements of an indicator or a strategy that allow dierentde®nitions or inputs.FURTHER READINGKaufman, J.P. (1998) Trading Systems and Methods, John Wiley, Chichester.Peters, E.E. (1994) Fractal Market Analysis, John Wiley, Chichester.Schwager, D.J. (1998) Managed Trading, John Wiley, Chichester.Sherry, J.C. (1992) Mathematics of Technical Analysis, Probus Publishing Company, London.Vince, R. (1995) The New Money Management, John Wiley, Chichester.
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Index
Accuracy, 250, 252, 254, 257±61Active strategies, 174±81Adverse selection, 313, 336Agricultural commodity market, 382±3,387Akaike information criterion (AIC),252±4, 335Algorithm, de®nition, 438Annualized cumulative gain (ACG),255±61ARCH, 144±7, 154, 249see also Conditional heteroskedasticityArti®cial neural networks (ANN),249±61benchmarking, 249±50, 257forecasting accuracy, 250, 252, 254,257±61modelling procedure, 251±4results, 255±61Asset allocation, 113±20, 126, 377±8,398±404Asset pricing models, 112, 120, 155, 169,171, 288Asset returns, 153, 157±64Asymmetric information, 312±13Asymmetry:in ®nancial time series, 153±4of stock returns, 154±5
Autocorrelation, 113, 288±9, 349Autoregressive models, 125±30, 131,136±9, 147, 324Average pro®t per trade, 429±31de®nition, 421Average winner to loser, de®nition,421±2Averaging process, 357Back propagation multi-layerperceptron (MLP), 250, 257±9BAREP futures funds, 388±48, 388±418asset management structure, 388organization, 388±91Benchmarking, 208, 249±50, 257, 409±11Bid-ask spread, 352Black noise, de®nition, 422Bootstrap methodology, 7, 8±18, 20±1,37, 104, 152±3Bounce, 270±1Broadening pattern, 54, 59Brokerage, 393Buy-and-hold strategies, 29±35, 37,174±81, 345, 350±4CAPM, 112, 120CAPM beta, 29, 37Central banks, 276, 286, 288Channel rule, 135
442
Index
Chaos theory, 249, 364Chartist techniques, 249, 264±5, 266±9,398, 420Commissions des OpeÂrations de Bourse(COB), 404Commodity Futures and TradingCommission (CFTC), 368Commodity trading advisors, 368±75,379±80management, 378±9markets traded, 379±80, 382±6measures of performance, 368±75selection and allocation process,377±8trading style, 373±5, 377, 379, 380±6,387Conditional distribution, 323±4, 325±34Conditional heteroskedasticity, 8, 144±7,349see also ARCH; GARCHContinuous reproduction, 347, 349Contrarian strategies, 361±3, 398Cost, 368Crossover operator, 347Crowd psychology, 155CRSP index, 29±36, 37Currency appreciation, 187Currency depreciation, 209Customer accounts, 320Decreasing ineciency (DI), 317±18Degrees of freedom, de®nition, 438±9Directional strategies, 122±47, 174±81Discretionary trading, 1, 374, 379,380±6, 387Distribution, see Return distributionDiversi®cation:CTAs, 374, 377, 381±2managed futures, 367, 368, 376±7,379±80, 398±404Double top and bottom patterns, 55, 62Drawdown, 30, 313, 355, 356, 393,420±1, 426±9de®nition, 420±1
Drift, 22±3, 127±9, 136±8, 139±41, 142±4Dynamic strategies, 1, 28±36, 112±13Ecient frontier, 376Ecient markets, 2, 154, 276, 288, 297Emerging markets, 112±20Endogenous trading rules, 296±303Energy traders, 383Equal weight portfolio, 113, 116Equity curve trading, 437Equity traders, 383Error accounts, 320, 322, 324, 325±7Exchange Rate Mechanism (ERM), 279,286, 288Exogenous trading rules, 296±303Expected rule returns, 122±47, 169±71ARCH model, 144±5autoregressive models, 125±30, 136±9and conditional heteroskedasticity,144±7of directional forecasters, 122±47GARCH model, 146Gaussian process, 126±30, 131, 136,142±4, 147maximizing, 129±30Monte Carlo simulations, 145±6and moving-average based rules,135±44price-trend model, 136, 139±41, 145±6random walk, 128, 136, 137, 147in UK stock and futures markets,169±71FCIMTs, 404, 414Filter rules, 274, 275, 276implementing, 265±6measuring returns, 269pro®tability, 271±3Financial time series, 153±4Financial traders, 383±4Fitness, 350±2Forecasting strategies, 122±47, 174±6,255±61, 288±9, 296±300Foreign exchange markets, 6±38,
Index183±244, 250, 255±61, 265,279±96ANN model forecasts, 250, 255±61autocorrelation, 288±9discretionary or systematic traders,384±5Garch model, 18±19, 23head-and-shoulders rule, 265interest rate dierentials, 22±3, 37,187, 207, 209, 279±80, 289±96kurtosis, 285±6Long±Short Across trading rules, 184,185, 204, 208interest rate strategies, 206, 209,218, 219, 237, 244momentum strategies, 206, 219moving-average rules, 206, 208,209, 218, 219, 237, 244Long±Short Within trading rules, 184,185, 204, 208, 219interest rate strategies, 205, 218,219, 237momentum strategies, 205, 206moving-average rules, 205±6, 208,218, 219, 237market ineciency, 218moving-average rules, 184±5random walk model, 8-18regime shift bootstrap, 9, 20±1, 37simulated method of momentsestimates, 23±8Forward premiums, 280Fractional Gaussian process, 136, 142±4France, Treasury bond future market,320±36FT100 futures market, 155, 169, 170FT100 index, 153, 155, 169, 170±1Fund managers, 313±17, 318, 336see also Commodity trading advisorsFund providers, 313±17, 336Funds:hedge, 286see also Managed futuresFutures, see Managed futures; S&P 500futures
443
Futures market:French Treasury bond, 320±36FT100 futures market, 155, 169, 170LIFFE, 280GARCH, 113, 146±7, 153, 249trading rules model, 8±9, 18±19, 23, 37see also ConditionalheteroskedasticityGaussian kernel, 48Gaussian process, 123, 126±30, 131, 147,414fractional, 136, 142±4Genetic algorithms, 345±64advantages, 347basic features, 346±9or buy-and-hold strategy, 345, 350±4trading rules evolved from, 345±6,348, 349±52, 363±4Genetic programming, 348±9, 363Genomes, 347, 348Global Financial Database, 186Global investment, 368Goodness-to-®t tests, 63±4, 65, 84±93Head-and-shoulders rule, 53±4, 58,264±76de®ning and identifying, 266±9measuring returns, 269±71noisy, 274±5, 276pro®tability, 271±3pro®tability increment, 273±5stand alone, 273, 275Hedge funds, 286Hedging, 185, 319, 363±4Heteroskedasticity, see ARCH;Conditional heteroskedasticity;GARCHHorizon analysis, 373Incentive compatability, 315±17Indicator, de®nition, 439
444
Index
Ineciency, see Decreasing ineciency(DI); Market eciencyInformation, asymetric, 312±13Information theory, 312±13Interest rate dierentials, foreignexchange markets, 187, 207, 209Interest rate traders, 385Interest rates, 22±3, 37, 279±96autocorrelation, 288±9and foreign exchange market, 22±3,37, 279±96Interest-adjusted currency returns, 218International corporations, 288Investor reaction, 357±9, 363±4JP Morgan Global Bond, 409±11Kernel regression, 47±51, 55±7selection of bandwidth, 48±51Kleinwort Benson Investment (KBMI)averaged portfolio, 113, 116±17Knight±Satchell±Tran process, 154±5,157±64, 168± 9, 171Kolmogorov±Smirnov test, 64±5,93±104, 105±8Kurtosis:in currency and interest rate markets,285±6in exchange rate shifts, 9±10, 15±17in mean-variance analysis model, 112and portfolio strategies, 175, 178±9,181Lags, 156, 252±4, 297Largest loser, de®nition, 421Leverage, 28, 398, 404LIFFE futures market, 280Limited liability:CTAs, 368traders, 316, 317, 318Linear rules, 131±3, 134, 144±7Linguistic barriers, technical analysis,42±3Liquidation rule, 316±17, 318
Local polynomial regression, 51Lognormal-normal subordinatedprocess, 154Long±Short Across trading rules, seeunder Foreign exchange marketsLong±Short Within trading rules, seeunder Foreign exchange marketsLosses, 325±34see also Stop-loss rulesManaged futures, and multiple CTAs,367±87asset allocation, 377±8diversi®cation, 367, 368, 376±7measuring performance, 368±75Mapping studies, 393±4Market conditions, de®nitions, 422±3Market eciency, 2, 154, 218, 276, 288,297Market equilibrium, 319, 337Market ineciency see Market eciencyMarkowitz optial portfolio, 114, 115±18,119±20MATIF SA data, 320Max drawdown, 420±1, 426±9de®nition, 420±1Mean reversion, 323±4, 325±7, 330, 336Mean-variance analysis, 112±20Metal traders, 385Methodology, de®nition, 439Minimum variance portfolio, 113±14,115±18, 120, 301, 376Modern Portfolio Theory, 2, 376±7Momentum, 244Momentum indicators, 133Momentum strategies ± foreignexchange markets:Long±Short Across trading rules, 206,219Long±Short Within trading rules, 205,206Monetary de®nition of trend, de®nition,422
IndexMoney management, 398±404, 429,430de®nition, 439Monte Carlo simulations, 104, 126,145±6Moral hazard, 313±18, 336Morgan Stanley Global Equity, 409±11Moving-average rules, 10±15, 28±36,135±44, 152±71, 288±9, 296±9arithmetic, 156and expected rule returns, 135±44foreign exchange markets, 184±5geometric, 155, 156±7, 164±9implementation tests, 28±36length, 10±11, 13long-run, 205Long±Short Across trading rules, 206,208, 209, 218, 219, 237, 244Long±Short Within trading rules,205±6, 208, 218, 219, 237naive, 154±5, 159±64random walk, 10±15and sequential trading strategies,154±5, 158±64, 168±71short-run, 205spot currency exchange rates, 288and time lags, 156, 297as trading signal, 152±71MSCI currency index, 208Multi-advisor portfolios, 367, 376±7,379±80Multi-market portfolios, 402±4, 405, 418Multivariate normal distribution, 175,179±80Myopic strategy, 113Nadaraya±Watson kernel estimator, 48Naive trading rules, 154±5, 159±64, 266Neo-classical theory, 319, 320, 323±4,327, 336Net pro®t, de®nition, 420Net pro®t, total, 420, 423±6Neural networks, see Arti®cial neuralnetworks (ANN)Noise, 45, 274±5, 276, 325, 357, 359
445
black, 422pink, 423, 434white, 423, 435Non-pro®t maximization, 276Nonlinearity, 135, 249Normal distribution:bivariate, 176±9, 181multivariate, 175, 179±80Null models:currency market, 8±28, 37moving average rule, 152±3Optimal investment size, 429Optimization, 312, 347, 431±2, 434,436±8de®nition, 439Option rule returns, 126Options market, 345±6, 359±63Out-of-sample trading rules, 361Own accounts, 320Parameter, de®nition, 439Parity theorem, 281Partial correlation function (PACF),252±4Pattern recognition, 43±106automation, 52±62de®nitions of patterns, 53±5smoothing estimators, 45, 46±51kernel regression, 47±51see also Technical analysisPer cent pro®table, de®nition, 421Performance, 114±20, 301±3, 322±4, 367,368±75average pro®t per trade, 429±31commodity trading advisors, 367,368±75de®nitions of market conditions,422±3de®nitions of performance data, 420±2drawdown and max drawdown,420±1, 426±9Epsilon futures funds, 405, 409±11
446
Index
Performance (cont.)evaluation in technical analysis,419±39importance, 419±20mean-variance analysis model, 114±20measures of, 301±3, 368±75robustness tests, 431±8optimization of diversi®edparameters, 436±8parameter diversi®cation, 435±6parameter selection anddistribution, 431±5and stop-loss strategies, 322±4total net pro®t, 420, 423±6trading report performance summary,420Performance data, de®nitions, 420±2Performance Futures Fund, 414Persistence, 18±19, 20, 154±5, 162±3Pink noise, 434de®nition, 423Portfolio distribution, 174±81Portfolio insurance strategies, 126, 313Portfolios:equal weight, 113, 116Markowitz optimal, 114, 115±18,119±20minimum variance, 113±14, 115±18,120, 301, 376multi-advisor, 367, 376±7, 379±80multi-market, 402±4, 405, 418performance monitoring, 367±8proxi simulation, 411±14rebalancing, 113, 114-15, 117, 119, 319Price signals, 123±4, 133±5, 345±6,357±64Price-trend model of expected returns,145±6Principal-agent model, 313±31, 336Probability curves, 411±14Probability distribution, see ReturndistributionPro®t maximization, 129±30, 313±14,336
Pro®ts:head-and-shoulders rule, 264±76incremental, 273±5stop-loss rules, 325±34up and down futures markets, 368very low, 334±6see alsoExpected rule returnsOption rule returnsRealized returnsReturnsRule returnsProxi portfolio simulation, 411±14Put-call ratio, 359, 360±3Put-option strategy, 126, 313, 359Quadratic minimization, 300±1Random walk:active or passive strategies, 176±9, 181asset prices, 155, 169, 171, 288expected returns, 123, 128realized returns, 153technical trading rules, 8, 10±18Rational expectations, 312Realized returns, 152±4, 157±64, 164±9see also ReturnsRebalancing, 113, 114±15, 117, 119, 319Rectangle pattern, 54±5, 61Refco trader evaluation system, 367,368±75, 376, 378±9, 380Regime shifts, 9, 20±1, 37Return distribution:bivariate normal, 176±9, 181conditional, 323±4, 325±34elliptical, 175, 179±81Gaussian, 126linear, 144±7multivariate normal, 175, 179±80realized returns, 153±4, 157±64, 164±9trading rules and risk-free assets,28±36truncated bivariate, 126, 147variance, 127, 129
IndexReturn signals, 133-5Returns:realized, 152±4, 157±64, 164±9riskiness, 15±17rule, 122±47see alsoExpected rule returnsOption rule returnsPro®tsReturn distributionRisk, 15±17, 244, 302, 319, 320, 355±6measure of, 302, 355, 356monitoring, 368neo-classical theory, 319, 320returns and degree of, 15±17trading rule, 355±6Risk management, 430Risk-free assets, 28±36Risk-return portfolio pro®le, 367, 376Robustness, de®nition, 439Rule returns, 122±47see alsoExpected rule returnsOption rule returnsRules, see:Filter rulesHead-and-shoulders ruleMoving-average rulesStop-loss rulesTechnical trading rulesTrading rulesRunup, de®nition, 421S&P 100 index (OEX), 359±60, 363S&P 500 futures, 345±64buy-and-hold strategies, 345, 350±4conditional heteroskedasticity, 349and genetic algorithm evolved rules,345±6, 348, 349±52, 355±6, 363±4S&P 500 index (SPX), 348, 359±60, 363Sequential trading strategies, 154±5,158±64, 168±71Serial dependency, 122
447
Sharpe ratio, 117±18, 120, 302±3, 355,369, 393in ANN forecasting model, 255±61Signals, see:Price signalsReturn signalsTrading rule signalsSilver, 435Simulated method of moments, 23±8Skewness, 9±10, 15±17, 112Slippage, 393, 398de®nition, 439Smoothing estimators, 45, 46±51kernel regression, 47±51Softs traders, 385Soros, George, 286Spot currency price, 280±96autocorrelation, 288endogenous and exogenous forecasts,299, 303kurtosis, 285±6Standard and Poor, see S&P 500 futuresStationarity, 431de®nition, 439Stochastic models, 122±47, 153, 157±64,176±9Stock index traders, 385±6Stock markets:UK, 169±71US, 28±36Stop-loss rules, 270, 312±37, 393de®nition, 319±20distribution of pro®ts and losses,323±4, 325±34empirical results, 324±36and market equilibrium, 319, 337mean reversion behaviour, 323±4,325±7, 330, 336and neo-classical theory, 319, 320,323±4, 327, 336performance, 322±4principal-agent model, 313±17, 336test for existence of, 319±24Strategies:active, 174±81
448
Index
Strategies (cont.)buy-and-hold, 29±35, 37, 174±81, 345,350±4contrarian, 361±3, 398directional, 122±47, 175dynamic, 1, 28±36, 112±20forecasting, 122±47, 174±6, 255±61,288±9, 296±300leverage, 28portfolio insurance, 126, 313put-option, 126, 313, 359sequential, 154±5, 158±64, 168±71see