
0.5700.1140.6310.8160.100
0.3490.0170.3470.8390.046
0.0100.9190.1180.0320.265
0.0500.9600.0870.0200.207
0.935
0.047
0.010
0.018
0.0260.934
0.6020.0870.6360.7780.061
0.0520.6660.1100.0770.089
0.0020.7250.0840.0050.214
0.915
0.033
0.018
0.034
0.0040.951
UKLong±Short Within
MomentumInt RateMA 4 6Long±Short AcrossMomentumInt RateMA 4 61 7MA 4 61; 2; 3 7Currency benchmarks MSCIEqualUSALong±Short Within
MomentumInt RateMA 4 6Long±Short AcrossMomentumInt RateMA 4 61 7MA 4 61; 2; 3 7Currency benchmarks MSCIEqual
0.014
0.178
0.8330.092
0.8730.176
0.3470.0320.386
0.5730.0870.577
0.0210.4070.0920.031
0.0200.6040.0320.082
0.2980.0420.4080.8620.114
0.5160.1770.6140.8250.081
0.3430.0390.4390.8370.099
0.1600.7370.0910.0030.074
0.1070.7910.0740.0660.057
0.932
0.002
0.037
0.014
0.0300.921
0.5180.1600.5960.7850.031
0.0090.1930.0920.0000.468
0.0610.1040.1360.0560.304
0.914
0.061
0.067
0.020
0.0260.925
Table 7.10 Correlations across countries for individual strategiesAustraliaLong±Short WithinMomentum 3-Month
AustraliaCanadaFranceGermanyJapanSwitzerlandUKUSAAustralia
Long±Short WithinInterest rate
AustraliaCanadaFranceGermanyJapanSwitzerlandUKUSAAustralia
Long±Short WithinMA 4 6
AustraliaCanadaFranceGermanyJapanSwitzerlandUKUSA
Canada
France
Germany
Japan
Switzerland
UK
USA
0.427
0.5390.759
0.5560.7280.926
0.3980.4350.4870.459
0.5700.7100.7970.8250.462
0.3500.5120.5240.5000.4060.439
0.4290.8300.6800.6720.4770.6840.498
Canada
France
Germany
Japan
Switzerland
UK
USA
0.680
0.5420.565
0.6600.8190.502
0.3920.5080.4100.468
0.6180.7450.4580.8410.418
0.3870.5090.4490.5420.3660.452
0.5130.6550.5900.6770.4740.6360.640
Canada
France
Germany
Japan
Switzerland
UK
USA
0.497
0.5560.745
0.5850.7530.937
0.3540.4920.4710.489
0.5890.7140.7770.8210.425
0.3720.5320.5490.5650.4510.475
0.4630.8630.7000.7130.4480.6940.524
AustraliaLong±Short AcrossMomentum 3-month
AustraliaCanadaFranceGermanyJapanSwitzerlandUKUSAAustralia
Long±Short AcrossInterest rate
AustraliaCanadaFranceGermanyJapanSwitzerlandUKUSAAustralia
Long±Short WithinMA 4 6 1 7
AustraliaCanadaFranceGermanyJapanSwitzerlandUKUSAAustralia
Long±Short WithinMA 4 6 1; 2; 3 7
AustraliaCanadaFranceGermanyJapanSwitzerlandUKUSA
Canada
France
Germany
Japan
Switzerland
UK
USA
0.762
0.7820.945
0.7630.9380.953
0.6150.7820.7930.787
0.7650.9270.9460.9320.762
0.7140.8910.9050.8940.7390.863
0.7720.9450.9510.9380.7870.9320.896
Canada
France
Germany
Japan
Switzerland
UK
USA
0.770
0.7460.941
0.7860.9820.957
0.5430.7920.7840.823
0.7190.9100.8770.9230.743
0.7230.9280.8990.9380.7540.869
0.7430.9530.9360.9680.7850.8980.920
Canada
France
Germany
Japan
Switzerland
UK
USA
0.781
0.8080.975
0.8010.9770.985
0.6420.8430.8450.850
0.7870.9560.9600.9620.817
0.7410.9110.9280.9280.7930.892
0.7840.9680.9720.9780.8390.9550.912
Canada
France
Germany
Japan
Switzerland
UK
USA
0.778
0.8100.960
0.8090.9580.987
0.6950.8580.8700.865
0.7900.9350.9610.9650.839
0.7680.9050.9230.9220.8390.897
0.7880.9730.9640.9640.8580.9450.922
244
Advanced Trading Rules
outperform other trend-chasing technical approaches. These results have beenstable over the previous twenty years across all base currencies and have beenparticularly strong during the 1995±2000 period. Potential diversi®cationbene®ts may also be obtained through combining the Long±Short Acrossinterest rate rule and moving-average rules. These strategies haveoutperformed the MSCI and Equal currency benchmarks for all the basecurrencies as well. In Okunev and White (2002) we found no evidence forthe presence of time-varying risk explanations for the Long±Short Acrossmoving-average rules. In additional tests not shown in this chapter we alsofound little evidence for a time-varying risk premium for the Long±ShortAcross interest rate strategy. In short, we do not believe that risk can fullyexplain the results of this chapter.In general, following Long±Short Across approaches will outperformstrategies that trade within individual currencies in isolation. That is, thepotential for excess returns is much greater when we consider the technicalperformance of all currencies with respect to each other when we set ourpositions. While individual speci®cations of select trading rules within a givencurrency may have historically performed quite well, we cannot ascertainwhether the result is driven by chance. This is especially true if only one basecurrency is considered when a trading rule is evaluated.We do not yet know why, but pure momentum as a strategy for currenciesdoes not appear to be a viable trading approach. This is in stark contrast towhat has been found for equities (Jegadeesh and Titman, 1993, 2001). It is notclear what fundamental dierence exists between momentum and movingaverage approaches, and one potential avenue for future research would be todetermine the conditions explaining why one approach might succeed and theother not. Perhaps a deeper process is at work dierentiating equity andcurrency markets.If this chapter makes any further contribution, we hope it will motivateothers to consider as broad a range of assets as possible when testing sets oftechnical trading rules. In addition, by averaging across many speci®cationsfor a given class of strategies, the studies will be as free as possible from expost selection bias criticisms. Even though we have found that the results inthis chapter are remarkably stable across base currencies, we recommend thattests be substantiated using multiple base currencies.We should emphasize that we do not necessarily advocate our approach asa speculative tool. The returns the moving-average strategies generate averageonly 7 per cent per year and they are not risk-free. Instead we expect our®ndings to be of use to those who have natural positions in a foreign currencyand who would like to tilt their exposure to select currencies to enhanceperformance. Any foreign exchange manager can calculate a moving average
The pro®ts to technical analysis in foreign exchange markets 245of returns for multiple currencies and look up interest rate dierentials. Wesimply advocate using these as tools when considering an institution's overallcurrency exposure.
REFERENCESArnott, R.D. and Pham, T.K. (1993) Tactical currency allocation, FinancialAnalysts Journal, 49, 47±52.Banerjee, A.V. (1992) A simple model of herd behavior, Quarterly Journal ofEconomics, 107, 797±817.Black, F. (1989) Equilibrium exchange rate hedging, Journal of Finance, 43,899±908.Brock, W., Lakonishok, J. and LeBaron, B. (1992) Simple technical trading rulesand the stochastic properties of stock returns, Journal of Finance, 47, 1731±64.Clarida, R.H. and Taylor, M.P. (1997) The term structure of forward exchangepremiums and the forecastability of spot exchange rates: correcting the errors,Review of Economic and Statistics, 79, 353±61.Fama, E.F. (1965) The behavior of stock market prices, Journal of PoliticalEconomy, 38, 34±105.Fama, E.F. (1984) Forward and spot exchange rates, Journal of MonetaryEconomics, 36, 697±703.Frankel, J.A. and Froot, K.A. (1990) Chartists, fundamentalists, and trading inthe foreign exchange market, American Economic Review, 80, 181±85.Frenkel, M. and Stadtmann, G. (2000) Trading rule pro®tability and interventions in the dollar±deutschmark market, Working paper.Froot, K.A. (1993) Currency hedging over long horizons, Bureau of EconomicResearch Working Paper 4355.Gastinaeu, G.L. (1995) The currency hedging decision: a search for synthesis inasset allocation, Financial Analysts Journal, 51, 8±17.Jegadeesh, N. and Titman, S. (1993) Returns to buying winners and selling losers:implications for stock market eciency, Journal of Finance, 48, 65±91.Jegadeesh, N. and Titman, S. (2001) Pro®tability of momentum strategies: anevaluation of alternative explanations, Journal of Finance, 56, 699±720.Kho, B. (1996) Time varying risk premia, volatility, and technical reading pro®ts:evidence from foreign currency futures markets, Journal of Financial Economics,41, 249±90.Kritzman, M. (1989) Serial dependence in currency returns: investment implications, Journal of Portfolio Management, 16, 96±102.LeBaron, B. (1999) Technical trading rule pro®tability and foreign exchangeintervention, Journal of International Economics, 49, 125±43.LeBaron, B. (2000) The stability of moving average technical trading rules on theDow Jones Index, Derivative Use, Trading & Regulation, 5, 324±38.Levich, R.M. (1985) Empirical studies of exchange rates: price behaviour, ratedetermination and market eciency, in Handbook of International Economics(eds R.W Jones and P.B. Kenen), 2, 980±1036.
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Levich, R.M. (Fall, 1989) Is the foreign exchange market ecient? Oxford Reviewof Economic Policy, 5, 40±60.Levich, R.M. (1989) Forward rates as the optimal future spot rate forecast, inExchange Rate Forecasting (eds C. Dunis and W. Feeny), Woodhead-Faulkner,Cambridge, pp. 75±98.Levich, R.M and Thomas, L.R. (1993) The signi®cance of technical trading-rulepro®ts in the foreign exchange market: a bootstrap approach, Journal ofInternational Money and Finance, 12, 451±74.Marsh, I.W. (2000) High-frequency Markov switching models in the foreignexchange market, Journal of Forecasting, 19, 123±34.Neely, C.J. (1998) Technical analysis and the pro®tability of U.S. foreignexchange intervention. Federal Reserve Bank of St Louis Review, July/August,3±17.Neely, C.J. (2000) The temporal pattern of trading rule returns and central bankintervention: intervention does not generate technical trading rule pro®ts,Working Paper, St Louis Federal Reserve Bank.Neely, C.J. and Weller, P. (2001) Intraday technical trading in the foreignexchange market, Working Paper, St Louis Federal Reserve Bank.Neely, C.J. and Weller, P. (2001) Technical analysis and central bank intervention, Journal of International Money and Finance, 20, 949±70.Neely, C.J., Weller, P. and Dittmar, R. (1997) Is technical analysis pro®table inforeign exchange markets? A genetic programming approach, Journal ofFinancial and Quantitative Analysis, 32, 405±26.Neftci, S.N. (1991) Naive trading rules in ®nancial markets and Weiner±Kolmogorov prediction theory: a study of technical analysis, Journal ofBusiness, 64, 549±71.Ntungo, C. and Boyd, M. (1998) Commodity futures trading performance usingneural network models versus ARIMA models, Journal of Futures Markets, 18,965±83.Okunev, J. and White, D. (2002) Do momentum-based strategies still work inforeign currency markets? Journal of Financial and Quantitative Analysis,forthcoming.Perold, A. and Schulman, E. (1988) The free lunch in currency hedging: implications for investment policies and performance standards, Financial AnalystsJournal, 44, May/June, 45±50.Raj, M. (2000) Transaction data tests of eciency in the Singapore futuresmarkets, Journal of Futures Markets, 20, 687±704.Schulmeister, S. (1988) Currency speculation and dollar ¯uctuations, QuarterlyReview, Banca Nationale del Lavoro, 167, 343±65.Shleifer, A. and Summers, L.H. (1990) The noise trader approach to ®nance,Journal of Economic Perspectives, 4, 19±33.Sullivan, R., Timmermann, A. and White, H. (1999) Data-Snooping, TechnicalTrading Rule Performance, and the Bootstrap, Journal of Finance, 54, 1647±91.Surajaras, P. and Sweeney, R.J. (1992) Pro®t-Making Speculation in ForeignExchange Markets, Westview Press, Boulder, CO.
The pro®ts to technical analysis in foreign exchange markets 247Sweeney, R.J. (1986) Beating the foreign exchange market, Journal of Finance, 41,163±82.Sweeney, R.J. (1988) Some new ®lter rule tests: methods and results, Journal ofFinancial and Quantitative Analysis, 23, 285±300.Sweeney, R.J. (1997) Do central banks lose on foreign exchange intervention? Areview article, Journal of Banking and Finance, 21, 1667±84.Szakmary, A.C. and Mathur, I. (1997) Central bank intervention and trading rulepro®ts in foreign exchange markets, Journal of International Money andFinance, 16, 513±35.Taylor, S.J. (1992) Eciency in the yen futures market at the Chicago MercantileExchange, in Rational Expectations and Eciency in Futures Markets,Routledge, London, pp. 109±28.Taylor, S.J. (1994) Trading futures using a channel rule: a study of predictivepower of technical analysis with currency examples, Journal of Futures Markets,14, 215±35.Taylor, M.P. and Allen, H. (1992) The use of technical analysis in the foreignexchange market, Journal of International Money and Finance, 11, 304±14.
NOTES1. Surajaras and Sweeney (1992) ®nd that optimized Long±Short Across tradingstrategies underperform optimized Long±Short Within methods. Ourapproach does not attempt to identify the optimal speci®cation for a giventrading rule. Instead, we evaluate the performance of selected classes oftrading rules by averaging returns across multiple parameterizations.2. In fact, we show that the very best strategy from the momentum classunderperforms the moving-average class as a whole.3. Because we employ one-month trading strategies, we should ideally use onemonth yields in our dataset. However, we did not have access to this data forall the currencies for the time period of the analysis. In Okunev and White(2002) we showed through bootstrapping tests that using this proxy for thecash rate does not explain the returns earned by the moving-average strategy.In general, very little dierence exists between the one-month rate and thethree-month rate expressed on a one-month basis.4. While the Long±Short Across strategies could, in theory, be considered zerocost and the resulting returns in®nite, we choose to frame the returns in termsof an unlevered position in currency futures where full margin is given forboth long and short positions. The Long±Short Within strategies are not zerocost as it is possible to go long or short in all seven non-domestic currenciesduring any given month.5. Return-based momentum strategies are preferred as the price momentumstrategy would tend to favour currencies with greater price adjustments suchas the yen. The largest change in price may not re¯ect the largest change inpercentage terms.6. Note that if a given base currency has the lowest interest rate among all eightbase currencies, it will still go short a currency with a higher interest rate since
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Advanced Trading Rules
the rule compares only the non-domestic interest rates with each other.Conversely, if a given base currency has the highest interest rate, it will stillgo long a currency with a lower interest rate.7. The sum of the weights for the long positions will be equal to the weight of theshort position.8. As will be quite evident in section 7.4, we face a dicult space constraint inthe presentation of the results. Because of this, we will have to discuss some ofthe results of the chapter without giving supporting tables. In general, ourobjective is to test the moving-average rules against the very best speci®cationpossible for the momentum rules. The interest rate strategy, by construction,has only one speci®cation.9. Using all 354 moving-average strategies as a class would lower the returns by®ve to ten basis points each month for the base currencies considered.10. An additional benchmark not tested might be a policy of completely hedgingcurrency exposure through the use of futures contracts. In this case, thebenchmark expected return would be the interest rate dierential between thetwo countries. The average interest rate dierential may be calculated bysubtracting the mean return to the MSCI-weighted and Equal-weightedcurrency benchmarks of Table 7.1 from Table 7.2. Because these dierencesare typically lower in magnitude than the base currency returns identi®ed inTable 7.1, any test that shows statistical signi®cance relative to the basecurrency returns would likely have even greater signi®cance using interest ratedierentials.11. We chose to use the information ratio instead of the Sharpe ratio as noconsensus exists regarding the appropriate risk-free rate for a zero-cost, zeroexpected return strategy in international currency markets.12. We did not include a transactions cost in the analysis. Most studies use a tenbasis point round-trip transactions cost for trading in currency futuresmarkets.13. This test is identical to the standard t-test for statistical signi®cance on excessreturns.
Chapter 8The economic value of leading edgetechniques for exchange rate predictionCHRISTIAN L. DUNIS
8.1 INTRODUCTIONDuring the past decade, empirical evidence has emerged that pockets ofpredictability do exist in ®nancial markets. Academics have developed newmathematical and statistical tools to help predict future price movements.These new techniques, which rely heavily on the analysis of nonlinearities, arenow used by some major trading institutions and fund managers and there isan ever increasing interest from large corporates too.Today's ®nancial markets are characterized by a large number of participants, with their dierent appetites for risk, their dierent time horizon andtheir dierent motivations and reactions to unexpected news. In the circumstances, it would come as a surprise if all these complex interactions were toaverage out in a linear fashion. Furthermore, the introduction of nonlinearities in the modelling approach should allow one to explain some price movesthat seemed random previously without resorting to stochastic mechanisms.The development in nonlinear modelling spans a wide range of approaches,from formalizing chartist techniques to arti®cial neural networks (ANNs),from ARCH/GARCH processes to chaotic dynamics.Combined with extensive data banks and the greater availability ofpowerful computers, these new techniques now make it possible to devisesystems that can help take and manage risk positions in dierent assetmarkets.This chapter investigates the application of ANNs to high frequencyforecasting of the following exchange rates: the GBP/DEM, the DEM/FRF, the DEM/ITL, the USD/DEM, the USD/CHF and the DEM/JPY.For benchmarking purposes, our models' results are compared to those oftwo naive linear models. They are evaluated not only on the basis of their
250
Advanced Trading Rules
respective forecasting accuracy, but also on the basis of their economicsigni®cance, i.e. the models are also tested by means of a trading strategy.Such tests are necessitated by the fact that the expected returns from highfrequency forecasts can easily be wiped out by the associated transactioncosts and the time lags between when the price is recorded, when the model isrun and, ®nally, when the order is executed.In section 8.2, we brie¯y describe the principles of ANNs, the datapreprocessing they require and the modelling procedure that we haveadopted. In section 8.3, we present some of our ®rst results and some furtherexperiments that we conducted.8.2 BASIC CONCEPTS, DATA PROCESSING ANDMODELLING PROCEDUREThe reason why we have chosen the ANN technology for high frequencyforeign exchange forecasting is fairly simple: having used linear models andnonlinear parametric ®lters for several years, we wished to further enlarge ourtoolbox of forecasting techniques by adding models where no speci®cfunctional form was a priori assumed. 1 It can be shown, as in Refenes,Bentz and Burgess (1994) for instance, that ANNs are equivalent to nonlinearnonparametric models. Furthermore, following Cybenko (1989) and Hornik,Stinchcombe and White (1989), it can be demonstrated that speci®c ANNs, ifthey are suciently large, can approximate any continuous function. 2The general speci®cation of the intraday foreign exchange models presented in this chapter therefore uses ANN methodology. The networkarchitecture that we have used in practice is reasonably straightforward. Ifthere are many dierent types of ANN models, we chose probably the mostcommonly used, i.e. the backpropagation multi-layer perceptron (MLP)which feeds its inputs along a series of weighted connections and applies anonlinear transformation in its processing elements (see Figure 8.1).ANNs are a tool for determining the relative importance of an input (or acombination of inputs) for predicting a given outcome. They are a class ofmodels made up of layers of elementary processing units, called neurons ornodes, which elaborate information by means of a nonlinear transferfunction. Most of the computing takes place in these processing units (formore details, see Simpson, 1990). The input signals come from an input vectorA  a1 ; a2 ; . . . ; an  where ai is the activity level of the i th input. A series ofweight vectors Wj  w1j ; w2j ; . . . ; wnj  is associated with the input vector sothat the weight wij represents the strength of the connection between the inputai and the processing unit bj . Each node may additionally have also a biasinput j modulated with the weight w0j associated with the inputs. The total
Economic value of leading edge techniques for exchange rate prediction
251
1Figure 8.1 ANN architecture
input of the node bj is formally the dot product between the input vector Aand the weight vector Wj , minus the weighted input bias. It is then passedthrough a nonlinear transfer function to produce the output value of theprocessing unit bj :Xnai wij w0j j  f Xi bj  fi1
In our case, we used a bilogistic sigmoid: 3f Xi  
21  e Xi
1
At the beginning, the modelling process is initialized with random valuesfor the weights. The output value of the processing unit bj is then passed on tothe single output node of the output layer. The ANN error, i.e. the dierencebetween the ANN forecast and the actual value, is analysed through the rootmean squared error. The latter is systematically minimized by adjusting theweights according to the level of its derivative with respect to these weights.The adjustment obviously takes place in the direction that reduces the error.As can be expected, ANNs with two hidden layers are more complicated. Ingeneral, they are better suited for discontinuous functions. They tend to havebetter generalization capabilities, but are also much harder to train. In
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Advanced Trading Rules
summary, ANNs depend crucially on the choice of the number of hiddenlayers, the number of nodes and the type of nonlinear transfer function (inour case, a bisymmetric sigmoid).A good predictive model should be capable of forecasting with a reasonabledegree of accuracy not only in-sample, but also out-of-sample, i.e. it shouldbe able to generalize to previously unseen data. Preventing over®tting of themodel is crucial. This is achieved by using, on top of the in- and out-ofsample data sets (respectively the `training' and the `test' data sets in ANNjargon), a third data set called the `validation' set. We show an example ofsuch a partition of the total data set for the DEM/FRF (Figure 8.2).Periodically, during the training period, the error of the ANN is measuredon the validation set. 4 Thus, over®tting is avoided by training the ANNon the in-sample period until the forecasting error on the validation set goesup signi®cantly. Indeed, the ®nal ANN chosen for the USD/CHF is the onewith the lowest error on the validation set (see Figure 8.3). Note also thenecessity of having powerful computers as ANN training ®nished after 15 000epochs (each ANN model took in the order of 8 hours to train on aSunSparc 20).Input selection, data scaling and preprocessing are of crucial importance tothe successful development of ANN models (Klimasauskas, 1994; Deboeckand Cader, 1994).Potential inputs were selected using traditional statistical analysis: theseincluded the raw exchange rate series and lags thereof, descriptive statisticsand data transformations. Input selection relied mostly on correlationanalysis to detect valuable input variables and cross-correlations were usedto avoid multicolinearity as this may cause certain inputs to seem lessimportant than they really are. Correlations were calculated for the entiredata set and independently for the three subsets to check for their relativestability over time. Inputs showing an unstable correlation (or, even worse,a reversal in the sign of the correlation) with the output