simulations.5 George Kuo derives some exact results about the probabilistic characteristics of realized returns from two simple moving-average trading rules. The®rst rule needs only the information contained in the asset return at thepresent time to issue trading signals while the second rule requires the wholepast history of the asset price to do so.6 Emmanuel Acar and Stephen Satchell establish the distribution of returnsgenerated by a portfolio including two active strategies assuming thatunderlying markets follow an elliptical distribution. The timing is triggeredby linear forecasts for the sake of tractability. The most important ®nding isthat conventional portfolio theory might not apply to active directionalstrategies even when the underlying assets follow a multivariate normaldistribution.The second section of this book demonstrates that the foreign exchangemarkets may be seen as inecient given the number of pro®table strategieswhich can be built out of varied forecasts (four chapters).
4
Advanced Trading Rules
7 John Okunev and Derek White evaluate the performance of multipleclasses of foreign exchange trading rules across eight base currencies.Speci®cally, they compare trading rules that focus on individual currencieswith those that follow a long±short strategy across multiple currencies. Thetrading rules include pure momentum, buying/selling based upon relativeinterest rates, and moving-average rules. They ®nd that a long±short strategyacross multiple currencies outperforms trading rules that focus on individualcurrencies. In addition, they ®nd that signi®cant bene®ts may accrue bycombining long±short moving-average rules across multiple currencies withlong±short positions based upon relative interest rates.8 Christian Dunis considers Arti®cial Neural Networks (ANNs), anddiscusses their application to economic and ®nancial forecasting and theirincreasing success. This chapter investigates the application of ANNs tointraday foreign exchange forecasting and stresses some of the problemsencountered with this modelling technique. As forecasting accuracy does notnecessarily imply economic signi®cance, the results are also evaluated bymeans of a trading strategy.9 Kevin Chang and Carol Osler assess the incremental value of the head-andshoulders pattern (H&S), consistently cited by technical analysts as particularly frequent and reliable, relative to ®lter rules. On an incremental basis,they show that the H&S trading rules add noise but no value. Thus, a traderwould do no better, and possibly worse, by following both H&S and ®lterrules instead of ®lter rules only.10 Pierre Lequeux investigates the assumption that the interest rates marketleads the currency markets as money ¯ows from one country to another. Fora systematic trader the hypothesis is quite attractive; indeed if such a crosscorrelation exists it will enable him to devise pro®table trading strategies.Finally, the third section analyses the application of stop-loss rules andother technical strategies by futures traders (®ve chapters). The tradingmethodology and performance of futures funds managers is reviewed.11 Bernard Bensaid and Olivier De Bandt explain the existence of stop-lossrules in ®nancial institutions. They develop a principal/agent model, where aninvestment ®rm (the principal) has to rely on the expertise of a trader (theagent) to invest in a risky asset (a future contract, say). Using daily data onindividual positions in the French Treasury bond future market, they ®ndevidence that positions are more likely to be sold o when realized pro®ts arevery negative. More than 20 per cent of individual accounts seem to use stoploss strategies in their database.
Introduction
5
12 Risto Karjalainen uses genetic algorithm to ®nd technical trading rulesfor S&P 500 futures. The rules are found to be pro®table in an out-of-sampletest period, with reduced volatility compared to the buy-and-hold strategy. Itis also shown that there are characteristic patterns in option trading activitycoinciding with the trading rule signals. The results are consistent with shortterm overreaction that leads to a partial reversal of large returns on a fewdays' horizon.13 Derek Edmonds examines the merits of using managed futures as adiversifying vehicle for traditional investments. The author carries out an indepth examination of the performance characteristics of the two mostpopular schools of thought concerning trading: discretionary versus systematic. The relative performance for each style of trading is studied in each of thevarious market sectors, yielding some surprising results.14 Edouard Petitdidier and David Obert explain precisely BAREP's management and techniques used to trade futures: choice of futures markets, creationand testing of strategies and money management. This structure hasdeveloped a Futures Funds' asset management based on two leadingconcepts: Technical non-discretionary asset management, with investmentstrategies based on models of historical behaviour in futures markets. The®nal section describes the funds' performance from 1994 to 1997.15 Felix Gasser investigates the need for performance evaluation intechnical analysis. He studies not only the indicators and trading systemsthat are commonly applied by technical traders, but also the analytical dataused for evaluation.The range of forecasting strategies investigated in this book is large butnon-exhaustive. The pace of innovation is so fast that new trading conceptswill appear which might be better suited to future market conditions.However, we hope that these contributions provide a host of ideas to helpimprove the risk±return pro®le of any trader or investor in the foreignexchange and futures markets. We also feel that our book will act asbackground for academics and other researchers who would like to ®ndout more about this fascinating new area of ®nancial research.
Chapter 1Technical trading rules and regime shifts inforeign exchangeBLAKE LEBARON
1.1 INTRODUCTIONTechniques for using past prices to forecast future prices have a long andcolourful history. Since the introduction of ¯oating rates in 1973, the foreignexchange market has become another potential target for `technical' analystswho attempt to predict potential trends in pricing using a vast repertoire oftools with colourful names such as channels, tumbles, steps and stumbles.These market technicians have generally been discredited in the academicliterature since their methods are sometimes dicult to put to rigorous tests.This chapter attempts to settle some of these discrepancies through the use ofbootstrapping techniques.For stock returns, many early studies generally showed technical analysisto be useless, while for foreign exchange rates there is no early study showingthe techniques to be of no use. Dooley and Shafer (1983) found interestingresults using a simple ®lter rule on several daily foreign exchange rate series.In later work, Sweeney (1986) documents the pro®tability of a similar rule onthe German mark. In an extensive study, Schulmeister (1987) repeats theseresults for several dierent types of rules. Also, Taylor (1992) ®nds thattechnical trading rules do about as well as some of his more sophisticatedtrend-detecting methods.While these tests were proceeding, other researchers were trying to usemore traditional economic models to forecast exchange rates with much lesssuccess. The most important of these was Meese and Rogo (1983). Theseresults showed the random walk to be the best out-of-sample exchange rateforecasting model. Recently, results using nonlinear techniques have beenmixed. Hsieh (1989) ®nds most of the evidence for nonlinearities in dailyexchange rates is coming from changing conditional variances. Diebold andNason (1990) and Meese and Rose (1990) found no improvements using
Technical trading rules and regime shifts in foreign exchange
7
nonparametric techniques in out-of-sample forecasting. However, LeBaron(1992) and Kim (1989) show small out-of-sample forecast improvements.During some periods, LeBaron (1992) found forecast improvements of over 5per cent in mean squared error for the German mark. Both of these papersrelied on some results connecting volatility with conditional serial correlations of the series.This chapter breaks o from the traditional time series approaches and usesa technical trading rule methodology. With the bootstrap techniques of Efron(1979), some of the technical rules can be put to a more thorough test. This isdone for stock returns in Brock, Lakonishok and LeBaron (1992). 1 Thischapter will use similar methods to study exchange rates. These allow notonly the testing of simple random walk models, but the testing of anyreasonable null model that can be simulated on the computer. In this sense,the trading rule moves from being a pro®t-making tool to a new kind ofspeci®cation test. The trading rules will also be used as moment conditions ina simulated method of moments framework for estimating linear models.Finally, the economic signi®cance of these results will be explored. Returnsfrom the trading rules applied to the actual series will be tested. Distributionsof returns from the exchange rate series will be compared with those fromrisk-free assets and stock returns. These tests are important in determining theactual economic magnitude of the deviations from random walk behaviourthat are observed.Section 1.2 introduces the simple rules used. Section 1.3 describes the nullmodels used. Section 1.4 presents results for the various speci®cation tests.Section 1.5 implements the trading rules and compares return distributionsand section 1.6 summarizes and concludes.1.2 TECHNICAL TRADING RULESThis section outlines the technical rules used in this chapter. The rules areclosely related to those used by actual traders. All the rules used here are ofthe moving average or oscillator type. Here, signals are generated based onthe relative levels of the price series and a moving average of past prices:mat  1=L
L 1X
pt i
i0
For actual traders, this rule generates a buy signal when the current price levelis above the moving average and a sell signal when it is below the movingaverage. 2 This chapter will use these signals to study various conditionalmoments of the series during buy and sell periods. Estimates of theseconditional moments are obtained from foreign exchange time series, and
8
Advanced Trading Rules
these estimates are then compared with those from simulated stochasticprocesses. Section 1.4 of this chapter diers from most trading rule studieswhich look at actual trading pro®ts from a rule. Actual trading pro®ts will beexplored in section 1.5.1.3 NULL MODELS FOR FOREIGN EXCHANGE MOVEMENTSThis section describes some of the null models which will be used forcomparison with the actual exchange rate series. These models will be runthrough the same trading rule systems as the actual data and then comparedwith those series. Several of these models will be bootstrapped in the spirit ofEfron (1979) using resampled residuals from the estimated null model. Thisclosely follows some of the methods used in Brock, Lakonishok and LeBaron(1992) for the Dow Jones stock price series.The ®rst comparison model used is the random walk:log pt   log pt 1   "tLog dierences of the actual series are used as the distribution for "t andresampled or scrambled with replacement to generate a new random walkseries. The new returns series will have all the same unconditional propertiesas the original series, but any conditional dependence will be lost.The second model used is the GARCH model (Engle, 1982; Bollerslev,1986). This model attempts to capture some of the conditional heteroskedasticity in foreign exchange rates. 3 The model estimated here is of the form:r t  a  b1 r t 1  b2 r t 2  " tht 
0
21"t 1 
1=2
" t  h t zt
ht 1
zt  N 0; 1This model allows for an AR(2) process in returns. The speci®cation wasidenti®ed using the Schwartz (1978) criterion. Only the Japanese yen seriesrequired the two lags, but for better comparisons across exchange rates thesame model is used. 4 Estimation of this model is done using maximumlikelihood.Simulations of this model follow those for the random walk. Standardizedresiduals of the GARCH model are estimated as:"ptht
These residuals are scrambled and the scrambled residuals are then used torebuild a GARCH representation for the data series. Using the actualresiduals for the simulations allows the residual distribution to dier from
Technical trading rules and regime shifts in foreign exchange
9
normality. Bollerslev and Wooldridge (1990) have shown that the previousparameter estimates will be consistent under certain deviations from normality. Therefore, the estimated residuals will also be consistent. 5The third model has been proposed for foreign exchange markets in apaper by Engle and Hamilton (1990). It suggests that exchange rates followlong persistent swings following a two-state Markov chain. It is given by:rt  0  1 St  
0
P St  1 j St 1  1  p
1 St zt
P St  0 j St 1  1  1
p
P St  1 j St 1  0  1
q
P St  0 j St 1  0  qzt  N 0; 1
This model allows both the mean and variance for exchange rate returns tomove between two dierent states. Since this model is capable of generatingpersistent trends, it presents a strong possibility for generating the results seenusing the trading rules. Estimation is done using maximum likelihood. Forthis model, the simulations will use normally distributed random numbersfrom a computer random number generator.1.4 EMPIRICAL RESULTS1.4.1 Data summaryThe data used in this chapter are all from the EHRA macro data tape fromthe Federal Reserve Bank. Weekly exchange rates for the British pound (BP),the German mark (DM) and the Japanese yen (JY) are sampled everyWednesday from January 1974 to February 1991 at 12:00 pm EST.Returns are created using log ®rst dierences of these weekly exchangerates quoted in dollars/fx. Table 1.1 presents some summary statistics forthese return series. All three series show little evidence of skewness and areslightly leptokurtic. These properties are common for many high frequencyasset returns series. The ®rst ten autocorrelations are given in the rowslabelled n . The Bartlett asymptotic standard error for these series is 0.033.The BP shows little evidence of any autocorrelation except for lags four andeight, while the DM shows some weak evidence of correlation, and the JYshows strong evidence for some autocorrelation. The Ljung±Box±Piercestatistics are shown on the last row. These are calculated for ten lags andare distributed  2 10 under the null of independently identically distributed.The p-values are included for each in parentheses. The BP and JY series rejectindependence, whereas the DM series does not.
10
Advanced Trading RulesTable 1.1 Summary statisticsDescription
BP
DM
JY
Sample sizeMean  100Std.  100SkewnessKurtosis
8930.01621.43980.21075.5931
8930.06861.43500.35324.3735
8930.08751.40120.37855.1425
12345678910
0.04880.02480.03670.09590.01640.01350.00700.08620.03050.0047
0.06360.06090.00600.04140.02000.05700.00280.06250.01460.0414
0.11050.09620.05920.04460.03380.00020.03590.00600.00360.0833
Bartlett
0.0335
0.0335
0.0335
LBPp-values  2 10
20.16(0.027)
15.53(0.115)
26.41(0.003)
Summary statistics for BP (British pound), DM (German mark), JY(Japanese yen) weekly exchange rates from January 1974 to February 1991.
The interest rate series used are also from the EHRA macro data tape. Forthe dollar, the weekly eurodollar rate is used. For the pound, the internationalmoney market call money rate is used. For the mark, the Frankfurt interbankcall money rate is used, and for the yen, the Tokyo unconditional lender rate.Weekly rates are constructed ex post from the compounded rates fromWednesday to Tuesday. These rates can only be viewed as proxies for thedesirable situation of having a set of interest rates from the same oshoremarket at the same maturity. At this time that is not available.1.4.2 Random walk comparisonsIn this section, simulations are performed comparing conditional momentsfrom the technical trading rules with a bootstrapped random walk generatedfrom the actual returns time series scrambled with replacement. Threemoving-average rules will be used, the twenty-week, thirty-week and ®ftyweek moving averages. These are fairly common lengths used by traders. Wewill see that the results are not very sensitive to the lengths used. The movingaverage rules force us to start the study after a certain number of weeks have
Technical trading rules and regime shifts in foreign exchange
11
Table 1.2 BP random walk bootstrap
b
FractionBuySell
s
0.080 000.000 120.000 91
0.560 000.014 340.014 26
0.460 000.478 100.486 24
0.980 000.000 140.001 34
0.420 000.014 290.014 42
0.000 000.000 020.002 25
Fraction > XrateSimulation meanXrate mean
0.010 000.000 180.001 35
0.630 000.014 380.014 21
0.340 000.473 640.504 06
1.000 000.000 100.001 84
0.370 000.014 270.014 52
0.000 000.000 070.003 19
Fraction > XrateSimulation meanXrate mean
0.010 000.000 190.001 45
0.640 000.014 360.014 10
0.370 000.468 090.494 66
1.000 000.000 110.001 82
0.180 000.014 250.014 87
0.000 000.000 090.003 27
Average Fraction > XrateSimulation meanXrate mean
0.010 000.000 160.001 24
0.660 000.014 360.014 19
0.390 000.473 330.494 96
0.990 000.000 120.001 66
0.320 000.014 270.014 60
0.000 000.000 050.002 90
Rule
Result
Buy
(1, 20)
Fraction > XrateSimulation meanXrate mean
(1, 30)
(1, 50)
Buy±Sell
Buy refers to the mean 1 week return during buy periods, b , the standard deviation of thesereturns, and Fraction Buy is the fraction of buy weeks out of total weeks. Sell and s are the samefor the sell returns. Buy±Sell is the dierence between the buy mean and sell mean. The rowlabelled Fraction > Xrate shows the fraction of the 500 simulations which generate a value for thestatistic larger than that from the actual series. Simulation mean is the mean value for the statisticfor the simulated random walks, and Xrate mean is the value from the original series.
passed. For this chapter, all tests for all the rules begin after week ®fty. Thisgives the same number of weekly observations for all three rules.Table 1.2 presents the results comparing the actual series for the BP with500 simulated random walks. Six comparison statistics are computed in thistable. First, the column labelled `Buy' refers to the conditional mean duringbuy periods. This is:mb  1=Nb 
NX1
rt1 I bt
t0
where Nb is the number of buy signals in the sample and I bt is an indicatorvariable for a buy signal at time t. The second column, labelled `b ', looks atthe standard deviation of this same set of returns. This is:1=2NX1rt1 mb  2 I bt1=Nb t0
This gives a simple idea of how risky the buy or sell periods might be and tellsus something about what is happening to conditional variance. The thirdcolumn, labelled `Fraction buy', is just the fraction of buy weeks Nb =N. The
12
Advanced Trading Rules
next two columns, `Sell' and `s ' repeat the previous descriptions for the sellperiods. Let ms be the mean during the sell periods. The ®nal column, `Buy±Sell', refers to the dierence between the buy and sell means, mb ms .This table presents several results for each test. The ®rst is the fraction ofsimulated random walks that generate a given statistic greater than that forthe original series. This can be thought of as a simulated p-value. For thetwenty-week moving-average rules, this result is given in the ®rst row of thetable. For the BP series we see that 8 per cent of the simulations generated amean return greater than that from the actual series. The next row,`Simulation mean' shows the mean of mb for the 500 simulated randomwalks. The third row, `Xrate mean' shows mb for the exchange rate series. Forthe BP series the table reports a mean one-week buy return of 0.091 per centwhich is greater than the simulated mean of 0.012 per cent. The simulationsshow that this dierence is weakly signi®cant with 8 per cent of thesimulations generating a mb greater than 0.091 per cent.The second column shows the results for the standard deviations of the buyreturns b . The column shows that 56 per cent of the simulations hadstandard deviations greater than that in the original series. This clearlyshows no signi®cant dierence between the simulations and the originalseries. In other words, although the buys generate a larger mean, they donot have a larger variance. The next column reports that the fraction of buysto sells for the actual series, third row, is 0.486. This does not appear to beunusually large or small relative to the simulated random walks.For the sells, ms , for the BP series is 0.134 per cent which compares with0.014 per cent for the simulation. Table 1.1 shows that 98 per cent of thesimulated random walks generated ms statistics larger than 0.134, indicatingthat the sell period returns for the original series are unusually small whencompared with the random walk. The next column, s , shows that thesereturns are not dierent from the entire sample in terms of volatility.The ®nal column reports the dierence mb ms . For this rule, thedierence is about 0.2 per cent, but none of the simulated random walksgenerated such a large dierence between buy and sell returns.The next six rows of the table repeat the same results for the other tworules, the thirty- and ®fty-week moving-average rules. The results for theserules are similar to the ®rst two with the buy means unusually large and thesell means unusually small. There still appears to be no eect in volatility. 6The ®nal set of tests performs a joint test based on all three rules. Anaverage is taken for the statistics generated from each of the three rules. Forthe mean buys this would be:mb  1=3 mb 1; 20  mb 1; 30  mb 1; 50
13
Buy^sell difference
Technical trading rules and regime shifts in foreign exchange
Moving-average length (weeks)Figure 1.1 British pound buy±sell dierences
Finding the distribution of this statistic would require knowledge of the jointdistribution across all the rules. The results for each rule are clearly far fromindependent, so this would be a dicult job. With the simulated randomwalks the rules can now be compared with results for the same averagestatistics over the 500 simulated random walks. This section of the tableshows that the pattern for each of the individual rules is repeated in theaverage rules.A good question to ask at this point is how general these results are fordierent moving averages. This chapter has used only three dierent movingaverage rules. These are chosen to be close to those used by actual traders. Itis quite possible that there may be some data-snooping problems here in thatthese rules have already been chosen because of their past performance in thedata. This problem is partially accounted for in Figure 1.1, which displays thebuy±sell dierences for several dierent lengths of moving averages. It is clearfrom this ®gure that the results are not overly sensitive to the length of themoving average chosen.Tables 1.3 and 1.4, repeat the results for the DM and JY series. Turning tothe average rows, we see very similar results to Table 1.2. The buy±selldierences are large for both with p-values of 0.For the JY series, the standard deviations during the buy and sell periodsare not unusually small or large. For the DM series, some weak dierencesappear between the standard deviations during the buy and sell periods. For
14
Advanced Trading RulesTable 1.3 DM random walk bootstrap
b
FractionBuySell
s
0.030 000.000 700.001 77
0.680 000.014 310.013 98
0.320 000.562 730.586 01
0.990 000.000 650.001 12
0.310 000.014 220.014 54
0.000 000.000 050.002 88
Fraction > XrateSimulation meanXrate mean
0.040 000.000 670.001 69
0.900 000.014 340.013 52
0.270 000.578 160.618 77
1.000 000.000 700.001 12
0.008 000.014 210.015 26
0.000 000.000 030.002 81
Fraction > XrateSimulation meanXrate mean
0.050 000.000 690.001 64
0.960 000.014 340.013 30
0.550 000.600 500.597 86
0.960 000.000 660.000 95
0.010 000.014 170.015 55
0.000 000.000 030.002 59
Average Fraction > XrateSimulation meanXrate mean
0.030 000.000 680.001 70
0.870 000.014 330.013 60
0.430 000.580 240.600 85
1.000 000.000 670.001 06
0.120 000.014 200.015 12
0.000 000.000 020.002 76
Rule
Result
(1, 20)
Fraction > XrateSimulation meanXrate mean
(1, 30)
(1, 50)
Buy
Buy±Sell
the average across the rules using the buy standard deviations, the simulatedp-value is 0.87, indicating that 87 per cent of the simulations were morevolatile than the actual exchange rate series. For the sells, this value is 0.12,indicating that 12 per cent of the simulations were more volatile than theoriginal series. This shows some weak evidence that the buy periods were less
Table 1.4 JY random walk bootstrap
Rule
Result
Buy
b
FractionBuySell
s
(1, 20)
Fraction > XrateSimulation meanXrate mean
0.000 000.000 870.002 50
0.520 000.013 950.013 88
0.730 000.591 320.548 17
1.000 000.001 000.001 14
0.590 000.013 920.013 68
0.000 000.000 130.003 63
(1, 30)
Fraction > XrateSimulation meanXrate mean
0.000 000.000 890.002 60
0.490 000.013 970.013 91
0.790 000.614 370.551 56
1.000 000.001 000.001 16
0.530 000.013 880.013 72
0.000 000