to ®lterrules.14. Of course, it is still possible that the head-and-shoulders rule adds value tosome other technical rule.
Chapter 10Informative spillovers in the currencymarkets: a practical approach throughexogenous trading rulesPIERRE LEQUEUX
10.1 INTRODUCTIONThe concept of a global currency market, well established in the dealingcommunity, is generally accepted by all schools of thought ± be they thosethat describe themselves as favouring an approach according to fundamentals, technical analysis or quantitative analysis. A market move will trigger achain of events that will in time aect other markets by creating temporalimbalances in the equilibrium relationship that rules these markets. Describedmathematically, there is a strong belief in cross-correlation of an orderdierent from zero at various time lags.The very few that might contest this concept usually come back to theirsenses when a ®nancial crisis occurs. Market participants, indeed, becomepainfully aware of these dependencies between markets in times of extremevolatility. A recent example occurred in September 1992 when ®nancialshockwaves destabilized the ERM. During this well-documented crisis(Sease, 1992) huge losses and pro®ts were made overnight from derivativesand cash trading books. The level of correlation between the assets that wereat the basis of their diversi®cation changed drastically, resulting in largeunwanted equity swings.Because of the inter-market relationships, there is a common questamongst traders to try to ®nd which market will trigger another. The linkbetween currencies and interest rates is a well-known feature of the foreignexchange market. On 30 June, 1996, the currency section of the FinancialTimes reported: `The dollar fell sharply on the foreign exchanges on Friday,due partly to resurgent expectations of higher German interest rates aseuromark futures were sold o. Traders this week will be looking for furtherclues as to the likely timing and direction of future German and US interest
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Advanced Trading Rules
rate changes.' There is indeed a strong belief that the interest rates marketslead the currency market as money ¯ows from one country to another.Johnson (1994: 44±46) reported: `International long and short term bonds,notes and deposit rates abound with untapped insights into the future valuesof currencies.'For a systematic trader, such a line of thinking is quite attractive, since ifsuch cross-correlation does exist it might enable him or her to devise ecienttrading strategies. On the one hand, the correlation might generate moreaccurate buy or sell signals by using information with less noise. On the otherhand, if the cross-correlation is of order higher than zero, it will provide anew source of predictive information. Then an exogenous model might provemore eective than an endogenous one.In section 10.2 of this chapter we look at the statistical properties of interestrates and spot currency prices. We go on looking at some empirical facts onthe relationship between spot currency price and interest rate series. In section10.3, we explain the design of our endogenous and exogenous trading rulesand why we chose more particularly some time horizon than other. Wediscuss issues about transactions cost and performance evaluation. Finally,we look at the results for the endogenous 1 and exogenous 2 trading rules anddraw some conclusions.
10.2 THE SERIES AND THEIR STATISTICAL PROPERTIES10.2.1 The dataThe relatively tranquil nature of the forward premiums series fails to mirrorthe volatile behaviour of spot price currency exchange rates and, as a result,the forward premium is considered a poor forecaster (Levich, 1989).Accordingly, we have chosen instead to use the implied interest rates derivedfrom the three months' interest rates contracts traded on the Lie futuresmarket. Our opinion is that these instruments are more receptive to the biasinduced by the expectation of the markets' participants. We calculated theinterest rates dierential time series associated with various currency pairs.The logarithmic forward premium (discount) of a currency can be de®ned asLnd 1  i= 1  i 0 e (Bilson, 1993) where i is the interest rate of the basecurrency and i 0 the interest rate of the quoted currency. Because there is atime lag of six hours between the series of interest rates and spot rates, thiswill induce some spurious correlation. This is worth bearing in mind as it willmost certainly aect unfavourably the signals generated by the trading rulesstudied here. From the data in Table 10.1, we have built three types of time
Informative spillovers in the currency markets 281Table 10.1 Characteristics of the daily dataInstrument
Source
Period
Settlement
Spot GBP-USDSpot USD-DEMSpot USD-CHFFutures 3 months Euro dollarFutures 3 months EuroSterlingFutures 3 months EuroDeutschemarkFutures 3 months Euro Swissfranc
Reuters FXFX pageReuters FXFX pageReuters FXFX pageLie (1st available contract)Lie (1st available contract)
07/02/91±20/12/9507/02/91±20/12/9507/02/91±20/12/9507/02/91±20/12/9507/02/91±20/12/95
22:00 GMT22:00 GMT22:00 GMT16:00 GMT16:05 GMT
Lie (1st available contract)
07/02/91±20/12/95
16:10 GMT
Lie (1st available contract)
07/02/91±20/12/95
16:05 GMT
price series as de®ned in Equations (10.1), (10.2) and (10.3). Daily spot ratesreturn series:)Xt  Ln St =St 1 10:1St  spot price of the currency pair on day tDaily interest rates return series:It  interest rates variation on day t1  100 Ft =100It  Ln1  100 Ft 1 =100Ft  price of the interest rate future on day tDaily interest rates dierential return series:
9>>>>=
10:2
>>>>;
9Idt  interest rates diFerential variation on day t>>>>>1  100 FBt =1001  100 FBt 1 =100 >>=Idt  LnLn1  100 FQt =1001  100 FQt 1 =10010:3>>>FBt  price of the base currency interest rate future on day t >>>>;FQt  price of the quoted currency interest rate future on day t
The series of cumulated daily returns for the dierential of interest and thespot price of the associated currency pair do not seem to exhibit any obviousrelationships, except in some periods such as 1991±1992, when both curveshead in the same direction (Figures 10.1 to 10.3). The chartist `eyeball'method would not be very helpful in generating pro®table forecast in thiscase. This is in contradiction with the interest rate `parity theorem', whichsuggests that the forward rate is an unbiased predictor of the future spot rate.
Interest rates differential return
Spot rate return
Figure 10.1 Cumulated return series for USD-CHF spot and interest rates dierential
Interest rates differential return
Spot rate return
Figure 10.2 Cumulated return series for USD-DEM spot and interest rates
Interest rates differential return
Spot rate return
Figure 10.3 Cumulated return series for GBP-USD spot and interest rates
Informative spillovers in the currency markets 28510.2.2 Summary statisticsThe variety of hypotheses about the distributions of price changes and theirgenerating process is great, but most practitioners and academics agree thatdaily changes are leptokurtic 3 and that there is substantial deviation from aGaussian model (Olsen, 1995). The summary statistics of kurtosis and skewfor our daily returns series (Tables 10.2 to 10.4) support this view. Variousexplanations for the distribution instability have been proposed, the mostpopular among them being the process of reaction to cluster of informationthrough time that are not taken into account by market participants.The skewness statistics are used to assess the degree of asymmetry of adistribution around its mean. Positive skewness indicates a distribution withan asymmetric tail extending towards more positive values. Negative skewness indicates a distribution with an asymmetric tail extending towards morenegative values. In our case, most of the distributions analysed are symmetric,
Table 10.2 Daily spot rates return series
MeanMedianStandard deviationKurtosisStandardized kurtosisSkewnessStandardized skewnessMinimumMaximumCount
USD-DEM
GBP-USD
USD-CHF
0.000 020.000 000.007 731.9613.960.040.58890.032 510.034 901212
0.000 260.000 120.007 263.2122.790.233.23630.043 900.032 991212
0.000 030.000 000.008 431.9013.520.101.44150.035 510.038 371212
Table 10.3 Daily interest rates return series
MeanMedianStandard deviationKurtosisStandardized kurtosisSkewnessStandardized skewnessMinimumMaximumCount
Euro USD
Euro GBP
Euro DEM
Euro CHF
0.000 690.000 000.008 896.8548.700.537.520.058 710.045 991212
0.000 320.000 000.011 48159.291131.947.85111.520.239 470.051 071212
0.000 100.000 000.006 3110.1772.271.1616.440.055 920.024 101212
0.000 440.000 000.010 313.2122.810.223.160.058 590.048 341212
286
Advanced Trading RulesTable 10.4 Daily interest rates dierential return series
MeanMedianStandard deviationKurtosisStandardized kurtosisSkewnessStandardized skewnessMinimumMaximumCount
Di. USD-DEM
Di. GBP-USD
Di. USD-CHF
0.000 600.000 290.009 914.5232.100.141.950.052 440.058 611212
0.000 250.000 110.012 532.8520.280.223.180.073 330.063 111212
0.000 690.000 040.008 916.8748.830.527.440.058 810.046 281212
except for the GBP (and to a lesser extent DEM) interest rates series.This might be explained by a stronger and sustained monetary policy ofthe respective central bank over the period studied than, say, for the Swissfranc.Kurtosis characterizes the relative peakedness or ¯atness of a distributioncompared to the normal distribution. Positive kurtosis indicates a relativelypeaked distribution and negative kurtosis indicates a relatively ¯at distribution. In our case, not surprisingly, we have high coecients of kurtosisbecause our sample exhibits many outliers, a situation we would not expect to®nd in a normal distribution. This phenomenon is even more pronounced inthe interest rates series. This is the re¯ection of the structural behaviour ofmoney market rates, which usually exhibit small daily returns, but whichare subject to large adjustments whenever central banks change the level oftheir base rates. The behaviour of interest rates has been extensivelystudied and ample references can be found in the ®nancial literature (Murphy,1990).The standardized values for both kurtosis and skew outside the range of 2indicate that the observed data depart signi®cantly from a normal distribution. This is the case for all the observed series. The very high value ofkurtosis and skew shown for GBP series comes from the 1992 crisis when theUK puzzled the market by withdrawing from the European Rate Mechanism(ERM). This was due to increasing speculative pressures on the GBP, notablyfrom hedge funds such as the one headed by George Soros. The Bank ofEngland reacted by raising its interest rates in a very aggressive way at ®rstand then brought them to previously unseen low levels as it exited the ERM,to the dismay of other European countries. Overall, the rates implied by thefutures market went sharply from highs of near 13 per cent to lows of 5 percent over the period studied (Figure 10.4).
3 months implied interest rate
Figure 10.4 Implied three months interest rate for the UK pound
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Advanced Trading Rules
10.2.3 AutocorrelationsA market order may contain some information about perception of theunderlying fundamental value of the asset price level. A market maker willadjust his valuation as a function of the ¯ow of information (directly orindirectly) relative to the price of the asset he is trading. This is usuallyre¯ected through the autocorrelations statistic. We estimated the autocorrelations of lags one to ten for all the series. The autocorrelations re¯ectthe tendency of the series to repeat themselves through time, expressingas they do the magnitude of the dependencies in the series of variations. Ifwe have a statistically signi®cant positive number, it means that ourunderlying series tends to repeat itself through time (trending mode). If the coecient is negative,we are in the presence of a series which tends to reverse its past behaviour(contrarian mode      ) and, ®nally, if the series do notshow any signi®cant coecient of autocorrelations it is described as whitenoise, often described as a `random walk'. These coecients are important fora directional trader because they re¯ect the predictability of a given series.The higher the absolute value of the coecient the more likely it is that thetrader will be able to forecast the underlying market. The systematic traderwill be able to use either a contrarian or trend-following system depending onthe sign of the coecient of autocorrelations to trade underlying marketpro®tably.Market eciency depends upon rational, pro®t motivated investors(Arnott and Pham, 1993). However, the two largest participants in theforeign exchange markets have no direct pro®t motive. International corporations will try to hedge their currency risk while the task of the central bank isto dampen ¯uctuations in its currency rate. Serial dependencies in currencymarkets have been observed (Kritzman, 1989; Silber, 1994) and linked tocentral bank activity as well. The central banks tend to try to dampen thevolatility in their currency because stability assists trade ¯ows and facilitatesthe control of in¯ation level. A central bank might intervene directly in thecurrency market in times of high volatility, such as the ERM crisis in 1992, oract as a discreet price smoothing agent by manipulating their domesticinterest rate levels.The spot series (Table 10.5) do not seem to exhibit signi®cant autocorrelations in comparison with the price dierential series (Table 10.6).This infers a tendency to trend which is more evident in the interest rates timeprice series than in the foreign exchange market (more smoothing in theinterest rates market than in the currency one). This is a signi®cant ®nding forus, since in the following we will use moving averages to generate directionalforecasts on spot currency exchange rates. Moving averages are trend-
Informative spillovers in the currency markets 289Table 10.5 Autocorrelations for the currencies seriesLag
USD-DEM
USD-CHF
GBP-USD
12345678910
0.013 260.030 760.020 730.045 710.000 570.080 59*0.031 490.01890.044 380.019 76
0.000 740.021 150.012 480.016 590.002 580.070 06*0.043 420.038 790.02950.010 19
0.009 870.02470.009 030.038 230.034 180.092 78*0.013 950.042 540.003 140.015 18
P
0.001 33
0.016 26
0.0783
*Signi®cant at the level of 5%.
following trading rules and perform best in markets that exhibit positive serialdependencies.10.2.4 Inter-market correlationsWhen looking at two related variables, correlation analysis is frequently the®rst calculation done. The statistic should be looked at with caution as seriescan be linearly uncorrelated and nonlinearly dependent when in the presenceof non-normal series (DeRosa, 1996). Here we look at both parametric andnon-parametric methods. The Pearson product-moment correlation assumesthat the data is normally distributed. The results given by such an analysis(Table 10.7) will tend to exaggerate the impact of high variations and it will beparticularly sensitive to highly leptokurtic distributions.When the assumption of a normal distribution is not justi®able, thecorrelation can be calculated by the non-parametric Kendall method whichis then more robust. This measures the relative degree of agreement ordisagreement between the two variables. The calculation proceeds by ®rstordering one variable from smallest to largest, then reordering the secondvariable according to the ranks of the ®rst and, ®nally, calculating how wellthe ranks of the second variable agree with the ranks of the ®rst variable.The Kendall measure of correlation tends to be smaller because of thelesser impact of the leptokurtic form of the distribution (Table 10.8). This inturn indicates the non-normality of the series studied. Over the whole periodthe correlation between the interest series and the currency series wasminimal. Nevertheless, when one looks at the relationship on the basis of a`rolling 12 months', the picture is quite dierent. Indeed the ratio of
Table 10.6 Autocorrelations for the interest rates seriesLag
Euro USD
Euro GBP
Euro DEM
Euro CHF
Di. USD-CHF
12345678910
0.007 520.019 370.049 63*0.028 080.052 72*0.007 560.063 56*0.041 290.023 490.045 5
0.020 260.073 78*0.101 94*0.022 20.009 10.033 990.038 560.029 130.018 110.040 38
0.026 530.044 580.028 690.015 530.000 190.013 810.026 030.012 220.023 990.054 45*
0.057 49*0.028 660.040 080.021 740.045 480.027 450.017 850.020 520.014 360.012 53
0.008 650.019 530.049 69*0.027 480.052 3*0.007 10.063 31*0.041 260.023 530.045 67
0.020 780.057 35*0.022 690.003 760.059 49*0.001 430.031 530.019 170.029 280.053 28*
0.077 85*0.011 630.018 960.013 20.073 56*0.017 160.003 890.019 720.017 540.015 75
P
0.155 44
0.000 31
0.083 14
0.000 26
0.156 94
0.232 84
0.195 64
*Signi®cant at the level of 5%.
Di. USD-DEM
Di. GBP-USD
Informative spillovers in the currency markets 291Table 10.7 Pearson correlation coecients between spot and interestrates seriesInterest rates/spot StDollar ItNon-dollar ItDierential Idt
USD-DEM
GBP-USD
0.1380.1130.196
0.1610.1030.135
USD-CHF0.1430.0370.155
Table 10.8 Kendall rank correlation between spot and interest rates seriesInterest rates/spot StDollar ItNon-dollar ItDierential Idt
USD-DEM
GBP-USD
USD-CHF
0.0570.0550.097
0.0660.0810.047
0.0600.0010.08
correlation has been changing drastically over time shown to be unstable.This might be due to central banks adjusting their monetary policy and beingmore or less aggressive in their market interventions, depending on theprevailing economic factors.As illustrated in Figure 10.5, the correlation between the series of dailyvariations for the interest rates dierential and the currency spot prices havebeen as high as 40 per cent in the past but have steadily decreased over thepast few years. Indeed, recently the correlation has been negative. Meanwhilethe interest rate dierential (Figure 10.6) varied from levels of 8 per cent to4 per cent. This narrowing in the interest rates dierential might confuse themarket in terms of which direction to trade the currency exchange rate andthey probably use other sources of information in order to decide at whatlevel the exchange rate of the currency they trade should be. The question is:do interest rate dierentials aect currency variations and if so how? To try toanswer this question we investigate the relationship between the yearlyaverage interest rate dierential and yearly currency volatility and correlationbetween variation in the spot price and the dierential of interest rates.Figure 10.7 clearly shows the relationship between interest rates spread andthe level of correlation between the daily variation of interest rates dierentialand spot currency exchange rates. Respective R 2 of 0.945 for USD-DEM,0.841 for GBP-USD and 0.856 for USD-CHF were obtained when ®ttingeach series by a simple linear regression.We plotted the 250 days average dierential of interest rates versus the1-year volatility of the spot return (Figure 10.8). A linear regression was used
Figure 10.5 Rolling 12-month correlation between spot currency and corresponding interest rates series
Figure 10.6 Interest rate dierentials
2m
Figure 10.7 Correlation as a function of the interest rate dierential
2m
Figure 10.8 Volatility as a function of the interest rate dierential
296
Advanced Trading Rules
to model the scatter of data. The slope of the ®t re¯ects the relationshipbetween the interest rates dierential and the volatility of the currency pair.The higher the dierential, the higher the volatility.This time respective R 2 of 0.371 for USD-DEM, 0.541 for GBP-USD and0.612 for USD-CHF were obtained when ®tting each series by a simple linearregression. This is important for a trader as it implies that the higher thedierential of interest, the higher the risk but as well the possibility of greaterreward.These stylized facts are of interest because they contribute to the explanation of the source of pro®ts and losses for directional traders, as well as howsuch traders obtain their informational inputs for their decision process forwhen to buy or sell. For a systematic trader these ®nding are even moreimportant because not only do they underline the fact that currency directionsare partly determined by the variations in their interest rates dierential, butalso that the accuracy of the forecast that could be subsequently generatedwill depend upon the extent of the dierence in yield of the currency.Considerable work has been done in the ®eld of linkage between geographically separate but related markets (Olsen, 1995). Two of the most important®ndings in our case are:(1) when volatility is high, the price change in major markets tends tobecome highly correlated(2) correlation in volatility and prices appears to be asymmetric incausality between the USA and other countries.The US movement may aect other markets, but not vice versa.From the previously noted stylized facts, we show how some of the featuresof the interest rates market could be used to forecast direction of exchangerates in the currency market.
10.3 THE ENDOGENOUS AND EXOGENOUS TRADING RULES10.3.1 The timing methodUntil recently, economists regarded technical analysis as unprofessional andlacking in credibility, despite its widespread use by market practitioners.However, the increasing number of studies on the predictability of time priceseries suggest that the dismissal of technical analysis as a forecasting methodmight have been premature. In this context, it is also relevant to mention thehuge volume of assets managed in a systematic way by commodity tradingadvisors. Technical analysis covers a broad category of forecasting rules,amongst which the moving average would seem to be the most widely used by
Informative spillovers in the currency markets 297practitioners (Kaufman, 1987; Schwager, 1984) or academics (LeBaron, 1992;Taylor, 1986) alike. Trading rules have the advantage of enabling the traderto take decisions in the ®nancial markets without having to rely on ananalysis of the fundamentals (Dunis, 1989), the hypothesis being that allavailable information and economic market data ¯ows, are already fullytaken into account in the rate.The rule is used in the following way: when the rate of the instrumenttraded penetrates from below (above) a moving average of a given length, abuy (sell) signal is generated. A formal way to describe this decision rule isgiven by:9P  Pt 1      Pt m1 >>sell , Pt < t>=m10:4>Pt  Pt 1      Pt m1 >>;buy , Pt >m
where Pt is the price of the asset recorded once on each trading day t, alwaysat the same time of day, and m> 1 is the length (or order) of the movingaverage. Rules based on mathematical formulas using past pricesfPt ; . . . ; Pt m ; . . .g are well de®ned and objective in the sense that theirperformances can be assessed. The selection of the adequate order for themoving average is generally based on both the technical consideration of thepredictive quality and the need to determine price trends over a speci®c timehorizon for commercial use. This is usually done through the optimization ofthe risk±return ratio. Figure 10.9 provides an illustration of the use of themoving-average method.The moving-average rule is considered as a trend-following system becauseof its innate design. In a rising price environment the price will always behigher than the moving average, thus requiring a long position. Similarly, ashort position is called for in a falling price environment. In this way, thetrader will always follow the trend represented by the mean price. The tradingrule, although simple, is not optimal, as the signal will always `lag' the pricestructure. The rule will never sell near the high or buy near the low, so thetrader using it will always miss the ®rst part of the move and possiblysurrender a signi®cant proportion of the unrealised pro®ts before reversing aposition from long to short or vice versa. Nevertheless, the existence ofcentral bank price-smoothing action in the short-term interest rates andcurrencies markets, as described in the statistical analysis in this chapter,suggests that the abnormal pro®t from trend-following methods will persistover time and, as such, justi®es the use of simple trading rules to exploitmarket ineciencies (Silber, 1994).
Price
DayFigure 10.9 Moving-average trading rule
Informative spillovers in the currency markets 299To examine the properties of exogenous trading models versus endogenousones, we use the moving-average rules as previously described. We generatethe signals for the endogenous trading model by applying the moving-averagetrading rule on the past daily spot rates to forecast the spot series (system A).Similarly, the signals for the exogenous trading models will be generated byapplying the moving-average trading rule on the interest rates series toforecast the spot series (system B).In the design of our