0190.0230.1050.0210.0960.0250.0770.0360.12912.101(0.722)
0.0970.0010.0810.0030.0520.1220.1250.0140.0380.08914.357(0.843)
0.0700.0150.1040.0150.0500.0550.1190.0140.0710.09712.349(0.738)
0.0670.0570.0250.1060.0370.0930.0330.0650.1240.00212.288(0.734)
0.0980.0430.0820.0100.0140.0430.0370.0700.0300.0758.032(0.374)
n.a.n.a.n.a.n.a.n.a.n.a.n.a.n.a.n.a.n.a.n.a.n.a.
0.1060.0180.0240.0440.0060.1230.0360.0280.0080.0698.783(0.447)
0.1130.0230.0040.1030.0050.1090.0280.0120.0270.0609.948(0.555)
0.1240.0190.0180.0570.0390.1170.0350.0400.0120.0419.498(0.514)
USA
Mean Ret (%)Median Ret (%)Std Dev (%)t-statSkewnessKurtosis
0.0630.1832.8690.3460.5722.571
0.0680.0951.3560.7870.2280.828
0.0120.1323.2660.0570.0490.250
0.1120.1153.3540.5260.0090.151
0.1420.2703.6980.6040.7561.457
0.1530.3473.6430.6600.2570.079
0.1070.0243.2740.5150.2082.054
n.a.n.a.n.a.n.a.n.a.n.a.
0.0790.1242.7060.4610.2540.065
0.0150.0302.3070.1010.1140.217
Autocorrelations10.06720.03730.01540.147*50.05760.08170.00280.138*90.094100.032LBP (10)16.224p-value(0.907)
0.0310.0200.0040.0000.0120.0570.1140.1040.142*0.10514.692(0.856)
0.0630.1020.0800.0210.0700.0730.0850.0100.0760.02810.984(0.641)
0.0620.0890.0500.0140.0650.0550.0900.0090.0530.0258.127(0.384)
0.0660.0610.0290.0300.0330.1080.0140.0900.0720.0028.796(0.448)
0.1170.0780.0270.0020.0270.0960.0680.0060.0860.01410.387(0.593)
0.0960.0170.0180.0560.0120.1190.0390.0280.0080.0678.310(0.401)
n.a.n.a.n.a.n.a.n.a.n.a.n.a.n.an.a.n.a.n.a.n.a.
0.0980.0480.0530.0080.0120.1120.0290.0670.0680.0169.196(0.486)
0.1040.0770.0660.0160.0230.0720.0540.0720.0820.01610.193(0.576)
The dataset consists of interest-adjusted monthly returns for individual currencies from January 1980 to June 2000. The period consists of 246 months. The basecurrency is denoted on the far left and the columns to the right give the return statistics of the seven other currencies with respect to the base currency. MSCI andEqual returns are calculated relative to the base currency. The MSCI column is calculated using the MSCI weights excluding the base currency. The Equalcolumn calculates the currency return assuming an equal proportion allocated to the seven currencies. The Ljung and Box Q-statistic is denoted as LBP(10) andtests whether the 10 autocorrelations are jointly signi®cant. The p-value for the Q-statistic is given in the last row for each base currency. ** and * indicatesigni®cance at the 1 and 5 per cent levels.
204
Advanced Trading Rules
notable exception of the eighth and ninth autocorrelations of the French andGerman currencies with respect to each other.Table 7.2 provides similar summary statistics for the monthly interestadjusted currency returns. These are the actual returns that an investorwould face when trading in the currency markets. Of particular note, theinterest-adjusted currency returns are much smaller in magnitude than thebase currency returns. Any trading strategy relying on these returns wouldhave a much greater hurdle to overcome to exceed a benchmark of simplyholding the MSCI or Equal benchmark basket of currencies. Note that on aninterest-adjusted basis the rankings of performance dier markedly fromTable 7.1. The Swiss franc is now the worst-performing currency even thoughit was one of the strongest for base currency returns. The Australian dollar'sinterest-adjusted performance is no longer quite so poor, and the Japaneseyen has an interest-adjusted return very close to zero in magnitude. Theseresults can be easily explained by the very low historical interest rates in Japanand Switzerland and the high historical interest rate in Australia relative tothe other countries. While those who invested in Japan and Switzerlandwould have bene®ted from currency appreciation, the returns due to interestyields in these countries have been relatively modest.7.3 TRADING STRATEGIESWe analyse the trading strategies in this chapter from the following eight basecurrencies of reference: the Australian dollar, the British pound, theCanadian dollar, the French franc, the German mark, the Japanese yen,the Swiss franc, and the United States dollar. From the perspective of a givenbase currency a foreign exchange trader can initiate either long or shortpositions in up to seven non-domestic currencies during any given month. Aforeign exchange trader might take a position in a subset or all seven nondomestic currencies. We will analyse two divisions of foreign exchangetrading techniques. One technique is for the foreign exchange trader to takepositions (either long or short) in all seven non-domestic currencies everymonth. We will classify this division of trading as Long±Short Within. Forexample, from a US dollar base currency of reference, a foreign exchangetrader may initiate a long or short position in Australian dollars, Britishpounds, and Japanese yen while shorting Canadian dollars, French francs,German marks, and Swiss francs. The second technique is for a foreignexchange trader to take positions in only a subset of the seven non-domesticcurrencies during any given month. We will classify this second division oftrading rule as Long±Short Across. Long±Short Within trading rules will notconsider other non-domestic currencies when setting a long or short position
The pro®ts to technical analysis in foreign exchange markets 205in an individual currency. Long±Short Across trading rules will evaluatewhether to trade in a given non-domestic currency and the type of position(long or short) by comparing technical performance across non-domesticcurrencies. Within each division we will analyse three classes of foreignexchange trading rules: momentum, interest rate-based strategies, and movingaverage rules.Within the Long±Short Within division, all non-domestic currencies willeither be bought or sold every month depending upon the class of tradingrules followed. For momentum strategies, a non-domestic currency will bebought/sold if the prior n-month base return of the currency is positive/negative. The interest rate strategies will dictate that a non-domestic currencybe bought/sold if the non-domestic interest rate is greater than/less than thelocal interest rate. The motivation for following the interest rate strategy canbe easily seen by examining Equation (7.4). By buying/selling high/lowinterest rate currencies, the foreign exchange trader is guaranteed of lockingin a return equal to the interest rate dierential between the non-domestic anddomestic currency. If a foreign exchange trader believes that any remainingreturn is random noise, then following this strategy should yield positiveexcess returns. The ®nal class of trading rules is to use moving-averagestrategies. A moving-average rule requires that a currency be bought/sold ifthe short-run moving average is greater than less than the long-run movingaverage of prior base currency returns.We now need to de®ne the moving average rules. At time t the short-runmoving average and the long-run moving average are computed as:SRj;t LRk;t 
RB;t  jRB;t  k
1SRj;t 1j1LRk;t 1k
7:67:7
where SRj;t is the short-run moving average at month t using the prior jmonths of returns and LRk;t is the long-run moving average at month t usingthe prior k months of returns. 5 A given short-run/long-run moving-averagerule, MA j; k, would require a currency be bought at time t if SRj;t > LRk;tor sold at time t if SRj;t < LRk;t .Within the momentum class, we examined trading rules based upon priorone-month, three-month, six-month, nine-month, and one-year base currencyreturns. By construction, only one trading rule exists for the interest ratetrading rule class. For the moving-average rules, the short-run movingaverage values from one to twelve months and the long-run moving averagevalues from two to thirty-six months. For all combinations of short-run,long-run moving-average rules, the number of months used to compute the
206
Advanced Trading Rules
short-run moving average must be less than the number of months used tocompute the long-run moving average. For example, using a short-runmoving average of one month, we determine the currency positions using:SR1;t LR2;t ; SR1;t LR3;t ; . . . ; SR1;t LR36;t . Using a short-run movingaverage of two months, we determine the currency positions using:SR2;t LR3;t ; SR2;t LR4;t ; . . . ; SR2;t LR36;t . In total, we evaluate 354moving-average combinations. In eect, the moving-average class is givinga weighted allocation to the seven non-domestic currencies as dierentmoving-average rules will provide dierent buy/sell signals for individualcurrencies. The returns to the moving-average class in the Long±Short Withindivision will be determined by averaging the returns of all combinations ofmoving-average rules for each non-domestic currency each month and thenaveraging the returns across the seven non-domestic currencies each month.In this way, we will construct the monthly returns to the moving-average classof trading rules in the Long±Short Within division.Within the Long±Short Across division, the momentum trading rule willbuy the non-domestic currency with the highest prior n-month base currencyreturns and short the non-domestic currency with the lowest prior n-monthbase currency returns. Unlike the momentum rule in the Long±Short Withindivision, only two non-domestic currencies will be traded in any given month.The interest rate strategy will buy the non-domestic currency with the highestinterest rate and short the non-domestic currency with the lowest interestrate. 6 For the Long±Short Across division, we will evaluate two classes ofmoving-average rules. One class of moving-average rules will determineSRj;t LRk;t and then buy/sell the currency with the greatest/smallestdierence. We will refer to this ®rst class of moving-average rules asMA 1 7. The second class of moving-average rules will buy the threecurrencies (equally weighted) with the greatest dierence SRj;t LRk;t andshort the currency with the smallest value of SRj;t LRk;t . 7 We will refer tothis second class of moving-average rules as MA 1; 2; 3 7. With bothclasses of moving-average rules we will once again average across the returnsfor multiple parameterizations each month to calculate the monthly return.As we have been careful to state, we do not wish to evaluate individualspeci®cations of trading rules. Instead, we wish to consider broad classes oftrading rules. To do this, we average across the return series for all theindividual speci®cations of trading rules within one class to determine theoverall performance for a given class of trading rules. Okunev and White(2002) found that the moving-average class within the Long±Short Acrossdivision has performed quite well throughout the 1980s and the 1990s. Wetherefore view this class as the benchmark by which to compare the otherstrategies.
The pro®ts to technical analysis in foreign exchange markets 207We generally found the momentum trading rules in both divisions toperform very poorly compared with the interest rate rules and the movingaverage rules. In fact, we found the best performing momentum rule tounderperform both the interest rate and the moving-average rules. In order topresent the momentum trading rules in the most favourable manner withrespect to our benchmark, we will show only the results for the three-monthmomentum. 8 We did, however, in separate tests evaluate the one-month, sixmonth, nine-month, and one-year momentum trading rules.For the moving-average rules, we will present only the results for the shortrun moving average ranging from four to six months and the long-runmoving average ranging from ®ve to thirty-six months. Okunev and White(2002) found the performance for this particular range of parameterizationsto be stable across time and base currencies of reference. This subset willcomprise 93 combinations of moving-average rules and we will average acrossthe returns of the individual speci®cations when calculating the monthlyreturns to the moving-average class. The complete results and analysis for the354 moving-average rules as a class are given in Okunev and White (2002). 9In the end, for the Long±Short Within division we will present the resultsfor the three-month momentum rule, the interest rate rule, and the movingaverage class comprising rules MA 4; 5 MA 6; 36. In the Long±ShortAcross division we will present the results for the three-month momentumrule, the interest rate rule, and two moving-average classes comprising rulesMA 4; 5 MA 6; 36. One moving-average class will go long in onecurrency and short in another currency based upon the dierence betweenthe short- and long-run moving average. The second moving-average classwill go long in the top three currencies and short in the lowest currency asmeasured by the dierence between the short- and long-run moving average.For both the momentum and the moving-average rules we will use basecurrency returns to determine the buy/sell signals. The actual realized returns,however, will depend upon interest-adjusted currency returns. As Table 7.2shows, the interest-adjusted returns are markedly lower in magnitude than thebase currency returns. This will make earning excess returns in foreignexchange markets through any trading rule much more dicult. The testsare repeated using each currency as the base currency.7.4 RESULTSIn the presentation of the results we will examine several summary performance measures for the classes of trading rules. Most will be self-evident, buta few will require explanation. One measure we will examine closely is theinterest dierential performance for each of the strategies. The formula to
208
Advanced Trading Rules
calculate the interest dierential is given by Equation (7.4) and is simply thecomponent of total realized return due to locking in the dierence in interestrates between the non-domestic and the domestic currency. We are assumingfor the purposes of this study that all transactions are conducted through theuse of futures contracts and that the initial contract price is set by the futuresprice. The futures price, as detailed by Equation (7.2), incorporates theinterest dierential and must hold strongly in the absence of arbitrage.In short, buying/selling a non-domestic currency with a higher/lower interestrate than the interest rate with the domestic currency will result in apositive return before consideration of movements in the underlying exchangerate.Another measure we will examine is the monthly performance of thetrading strategies with respect to three dierent benchmarks. No consensusexists regarding the appropriate benchmark for risk-adjusting the strategies.If currency returns are unpredictable, one might argue the appropriatebenchmark is a zero expected return. On the other hand, an appropriatebenchmark might be to maintain a currency exposure with the samecomposition as a broad international index such as the MSCI. However,using the MSCI currency index may likewise be an inappropriate benchmarkto use to evaluate currency performance. The MSCI has, at times, givenexcessive weight to one individual currency ± most recently, the US dollar. Asa basis of comparison, a benchmark that equally weights currency exposureshould also be relevant. These benchmarks are computed using the basecurrency returns presented in Table 7.1. 10 We will also attempt to risk-adjustperformance by presenting the information ratio (mean return divided bystandard deviation) for each of the trading rule strategies. 11Table 7.3 presents summary results of the monthly returns for the tradingrule classes as well as the MSCI and Equal currency benchmarks over theentire sample period. We can see that all the trading rule classes examined inthis chapter have positive mean monthly returns for all the base currencies ofreference. 12 In general, the trading rules in the Long±Short Across divisionhad much higher mean returns than the trading rules in the Long±ShortWithin division. In all cases, both moving-average classes in the Long±ShortAcross division had mean returns signi®cantly dierent from zero with thestrategies performing the best in Australia and the worst in Switzerland. Forall base currencies, the moving-average classes in the Long±Short Acrossdivision would have generated annual returns of at least 6 per cent. With thepossible exception of Australia and Germany, the momentum rules have beenthe worst performing among the trading strategies.If performance is measured by the information ratio, the moving-averageclass in the Long±Short Within division also has performed markedly well
The pro®ts to technical analysis in foreign exchange markets 209over the sample period. In many cases, while the mean monthly return isrelatively low, the information ratio for this class of trading rule is actuallygreater than the information ratio for the moving-average class in the Long±Short Across division. That the risk for the moving-average rule in the Long±Short Within division is lower should not be surprising. All classes of tradingrules in the Long±Short Within division maintain a position in the seven nondomestic currencies every month, providing greater diversi®cation bene®tsthan that for the Long±Short Across strategies.The Long±Short Across interest rate rule also has performed quite well overthe sample period with the caveat that the risk level to this strategy is quitehigh and the resulting information ratio in many cases relatively low. In fact,for four of the base currencies the mean return to the interest rate rule was thegreatest among all the trading strategies. We can note that the performanceattributable to the interest rate dierential with the interest rate rule is oftengreater than the mean performance of the interest rate rule itself. Forexample, in the case of Canada the Long±Short Across interest rate rulehad a mean return of 0.484 per cent each month while the average return dueto investing in higher interest rate, non-domestic markets was 0.686 per centon average each month. Therefore, while the interest rate rule did experiencea positive mean overall return, the return due to currency appreciation of thestrategy was actually negative. In fact, in seven out of eight cases the interestrate rule performance suered due to currency depreciation. It is interestingto note that the return due to interest dierential for the moving-average andthe momentum rules is very nearly zero. That is, unlike the interest rate rules,the moving-average and momentum strategies experience positive returnsprimarily from pure currency movements.Another undesirable characteristic for the interest rate rules is that in alleight cases for the Long±Short Across and the Long±Short Within division, theinterest rate strategy returns were negatively skewed. This is in markedcontrast to the positive skewness of MA 1; 2; 3 7 for seven of the eightbase currencies.Analysis of the autocorrelation structure of returns reveals very little otherthan that both Long±Short Across moving-average rules are slightly negatively autocorrelated for all base currencies. Of particular note, the fourthautocorrelation for MA 1 7 is signi®cantly dierent from zero in seven outof eight cases.The paired t-tests presented in Table 7.3 measure the statistical signi®canceof excess monthly returns for the short-run, long-run moving-averagestrategies against the MSCI and Equal benchmarks. 13 The Wilcoxon test isa nonparametric test of the statistical signi®cance of the excess returns.Related to an examination of excess returns, Table 7.3 also provides the
Table 7.3 Performance of selected strategies: January 1980±June 2000Long±Short WithinLong±Short AcrossCurrency benchmarksÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐ ÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐ ÐÐÐÐÐÐÐÐÐ[Momentum] Interest[Momentum] Interest[MA 4 6 MA 4 63-month[rate][MA 4 6 3-month[rate]1 71; 2; 3 7 [MSCI][Equal]
[
Mean Ret (%)Median Ret (%)Std Dev (%)t-statInformation RatioInterest Dierential (%)SkewnessKurtosisAutocorrelations12345678910LBP (10)(p-value)Prob >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon testProportion >0 (%)Proportion >MSCI (%)Proportion >Equal (%)
[
Australia
0.1120.0842.7100.6480.0410.0160.6535.726
0.0800.2732.8410.4440.0280.3341.5606.437
0.2440.2242.6651.4340.0910.0170.3716.865
0.624**0.8433.5702.7390.1750.0090.3470.350
0.795**0.9423.4243.6390.2320.6101.0843.873
0.685**0.9073.3033.2540.2070.0970.4370.615
0.693**0.8582.9523.6800.2350.1090.5011.233
0.392*0.0213.0861.9910.1270.3081.3914.599
0.2910.0883.2901.3900.0890.2781.1803.178
0.0110.0330.1000.139*0.0950.0170.0530.172**0.0040.06918.763*(0.957)47.56144.3091.1991.70241.0570.7283.628**n.a.n.a.n.a.
0.0570.0600.0970.1040.0540.0480.0240.0420.0820.01310.081(0.567)56.09851.2200.8650.30854.0650.5671.444n.a.n.a.n.a.
0.0450.0530.0580.171**0.0770.0380.0970.0990.1090.00918.443*(0.952)56.09849.1870.5910.30946.3410.1832.096*100.0000.0000.000
0.203**0.1100.0250.137*0.0730.0700.142*0.0310.0340.06126.335**(0.997)58.13055.6910.8051.38555.2851.0940.909n.a.n.a.n.a.
0.0910.0940.0660.0380.0620.0790.0280.0860.0550.02510.926(0.637)67.07360.1631.3022.413*58.5371.5881.305n.a.n.a.n.a.
0.165**0.0490.0110.153*0.1150.1050.1050.0590.0380.07023.851**(0.992)61.78957.3171.0262.282*55.2851.3120.833100.000100.000100.000
0.130*0.0410.0140.1050.183**0.0610.0780.0900.0310.03520.229*(0.973)65.04157.3171.1012.144*57.3171.3971.705100.000100.000100.000
0.0310.0360.0730.1190.0460.0030.0530.0300.1170.02210.193(0.576)
0.0670.0190.0520.0970.0140.0240.0540.0370.0890.0027.307(0.304)
Canada
Mean Ret (%)Median Ret (%)Std Dev (%)t-statInformation RatioInterest Dierential (%)SkewnessKurtosisAutocorrelations12345678910LBP (10)(p-value)Prob >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon testProportion >0 (%)Proportion >MSCI (%)Proportion >Equal (%)
0.251*0.2001.9382.0320.1300.0190.0320.529
0.304**0.3241.6472.8940.1850.2490.3981.724
0.331**0.3311.8502.8070.1790.0510.3961.038
0.3070.3683.8331.2560.0800.0150.0811.763
0.4840.7764.2451.7860.1140.6860.9832.703
0.597**0.5323.6062.5980.1660.0940.0392.925
0.589**0.5903.1032.9770.1900.0780.3443.725
0.2100.0961.8531.7780.1130.1930.0680.562
0.0930.1492.3310.6250.0400.1450.