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Cash flow
DaysFigure 12.5 The cumulative cash balance for a portfolio of 100 trading rules for S&P 500 futuresduring the test period from December 1988 to August 1993. The horizontal axis corresponds to thetrading days and the vertical axis to the cumulative cash balance. The thick line corresponds to theportfolio of trading rules and the thin line to the buy-and-hold strategy
12.4.2 Trading rule riskMeasuring the trading rule risk is obviously important. So far, the resultsindicate that the trading rules led to slightly higher pro®ts in the out-ofsample period than a simple buy-and-hold strategy. The dierence is notgreat, however, and there have been periods of up to two years when therules' performance lagged the passive holding policy. Even the small increasein the pro®ts might, of course, be due to bearing increased risk. On the otherhand, even matching the market would be a good result if the rules reducedrisk. The trading rule risk is measured below by the Sharpe ratio and by themaximum drawdown of the cash balance. The results are compared to thebuy-and-hold strategy. The risk measures are also computed for a portfolio oftrading rules, with the signals aggregated into a daily net position.The Sharpe ratios were computed for the average cash ¯ow in successivetwenty-day periods, corresponding roughly to monthly cash ¯ows (the resultswere similar for dierent periods). The annualized Sharpe ratio for the buyand-hold strategy in the test period was 0.63. The average Sharpe ratio for the100 trading rules was 0.79. Had the rules been used as portfolio, the Sharperatio would have increased to 1.15. Based on these results, the trading rulesdo not appear to be particularly risky.
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DrawdownFigure 12.6 The distribution of the maximum drawdown for the 100 trading rules for S&P 500futures during the test period from December 1988 to August 1993. The drawdown is de®ned as thegreatest decline in the cumulative cash position before a new high balance is reached
Another measure of risk often used in practice is the drawdown of equity.Here, the maximum drawdown was de®ned as the greatest decline of the cashposition before a new high balance was reached. For the buy-and-holdstrategy, the maximum drawdown of 40 675 dollars occurred between 9October, 1989 and 10 October, 1990. The average drawdown for the tradingrules was 41 343 dollars (the median was 39 187 dollars). The drawdownranges from 22 215±81 300 dollars. As Figure 12.6 shows, the distribution isskewed. The drawdown was bigger than for the passive strategy for only 39rules out of the 100. Again, diversi®cation across the rules is advantageous, asthe maximum drawdown for the portfolio was 33 703 dollars (between 19July, 1990, and 11 October, 1990), smaller than for an average trading rule.Using the risk measures considered earlier, it appears that the trading rulesare not more risky than a buy-and-hold strategy. Moreover, a signi®cantreduction of risk (30 per cent lower volatility) can be achieved by combiningthe rules into a portfolio, where the daily net position is aggregated across therules. Despite the relatively low volatility, however, the trading rules do carrya risk of underperforming the market for long periods of time. There is alsothe possibility that the trading rules make money by assuming a risk of beingon the wrong side of the market on rare occasions, and the risks were simplynot realized during the relatively short test period.
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12.5 ANALYSING TRADING RULE SIGNALSSo far, we have found that the trading rules found by the genetic algorithmled to pro®ts comparable to a buy-and-hold strategy but with somewhatsubdued volatility. The next question we address is how did the trading rulesachieve their performance, i.e. what kinds of price patterns did they rely on?We start by looking at the daily cash ¯ow in `event time', i.e. time relative tothe trading rule signals. This is done by labelling each day relative to thesignal, and averaging the cash ¯ows across the rules and across the eventdays. As shown below, a surprisingly clear pattern emerges when we look atprices in this way. Of course, the pattern is only evident because the averagingprocess cancels out much of the noise in the market; any individual tradingrule signal is unlikely to be preceded by an equally smooth return sequence.This section only looks at the average behaviour of the 100 rules that weresaved. While this helps to smooth out the noise in the data, it also masksindividual dierences. A more detailed analysis for dierent groups of rules ispresented by Karjalainen (1994).12.5.1 Price patternsFigure 12.7 shows the cash ¯ow in event time for transitions from long toshort positions, averaged across the 100 rules for each day. For instance, cash¯ow for day 1 is the average cash ¯ow on the last day in a long position, day2 the cash ¯ow on day next to last, etc. Similarly, day 0 is the ®rst day in ashort position, day 1 the second day, etc. Figure 12.7 indicates that the rulestend to switch from a long position to a short one after a sequence of positivereturns, triggered ®nally by an exceptionally large price increase. Figure 12.8shows the transitions from short to long positions, with days labelled in asimilar manner. It appears that the rules switch from a short position to along one after a day or two of negative returns, triggered by a large pricedecline. Although ®gures are omitted to save space, very similar patterns werealso evident in the training period.The observed price patterns suggest that the trading rules at least partlyrely on the reversal of returns on a short horizon. These ®ndings areconsistent with evidence from stock markets. For instance, Bremer andSweeney (1991) found that daily stock returns smaller than 10 per centare partially reversed during the following two days. Brown, Van Harlow andTinic (1988) reported that returns smaller than 2.5 per cent rebounded by acumulative 0.53 per cent by the 60th day after the event. For a summary ofrelated evidence, see De Bondt and Thaler (1989).One possible interpretation of these ®ndings is an overreaction by investorseither to news or to recent price changes themselves (there is evidence that
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Day
Figure 12.7 The average daily cash ¯ow in event time for transitions from long to short positionsfor the 100 trading rules for S&P 500 futures during the test period from December 1988 to August1993. The horizontal axis corresponds to the event time, relative to the signal on day 1. The verticalaxis corresponds to the average cash ¯ow for each event day (500 times the price change). Thedashed horizontal line indicates the average daily cash ¯ow for the 100 rules
Cash flow
Day
Figure 12.8 The average daily cash ¯ow in event time for transitions from short to long positionsfor the 100 trading rules for S&P 500 futures during the test period from December 1988 to August1993. The horizontal axis corresponds to the event time, relative to the signal on day 1. The verticalaxis corresponds to the average cash ¯ow for each event day (500 times the price change). Thedashed horizontal line indicates the average daily cash ¯ow for the 100 rules
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investors ®nd recent price movements salient information that they take intoaccount when making decisions; see Schachter et al., 1987). As newinformation comes in, returns are partially reversed as investors realize thatthe initial reaction was disproportionate. Put another way, sometimes theprices are moved by `noise', and the price movements without a fundamentalreason are then corrected over the next couple of days. However, one shouldkeep in mind the fact that the time period considered here is relatively short.As alluded to above in the section on trading rule risk, it is possible that largereturns that the rules bet against do sometimes lead to even larger returnswhich justify the initial reaction of the markets. The rules may have simplymade money because they assumed the risk of rare events that just did notmaterialize during the training or test periods.12.5.2 Option trading activityIf the price patterns observed earlier re¯ect overreaction by the markets,assessment of investor sentiment becomes important. Option data areparticularly interesting in this respect, since option markets oer a moredetailed picture of market behaviour that can be achieved by looking at theunderlying market alone. In this section, we study volume and open interestdata for options to see where there are any regularities corresponding to theobserved price patterns and the timing of the trading rule signals.In the past, researchers have usually looked at a so-called `put-call ratio',i.e. the ratio of put option volume to call volume, sometimes smoothed bytaking a moving average. The reasoning behind the ratio is that when tradingis concentrated on the put options (i.e. the put-call ratio is high), investorsentiment is bearish. From a contrarian viewpoint, this is considered to be abuy signal. Similarly, a low put-call ratio is thought to be an indicator orbullish sentiment, which is taken as a signal to sell. Billingsley and Chance(1988) tested two such indicators using data from the S&P 100 options, butfound no evidence of abnormal stock market returns after transaction costs.Chance (1990) showed that the correlation between the S&P 500 return andthe put-call ratio was largely contemporaneous. However, he also found thatsome of the trading strategies he tested were at least marginally pro®table,especially in futures where transaction costs are low.There are several active markets for options related to S&P 500 futures,including options for the S&P 100 index (OEX), options for the S&P 500index (SPX), as well as options for the futures themselves. Of these threemarkets, the S&P 100 options are the most liquid, being in fact the mostactively traded option market in the world. There is also evidence that OEXoptions are actually priced o the S&P 500 futures (Figlewski, 1988). Because
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trading volume and open interest data for all the tree markets are highlycorrelated with one another, OEX data was used in the following tests.Using a methodology similar to looking at cash ¯ows in event time, weanalysed the option data relative to the trading rule signals during the testperiod from December 1988 to August 1993. Put-call ratios were formed forboth the trading volume (as in the previous research) and for open interest. Inthe trading volume put-call ratio, there was indeed a pattern where put-callratio declines to its trough on the precise day that the rules switch over from along position to a short one, and bounces back during the next few days.Similarly, the put-call ratio achieved its peak on the day when the rules send abuy signal.While the volume data were suggestive, the open interest data turned out tobe even more revealing. Figure 12.9 shows the open interest put-call ratio(PCO) in event time. For transitions from long to short positions, the put-callratio steadily increases before the trading rule signal, and keeps growing foranother three to four days afterwards. Figure 12.10 shows that the pattern forbuy signals is essentially a mirror image from the sell signals. Were the two®gures pasted together, we would see a pattern very much resembling asinewave, with the put-call ratio ¯uctuating from peak to trough, with the
PCO
DayFigure 12.9 The open interest put-call ratio (PCO) in event time for transitions from long to shortpositions for the 100 trading rules for S&P 500 futures during the test period from December 1988 toAugust 1993. The horizontal axis corresponds to the event time, relative to the signal on day 1. Thevertical axis corresponds to the average put-call ratio for each event day. The dashed horizontal lineindicates the average put-call ratio for the 100 rules
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PCO
DayFigure 12.10 The open interest put-call ratio (PCO) in event time for transitions from short tolong positions for the 100 trading rules for S&P 500 futures during the test period from December1988 to August 1993. The horizontal axis corresponds to the event time, relative to the signal on day1. The vertical axis corresponds to the average put-call ratio for each event day. The dashedhorizontal line indicates the average put-call ratio for the 100 rules
curve punctuated by the trading rule signals at the midpoint between theextremes.Figures 12.11 and 12.12 show the open interest put-call ratio during thecombined training and selection period. The option data exhibit patterns verysimilar to the test period. This suggests that the trading rules worked out-ofsample because the market behaved similarly across the dierent periods.There is some evidence, however, of a fastened pace in the markets. The peaksand troughs tend to follow each other with a higher frequency in the testperiod, compared with the more tranquil training years. The trading volumedata are also largely similar to the test period, except that the put-call ratioachieves its extrema one to three days after the signal.To summarize the analysis of the trading rule signals, it was found that therules made bets against the market, stepping in and buying when prices felland selling after large price increases. In the time period studied here, thestrategy was pro®table because large returns were partially reversed after afew days. A study of option data on a related market showed that the rulesheld long positions when the open interest and volume was concentrated oncall options, and were short when the option trading activity was focused onputs. The results are consistent with a contrarian view of the markets where
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Day
Figure 12.11 The open interest put-call ratio (PCO) in event time for transitions from long toshort positions for the 100 trading rules for S&P 500 futures during the training and selection periodsfrom June 1983 to November 1988. The horizontal axis corresponds to the event time, relative to thesignal on day 1. The vertical axis corresponds to the average put-call ratio for each event day. Thedashed horizontal line indicates the average put-call ratio for the 100 rules
PCO
DayFigure 12.12 The open interest put-call ratio (PCO) in event time for transitions from short tolong positions for the 100 trading rules for S&P 500 futures during the training and selection periodsfrom June 1983 to November 1988. The horizontal axis corresponds to the event time, relative to thesignal on day 1. The vertical axis corresponds to the average put-call ratio for each event day. Thedashed horizontal line indicates the average put-call ratio for the 100 rules
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bullish sentiment precedes price declines and bearish sentiment peaks beforeprice increases. While the observed patterns may be due to rational hedgingactivity, the fact remains that the patterns are there, even though the optiondata were not used as inputs to the genetic algorithm. The patterns werestable throughout the years, allowing the algorithm to ®nd rules in thetraining period that generalized to an out-of-sample test period.12.6 CONCLUSIONSIn this chapter, a variant of genetic algorithms called genetic programmingwas used to ®nd technical trading rules for S&P 500 futures, using daily pricesas inputs. The rules were found using a training period from March 1983 toDecember 1986, and one rule from each of the 100 trials was saved as long asit also worked in a selection period from March 1987 to December 1988. Therules were tested out-of-sample from March 1989 to September 1993. It wasfound that the rules led to pro®ts slightly higher than the buy-and-holdstrategy in the test period, with smaller realized risk. The rules were typicallycontrarian, betting against large price movements. There were also identi®able patterns in the put-call ratios for related S&P 100 index (OEX) options.In particular, the volume and open interest were systematically higher in calloptions than in put options before the rules switched from long to shortpositions, and vice versa.The results indicate that the trading rules found by a genetic algorithm ledto higher risk-adjusted pro®ts than a passive holding policy in the out-ofsample test period in one of the most ecient ®nancial markets. However, itwould be premature to claim that such rules could be expected to consistently`beat the market'; perhaps they simply made pro®ts by assuming a risk of rareevents that did not materialize during the time period we studied. Even if thatwere not the case, the rules still had to bear the risk of underperforming themarket for periods of up to two years. For investors with the S&P 500 indexas the benchmark, such rules might not be very attractive. Nevertheless, theresults certainly encourage further applications of genetic algorithms in®nance. In developing practical trading rules one would probably not wantto limit oneself to using past prices only in the information set.From a theoretical viewpoint, the ®ndings about the option put-call ratiossuggest that there is a link between changes in investor sentiment and tradingrule signals. The results are consistent with overreaction of investors either tonews or to price changes themselves. However, without a more detailed studyof the motivation and actual decisions of investors in these markets we cannotactually show that the price patterns we found are caused by irrationalchanges in investor sentiment; it is possible that patterns re¯ect rational
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hedging activity. Still, the fact that the patterns in option data exist and areconsistent across training and test periods implies that the trading rule resultsare not (even inadvertently) caused by data snooping or over®tting. In otherwords, there are genuine patterns in market behaviour based on past pricesonly, and genetic algorithms oer one way of ®nding these patterns. We arenot claiming that there is a deterministic mechanism that drives the market, asa simplistic application of chaos theory would imply. Rather, it seems thatinvestors' reactions to either exogenous information (news) or endogenousinformation (recent price changes) follow patterns that are systematic enoughto detect when one looks at a suciently large number of events that triggertrading rule signals.REFERENCESAllen, F. and Karjalainen, R. (1993) Using genetic algorithms to ®nd technicaltrading rules, Rodney L. White Center, The Wharton School, University ofPennsylvania, Working paper, 20±93.Antonisse, H.J. (1991) A grammar-based genetic algorithm. In Foundations ofGenetic Algorithms (ed. G.J. Rawlins), Morgan Kaufmann, San Mateo, California, pp. 193±204.Arthur, W.B., Holland, H.J., LeBaron, B., Palmer, R. and Taylor, P. (1996) Assetpricing under endogenous expectations in an arti®cial stock market, Santa FeInstitute, Santa Fe, New Mexico, Working paper 96±12±093.Bauer, R.J. Jr. (1994) Genetic Algorithms and Investment Strategies, Wiley, NewYork.Beasley, D., Bull, D.R. and Martin, R.R. (1993) An overview of geneticalgorithms: part I, fundamentals, University Computing, 15, 2, 58±69.Billingsley, R.S. and Chance, D.M. (1988) Put-call ratios and market timingeectiveness, Journal of Portfolio Management, Fall, 25±8.Bremer, M. and Sweeney, R.J. (1991) The reversal of large stock-price decreases,Journal of Finance, 46, 2, 747±54.Brock, W., Lakonishok, J. and LeBaron, B. (1992) Simple technical trading ruleand the stochastic properties of stock returns, Journal of Finance, 47, 5, 1731±64.Brown, K.C., Van Harlow, W. and Tinic, S.M. (1988) Risk aversion, uncertaintyinformation and market eciency, Journal of Financial Economics, 22, 355±85.Chance, D.M. (1990) Option volume and stock market performance, Journal ofPortfolio Management, Summer, 42±51.Colin, A.M. (1994) Genetic algorithms for ®nancial modeling. In Trading on theEdge (ed. G.J. Deboeck), Wiley, New York, pp. 148±73.Davis, L. (1994) Genetic algorithms and ®nancial applications. In Trading on theEdge (ed. G.J. Deboeck), Wiley, New York, pp. 133±47.Deboeck, G.J. (ed.) (1994) Trading on the Edge, Wiley, New York.De Bondt, W.F.M. and Thaler, R.H. (1989) A mean-reverting walk down WallStreet, Journal of Economic Perspectives, 3, 1, 189±202.
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Dorsey, R.E. and Mayer, W.J. (1995) Genetic algorithms for estimation problemswith multiple optima, nondierentiability, and other irregular features, Journalof Business & Economic Statistics, 13, 53±66.The Economist (1993) Frontiers of ®nance, 328 (7832), 9 October, a survey.Figlewski, S. (1988) Arbitrage-based pricing of stock index options, Review ofFutures Markets, 7, 2, 250±70.Fogel, L.J., Owens, A.J. and Walsh, M.J. (1966) Arti®cial Intelligence throughSimulated Evolution, Wiley, New York.Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and MachineLearning, Addison-Wesley, Reading, Massachusetts.Holland, J.H. (1962) Outline for a logical theory for adaptive systems, Journal ofthe Association for Computing Machinery, 3, 197±217.Holland, J.H. (1975) Adaptation in Natural and Arti®cial Systems, University ofMichigan Press, Ann Arbor, MI.Holland, J.H. (1976) Adaptation. In Progress in Theoretical Biology (eds R.Rosen and F.M. Snell), Vol. 4, Academic Press, New York, pp. 263±93.Holland, J.H. (1980) Adaptive algorithms for discovering and using generalpatterns in growing knowledge-bases, International Journal of Policy Analysisand Information Systems, 4, 3, 217±40.Karjalainen, R. (1994) Using genetic algorithms to ®nd technical trading rules in®nancial markets, PhD dissertation, University of Pennsylvania.Koza, J.R. (1992) Genetic Programming: On the Programming of Computers byMeans of Natural Selection, MIT Press, Cambridge, MA.Lukac, L.P. and Brorsen, B.W. (1990) A comprehensive test of futures marketdisequilibrium, Financial Review, 25, 4, 593±622.Meyer, T.P. and Packard, N.H. (1992) Local forecasting of high-dimensionalchaotic dynamics. In Nonlinear Modelling and Forecasting (eds M. Casdagli andS. Eubank), Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol.XII, 249±263, Addison-Wesley, Reading, MA.Nissen, V. (1993) Evolutionary algorithms in management science, Interdisziplinaeres Graduiertenkolleg, Universitaet Goettingen, Papers on Economics andEvolution, 9303.Packard, N.H. (1990) A genetic learning algorithm for the analysis of complexdata, Complex Systems, 4, 543±72.Rechenberg, I. (1973) Evolutionsstrategie: Optimierung technischer Systeme nachPrinzipien der Biologischen Evolution, Frommann-Holzboog Verlag, Stuttgart.Schachter, S., Ouellette, R., Whittle, B. and Gerin, W. (1987) Eects of trend andof pro®t or loss on tendency to sell stock, Basic and Applied Social Psychology,8, 4, 259±71.Schwefel, H.-P. (1981) Numerical Optimization of Computer Models, Wiley,Chichester.Sweeney, R.J. (1988) Some new ®lter rule tests: methods and results, Journal ofFinancial and Quantitative Analysis, 23, 3, 285±300.Syswerda, G. (1989) Uniform crossover in genetic algorithms. In Proceedings ofthe Third International Conference on Genetic Algorithms (ed. D.J. Schaer),Morgan Kaufmann, San Mateo, CA, 2±9.
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Taylor, S. (1986) Modeling Financial Time Series, Wiley, New YorkWhitley, D. (1989) The GENITOR algorithm and selection pressure: Why rankbased allocation of reproductive trials is best. In Proceedings of the ThirdInternational Conference on Genetic Algorithms (ed. D.J. Schaer), MorganKaufmann, San Mateo, CA, 116±21.
ACKNOWLEDGMENTSThis article is based on my dissertation at the Wharton School in theUniversity of Pennsylvania. I would like to thank my dissertationadvisors Paul Kleindorfer and Franklin Allen for their encouragement,support, and advice. Helpful comments and suggestions were also madeby Blake LeBaron, Colin Camerer, Larry Fisher, Steve Kimbrough,Michele Kreisler, Howard Kunreuther, Jim Laing, George Mailath,John Miller, and by the editors. Financial support by the Academyof Finland is gratefully acknowledged. Correspondence should beaddressed to Risto Karjalainen, Flat 4, 1 Greenaway Gardens, LondonNW3 7DJ. Email: risto.karjalainen@dial.pipex.com.
Chapter 13Commodity trading advisors and their rolein managed futuresDEREK EDMONDS
13.1 INTRODUCTIONThe primary purpose of this chapter is to examine the merits of usingmanaged futures as a diversifying vehicle for traditional investments, toanalyse the variables that are considered in the evaluation, selection andmonitoring processes of building a portfolio of traders, and ultimately toprobe into the characteristics of the traders that comprise a multi-advisorportfolio.Section 13.2 discusses the major advantages for investing in this asset class,including powerful arguments for diversi®cation, ability to potentially pro®tfrom all types of market conditions, access to global markets and limitedliability. In order to achieve the desired results, a sound system of analysingpotential traders needs to be employed. As a leader in the futures industry,Refco has developed a comprehensive quantitative and qualitative evaluationsystem that is used in the evaluation, selection and monitoring processes.These vital criteria are described in greater detail in section 13.3.Section 13.4 goes on to examine the Nobel-prize winning argument forincorporating a multiple group of non-correlated diversi®ed return streamsinto a single portfolio that results in an improved risk-return pro®le. Usingthis premise of a multi-advisor platform, section 13.5 details the step-by-stepprocess of customizing a program designed to suit an investor's needs as wellas a system for monitoring the ongoing performance of the portfolio.Finally, sections 13.6 and 13.7 delve into an in-depth examination of theperformance characteristics of the two most popular schools of thoughtconcerning trading. The relative performance for each style of trading isstudied in each of the various market sectors, yielding some surprising results.Conclusions drawn from this type of analysis may well provide invaluable
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insights into arriving at an eective mix of traders in a multi-advisorportfolio.13.2 BENEFITS OF INVESTING IN MANAGED FUTURESThe typically managed futures portfolio incorporates the services and tradingstrategies from one to several dozen individual commodity trading advisors(CTAs). The CTAs are professional money managers who are registered withthe Commodity Futures and Trading Commission (CFTC), the governmentalbody in the USA that is responsible for overseeing the activities in the USfutures markets. The major advantages for an investment in a multi-advisormanaged futures product are as follows.(1) Diversi®cation. Managed futures provide investment diversi®cationbecause of their low correlation with global stocks, bonds, real estateand venture capital. A multi-advisor fund oers further diversi®cationbecause the assets of the fund are allocated to multiple CTAs whotrade diversi®ed markets using proprietary strategies.(2) Pro®tability in `up' and `down' markets. Because the CTAs can tradefutures on both the long and short sides of a market, pro®ts can begenerated irrespective of the direction of any particular market.(3) Professional trading management. Investment decisions will be madeby proven professionals who are actively engaged in futures trading.(4) Risk monitoring. Refco has developed a set of risk managementsystems which will enable it to closely monitor the futures positionsof each advisor on a daily basis.(5) Global investment. Managed futures funds will allow investors toparticipate in the growth of the global markets.(6) Daily net asset value (NAV). The net asset value will be calculated on adaily basis based on the closing value of all positions.(7) Limited liability. The careful selection of managers, the conservativeuse of leverage, and the employment of daily risk management systemsare designed to limit the risk of managed futures funds and therebyprotect the investor.(8) Cost. Refco's managed futures funds have been designed with aninstitutional fee structure which will provide investors with a highlycompetitive cost structure.13.3 MEASURES OF INVESTMENT AND RETURNThe measurement of performance of a CTA trading futures and options is anarea that has received limited attention from the academic and practitioner.Refco has developed a comprehensive performance measurement system,which provides diagnostic analysis in addition to more traditional return
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review. The system has been developed to measure risk±return relationshipsand provides input to support the selection, monitoring and allocationdecisions. The performance measurement tools outlined next are presentedto demonstrate the quantitative and qualitative inputs recommended for ameaningful review of a CTA. The most dicult step in the model-buildingcycle is identi®cation of signi®cant information. This is because, although anumber