730.0330.0460.0070.0360.0300.0430.0750.0790.0176.041(0.188)61.38251.2200.0590.56147.9670.7311.723100.00045.161100.000
0.0790.0320.0530.128*0.0780.0110.0230.0390.0060.0128.415(0.412)54.47252.0330.1610.56853.2520.6310.625n.a.n.a.n.a.
0.0270.127*0.0870.0340.0190.0810.0320.0870.0850.00711.736(0.697)63.00856.9110.9781.33158.5371.4621.733n.a.n.a.n.a.
0.1060.0400.0490.139*0.1020.0150.0380.0290.0580.03612.646(0.756)59.35056.0980.7891.68058.1301.2952.144*100.000100.000100.000
0.0630.0210.0260.135*0.134*0.0120.0140.0100.0020.02110.236(0.580)60.56956.0980.8631.73759.3501.4192.750**100.000100.000100.000
0.0920.0030.0120.0910.0160.1210.0200.0100.0250.0648.958(0.464)
0.1060.0350.0050.0470.0480.1270.0290.0430.0150.0429.182(0.485)
USA
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 (%)
0.352**0.3191.9162.8780.1830.0420.0710.790
0.339**0.3531.4803.5950.2290.2450.8383.138
0.387**0.3501.8253.3290.2120.0430.2101.014
0.3410.3443.8851.3770.0880.0340.0651.829
0.4740.9414.1631.7850.1140.6850.9862.813
0.593*0.4983.6282.5630.1630.1050.0292.984
0.557**0.6063.1552.7670.1760.0860.3293.587
0.1520.0012.6780.8880.0570.0730.2620.021
0.0180.1412.2720.1240.0080.0320.1050.352
0.1160.0000.0190.0890.0860.0750.0680.0180.0220.06510.779(0.625)60.16355.2850.9481.50958.9431.8942.517*n.a.n.a.n.a.
0.134*0.0370.0660.129*0.0840.170**0.0390.146*0.0190.05324.893**(0.994)65.44756.5040.8921.988*63.8211.974*4.767**n.a.n.a.n.a.
0.141*0.0640.0070.151*0.1030.1040.0720.0170.0380.05618.961*(0.959)61.38254.8781.0951.06158.1302.049*1.891100.000100.000100.000
0.0470.0570.0210.1030.0680.0290.0470.0910.0480.0539.147(0.482)54.06554.8780.6301.34954.4721.2210.855n.a.n.a.n.a.
0.0130.150*0.0380.0120.0520.0540.0670.0900.1080.01913.278(0.791)62.60256.5040.8551.49260.1631.4512.795**n.a.n.a.n.a.
0.0900.0210.0120.153*0.0840.0330.0240.0690.0860.02913.132(0.784)59.75656.9111.4921.45158.1302.173*1.659100.000100.000100.000
0.0610.0310.0240.1010.1150.0270.0090.0340.0200.0447.983(0.369)61.38256.9111.5201.47360.1632.289*2.619**100.000100.000100.000
0.0740.0240.0320.0290.0050.130*0.0170.0570.0600.0287.973(0.369)
0.0720.0470.0410.0430.0030.0940.0380.0570.0680.0337.355(0.308)
This table shows performance measures and statistics for selected foreign exchange trading strategies. The base currency is denoted on the far left. The MSCIand Equal columns are reproduced from Table 7.1. The ®rst t-stat is used to test the signi®cance of the mean return relative to a null hypothesis of zero. The[Interest Dierential] rows give the mean monthly return due to the interest dierential of the non-domestic relative to the domestic currency. The Ljung andBox Q-statistic is denoted as LBP(10) and tests whether the 10 autocorrelations are jointly signi®cant. The p-value for the Q-statistic is given below the LBP(10)row. The [Prob >] rows give the percentage of the total months that the given strategy has exceeded zero, the MSCI benchmark, and the Equal benchmark. Thepaired t-test is used to test the signi®cance of the excess returns of each of the ranks and the long±short strategies relative to the MSCI benchmark and the Equalbenchmark. The Wilcoxon is a nonparametric test of the excess returns. The [Proportion >] rows give the percentage of the 93 MA combinations that exceedzero, the MSCI benchmark average return, and the Equal benchmark average return. ** and * indicate signi®cance at the 1 and 5 per cent levels.
218
Advanced Trading Rules
percentage of months the strategies had a positive return, a return greaterthan the MSCI currency benchmark, and a return greater than the Equalcurrency benchmark.For all base currencies, the moving-average and interest rate strategies inthe Long±Short Across division had a positive return in about 60 per cent ofthe months. The probabilities that the returns were greater than the MSCIand Equal benchmarks were also greater than 50 per cent for all basecurrencies, and for most currencies were above 55 per cent. For most basecurrencies, either the paired t-test or the Wilcoxon test also showed thestrategies to yield statistically signi®cant excess returns. However, thestatistical signi®cance of the moving-average and interest rate returns wasnot, in general, as great with the MSCI and Equal benchmark as they werewith the zero benchmark. As was documented in Okunev and White (2002),nearly all moving-average speci®cations have an average performance greaterthan zero, the MSCI currency benchmark, and the Equal currency benchmark.Tables 7.4 to 7.7 summarize the subperiod performance of the strategies.Clearly, the period 1980±1984 was the golden era for market ineciency inthe foreign exchange market. By examining Table 7.4 we can see that duringthis time, the Long±Short Across interest rate strategy generated annualreturns of over 12 per cent on average. In fact, all strategies in the Long±Short Across division performed markedly well. Even in the Long±ShortWithin division, all the trading rules generated substantial returns during thistime.At ®rst sight, one interesting result for the period 1980±1984 is that theLong±Short Within interest rate rule outperforms the Equal benchmarkduring 90 per cent of the months for Japan and 95 per cent of the monthsfor Switzerland. This result, however, is not as impressive as it ®rst appears.During this time both Japan and Switzerland had very low interest ratescompared to the other base currencies. Consequently, for both the Japaneseyen and the Swiss franc as base currencies, the Long±Short Within interestrate rule speci®ed long positions in nearly all non-domestic currencies most ofthe time. Because the interest rate rule gave equal weight to all non-domesticcurrencies, the positions in both Japan and Switzerland for the interest raterule were very close in construction to the Equal currency benchmark. TheEqual currency benchmark returns is determined using base currency returns,whereas the performance of the trading rules is determined using interestadjusted currency returns. Since the domestic interest rates in both Japan andSwitzerland were low relative to the non-domestic rates, the interest-adjustedcurrency returns were generally greater than the base currency returns.Because of this, any strategy (earning interest-adjusted currency returns)
The pro®ts to technical analysis in foreign exchange markets 219that gave equal, positive weight to all non-domestic currencies would beexpected to outperform the Equal currency benchmark (earning basecurrency returns). This can be easily seen by direct comparison of Equation(7.1) with Equation (7.3).Table 7.5 shows that during the 1985±1989 period the moving-averageclasses in both the Long±Short Within and the Long±Short Across divisionsexperienced substantial returns. The momentum and the interest rate rulesdid not fare nearly as well during this time period. During this time, German,Japanese and Swiss interest rates were much lower than the other countriesconsidered in the study. Because of this, the Long±Short Within interest raterule had returns greater than the Equal benchmark in most of the monthsduring this time period for the mark, the yen, and the Swiss franc.Table 7.6 shows the 1990±1994 period to be entirely dierent from theother subperiods in the analysis. While the two classes of moving-averagerules in the Long±Short Across division continued to generate positive meanreturns, the performance is not nearly as strong as in the other subperiodsconsidered. All the strategies in the Long±Short Within division performedrather poorly. It is not surprising that some might have thought technicalanalysis to be dead during the mid-1990s. The notable exception is that thethree-month momentum rule in the Long±Short Across division performedquite well during this time period. We should, however, remain somewhatsceptical concerning the potential of the momentum rule class. In separatetests, the one-month momentum rule also had very strong returns, however,the six-month, nine-month, and one-year momentum rules did not performparticularly well during this time. It is not at all clear that this particularresult for the three-month momentum rule is not entirely due to chance.Table 7.7 shows the Long±Short Across moving-average rules to performmarkedly well once again for all base currencies during the 1995±2000 period.In addition, the Long±Short Across interest rate rule has also generatedsubstantial returns during this time period. Because Japan's domestic interestrate was then extremely low, the Long±Short Within interest rate ruleoutperformed the Equal benchmark in all of the months during this timeperiod with the yen as the base currency.In general, the Long±Short Across MA 1; 2; 3 7 class outperforms allother classes for all base currencies over the period of the study. In general,this class has a higher mean return and information ratio than the otherstrategies considered by this study. The Long±Short Across interest rate rule isintriguing and it is perhaps possible that combining it with theMA 1; 2; 3 7 class could bene®t currency exposures. While the Long±Short Within moving-average class does not perform as well on average, itsrelatively low risk level and high information ratio may cause it to add some
Table 7.4 Performance of selected strategies: sub-period analysis: 1980±1984Long±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]
[
Canada
Mean Ret (%)Median Ret (%)Std Dev (%)t-statInformation RatioInterest Dierential (%)SkewnessKurtosisProb >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon testMean Ret (%)Median Ret (%)Std Dev (%)t-statInformation RatioInterest Dierential (%)SkewnessKurtosisProb >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon test
0.3620.1531.5031.8640.2410.0100.0830.14655.00050.0000.1620.01553.3331.4010.3170.489*0.5741.7032.2220.2870.1050.7341.16061.66761.6671.5021.03865.0002.311*0.847
0.2050.2831.5511.0250.1320.3293.41420.91261.66756.6670.2600.90565.0000.7862.017*0.684**0.5731.4893.5610.4600.3580.0490.60771.66763.3332.052*1.52470.0002.770**2.326*
0.3420.2581.5091.7540.2260.0230.1240.42858.33350.0000.1000.05956.6671.3810.4420.422*0.3061.5452.1160.2730.1550.8561.84063.33356.6671.3080.22165.0002.180*1.170
1.020*1.5033.8832.0350.2630.0021.0191.35066.66760.0001.3061.05361.6671.8980.8830.8181.2193.5141.8020.2330.0231.0102.13466.66763.3331.5291.14168.3332.083*1.921
1.318**1.4142.9163.5010.4520.8770.9123.00875.00070.0002.150*2.275*68.3332.869**1.1780.878*0.9733.1742.1420.2760.8540.8792.61471.66765.0001.8431.38468.3332.587**1.701
0.6991.3313.5261.5360.1980.1561.2732.07468.33360.0000.7801.34763.3331.4841.6640.6240.8983.2511.4870.1920.1401.2722.94563.33358.3331.2250.16968.3331.8672.105*
[
Australia
0.5300.9853.2471.2650.1630.1861.3893.40268.33356.6670.4610.50863.3331.2301.5610.3920.6192.9291.0370.1340.1211.2683.76966.66760.0000.8120.87665.0001.5421.251
0.3130.0321.8691.2970.1670.1883.06415.967
0.1420.2712.0290.5420.0700.2101.9138.111
0.0230.0001.2090.1440.0190.2710.2310.412
0.4600.4781.8571.9180.2480.2950.8071.127
France
Germany
Mean Ret (%)Median Ret (%)Std Dev (%)t-statInformation RatioInterest Dierential (%)SkewnessKurtosisProb >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon testMean Ret (%)Median Ret (%)Std Dev (%)t-statInformation RatioInterest Dierential (%)SkewnessKurtosisProb >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon test
0.2910.2831.7711.2720.1640.1370.0001.59563.33320.0003.937**3.394**30.0003.117**1.6420.512*0.3441.8732.1180.2730.0220.2642.04261.66738.3331.4321.48066.6670.2563.158**
0.0700.1081.7390.3130.0400.3820.9114.83555.00035.0002.810**0.92833.3332.431*1.8550.464*0.4711.4452.4890.3210.3360.4100.47571.66743.3331.963*0.20656.6670.0501.575
0.1960.1861.5960.9510.1230.0060.1301.86660.00028.3333.667**1.84826.6673.069**3.165**0.4160.3241.7201.8730.2420.0840.0232.00663.33340.0001.8510.94268.3330.2023.850**
0.930*1.3743.6161.9930.2570.0880.8701.72366.66748.3330.9880.25061.6670.1222.503*0.8661.1983.5751.8770.2420.0420.8821.68565.00050.0000.0470.06658.3330.9980.979
1.612**2.2773.1603.9510.5100.8451.1013.07875.00056.6670.6900.20665.0001.6201.3991.247**1.5833.1053.1110.4020.8940.9562.67073.33356.6670.8480.71465.0002.038*1.627
0.7591.0213.2921.7860.2310.1781.1772.58163.33348.3331.4560.76653.3330.5681.0090.6561.0653.1501.6140.2080.1471.2843.35763.33348.3330.5510.00055.0000.5000.294
0.7220.8033.1111.7980.2320.1931.2923.73465.00041.6671.7260.88356.6670.7201.8260.6620.7672.9961.7110.2210.1781.4545.23265.00048.3330.6160.23665.0000.5772.459*
1.337**1.2122.6503.9070.5040.2970.0692.198
0.980**0.8661.9883.8190.4930.3340.2942.070
0.885*0.7842.6912.5470.3290.1950.1401.735
0.4570.2102.0251.7470.2260.2150.0210.857
(continued )
Table 7.4 (continued)Long±Short WithinLong±Short AcrossCurrency benchmarksÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐ ÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐ ÐÐÐÐÐÐÐÐÐÐ[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 (%)SkewnessKurtosisProb >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon testSwitzerland Mean Ret (%)Median Ret (%)Std Dev (%)t-statInformation RatioInterest Dierential (%)SkewnessKurtosisProb >0 (%)Prob >MSCI (%)paired t-testWilcoxon testProb >Equal (%)paired t-testWilcoxon test
0.3200.5612.1661.1460.1480.0260.8404.34060.00050.0000.9540.39866.6672.064*2.393*0.662**0.6741.9692.6060.3360.1040.0472.48771.66733.3330.0552.834**60.0001.4011.090
0.1570.3472.2150.5490.0710.4420.6730.73960.00046.6671.5271.92190.0007.678**4.792**0.840**0.5942.1203.0700.3960.5110.4301.32075.00051.6671.1270.35395.0008.840**6.088**
0.0460.3862.1090.1680.0220.0291.2323.90360.00041.6670.3761.89968.3331.6832.893**0.593*0.4011.8752.4490.3160.1910.0432.41070.00038.3330.2901.69370.0001.2883.033**
0.973*1.3013.0362.4820.3200.0170.7161.76566.66760.0002.216*0.72165.0003.015**1.1780.7661.2083.4511.7200.2220.0380.8241.57465.00051.6670.2000.19161.6671.2011.516
0.848*0.9403.3111.9840.2560.8520.9932.17068.33358.3331.6810.67061.6672.520*0.5010.1670.5873.2770.3940