Portfolio Rebalancing: A Factor Model of Commodity Currencies

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Portfolio Rebalancing: A Factor Model of Commodity Currencies

takers of the commodities they export and conclude that there is only a unidirectionalcausality from commodity prices to the currencies. On the other hand, Clements andFry (2008) …nd evidence that supports the reverse and conclude that models that fail toaccount for endogeneity between currency and commodity returns may be misspeci…ed(see also, Chen, Rogo¤ and Rossi, 2008).Under the model proposed in this paper, spillovers from currency markets as wellas stock markets to the commodity market, and vice versa are allowed. Furthermore,spillovers to an asset from other asset markets are modelled through a lagged e¤ect offactors speci…c to other asset types, rather than a contemporaneous e¤ect. This featureof the model responds to a view that portfolio rebalancing activities may take place witha lag, rather than instantaneously and may be a reason why the uncovered equity paritycondition does not hold when a contemporaneous unconditional correlation measure isused.To preview the results, the factor model of currency, commodity and equity marketsreveals the existence of some linkages amongst the three markets. Contrary to anassumption often made in empirical and theoretical studies that commodity pricesare exogenous for small open economies, there is evidence of bidirectional causalitybetween the commodity prices and the currencies of commodity-exporting countrieslike Australia, New Zealand and Canada. Furthermore, it is found that the role of thecommodity market in interconnecting the exchange rate and the equity market providesan explanation as to why the data suggest a positive relationship between exchangerate and equity returns, which is against the prediction of the uncovered equity parityhypothesis.The remainder of the paper is organised as follows. Section 2 introduces the dataused in the analysis of this paper. In Section 3, the latent factor model is describedand empirical results are presented in Section 4. Section 5 provides an alternativespeci…cation of the factor model whereby the common factor is captured instead bythe observable U.S. equity return. Section 6 concludes.2 The DataBefore addressing the issues outlined above by modelling the joint determinants ofthe currency, commodity and equity returns in the multivariate latent factor model3


framework in the next section, a …rst look at the data set will help motivate the model.This section introduces the data set and provides a preliminary analysis of the data.2.1 Data descriptionThe data set consists of m = 3 “commodity currency”exchange rate variables, n = 1additional noncommodity currency, v = 2 commodity price variables and w = 4 equityreturn variables. The commodity currencies include the Australian dollar (AUD t ),the Canadian dollar (CND t ) and the New Zealand dollar (NZD t ). The Swiss Franc(SW F t ) is chosen to represent the additional currency for two reasons. Firstly, theSwiss France is one of the currencies found to have a correlation structure with equityreturns consistent with the uncovered equity parity condition based on the portfoliorebalancing hypothesis in Hau and Rey (2004, 2006). The British pound is used to representthe additional currency in Clements and Fry (2008). Although the United Kingdomis not a commodity-exporting country to the same extent as Australia, Canadaand New Zealand, it is a large commodity-importer and the correlation between theBritish pound and the commodity price is not trivial. 1 The German Mark and FrenchFranc are also a potential condidate but complications arise given the adoption of theeuro in 1999.Nominal exchange rates are expressed in terms of the U.S. dollar per unit of nationalcurrency. Nominal exchange rates, as opposed to real exchange rates, are modelledbecause the portfolio rebalancing hypothesis is a short-run concept. Furthermore,nominal exchange rates are used in the previous empirical studies (Hau and Rey, 2004;2006) which provide a point of comparison. Demeaned continuously compounding percentagereturns of currencies both commodity (CE i;t ) and non-commodity (NCE j;t )are computed by taking the monthly di¤erence of the natural logarithm of the nominalexchange rates, subtracting the sample mean and multiplying by 100. Given the de…-nition of the exchange rate, a positive currency return corresponds to an appreciationof the domestic currency against the U.S. dollar.The choice of v = 2 commodities includes a non-oil commodity price index (nonoil t )and an oil price index (oil t ). The non-oil commodity price index is obtained from the1 The sample correlations of the British pound and the non-energy commodity price index is 0.25;the British pound and the oil price index is 0.13; the Swiss Franc and the non-energy commodity priceindex is 0.15; and the Swiss Franc and the oil price index is 0.03.4


The vector Y t summarises the data:Y t = fCE i;t ; NCE j;t ; P C k;t ; EQ l;t g; (1)where i = AUD; CND; NZD for the Australian dollar, the Canadian dollar and theNew Zealand dollar; j = SW F for the Swiss franc ; k = nonoil, oil for the non-oilcommodity price and the oil price; and l = au; cn; nz; sw for the Australian, Canadian,New Zealand and Swiss stock markets, respectively. The sample period extends fromFebruary, 1980 when the IMF …rst began constructing the monthly index, to December,2008 (for a total of T = 347 observations). Since one may expect that portfoliorebalancing activities occur on an infrequent basis, quarterly data are also consideredas a comparison. That is, the sample period extends from Quarter 1, 1980 to Quarter4, 2008 (T = 116 observations) where the last observations of each quarter are used asthe frequency conversion method.2.2 Preliminary analysisThe monthly data set is contained in Figure 1. Tables 1 and 2 present descriptivestatistics and the variance-covariance and correlation matrices, respectively. Tablesand …gures summarising the quarterly data set are presented in the appendix. 4Table 1 indicates that the currency returns are less volatile than equity returns.The New Zealand dollar and the Swiss franc returns are the most volatile amongthe currencies. The oil price returns are almost four times more volatile than thenon-energy commodity price returns. The New Zealand stock market is the mostvolatile while the Swiss stock market is the least volatile. The large negative equityreturns of the four equity markets corresponds to the stock market crash in October1987. Although the Jarque-Bera tests indicate that none of the series are normallydistributed, normality is assumed for convenience of estimation in the latent factormodel. More evidence of normality is found when quarterly data is used.The correlations and covariances of the data summarised in Table 2 reveal someinteresting features. The commodity currencies are more positively correlated with eachother than with the Swiss franc. The correlations of the Australian dollar return withthe return of the Canadian dollar, the New Zealand dollar and the Swiss franc are 0.50,4 All calculations of the preliminary data analyses are performed in EViews 5.6


Figure 1: Percentage Demeaned Currency, Commodity Price and Equity Price MonthlyReturns (1980M2 to 2008M12)Australian dollarCanadian dollarNew Zealand dollarSwiss franc20202020101010100000­10­10­10­10­20­20­20­20­3085 90 95 00 05­3085 90 95 00 05­3085 90 95 00 05­3085 90 95 00 05Non­oil commodity price indexOil price indexAustralian equity price indexCanadian equity price index40404040202020200000­20­20­20­20­40­40­40­4085 90 95 00 0585 90 95 00 05­6085 90 95 00 05­6085 90 95 00 05New Zealand equity price indexSwiss equity price index4040202000­20­20­40­40­6085 90 95 00 05­6085 90 95 00 05Table 1: Descriptive Statistics of the Demeaned Currency, Commodity and EquityMonthly Returns (1980M2 to 2008M12)Max Min Std. dev. Jarque-Barra ProbabilityCurrenciesAUD 8.99 -17.85 3.14 334.2 0.00CND 5.88 -13.76 1.81 1388.4 0.00NZD 11.01 -24.76 3.46 1141.8 0.00SW F 12.74 -11.06 3.47 6.33 0.04Commoditiesnonoil 8.06 -16.66 2.39 855.0 0.00oil 45.68 -31.23 8.44 215.4 0.00Equitiesau 13.84 -55.77 5.41 15282.9 0.00cn 12.93 -26.06 4.81 452.5 0.00nz 21.73 -34.31 5.53 353.4 0.00sw 13.71 -28.64 4.41 589.2 0.008


Table 2: Correlations (upper diagonal), Variances (diagonal), and Covariances (lowerdiagonal) of the Demeaned Currency, Commodty and Equity Monthly Returns(1980M2-2008M12)Currencies Commodities EquitiesAUD CND NZD SW F nonoil oil au cn nz swCurrenciesAUD 9.85 0.50 0.65 0.23 0.30 0.18 0.30 0.33 0.18 0.19CND 2.85 3.26 0.37 0.16 0.29 0.16 0.29 0.41 0.15 0.21NZD 7.02 2.29 11.90 0.36 0.28 0.13 0.26 0.26 0.12 0.12SW F 2.54 1.01 4.31 12.01 0.15 0.03 -0.06 -0.02 -0.12 -0.22Commoditiesnonoil 2.27 1.26 2.27 1.21 5.68 0.32 0.10 0.23 0.02 0.07oil 4.73 2.37 3.83 0.96 6.50 71.01 0.07 0.09 -0.06 -0.05Equitiesau 5.04 2.79 4.93 -1.15 1.34 3.00 29.13 0.65 0.55 0.52cn 4.94 3.54 4.38 -0.41 2.67 3.55 16.83 23.08 0.38 0.54nz 3.10 1.48 2.22 -2.28 0.23 -2.85 16.36 10.15 30.46 0.42sw 2.60 1.70 1.89 -3.38 0.75 -2.00 12.38 11.52 10.25 19.38in the analysis of this paper.Although the multivariate, multicountry system is modelled jointly in a latent factormodel in the next section, Granger causality tests on a bivariate basis may provide apreliminary insight into directions of causality between the returns of these assets. Thetests concerning the causality from the currency returns are summarised in Table 4,the causality from the commodity returns in Table 5 and the causality from the equityreturns in Table 6.An interesting result from the bivariate Granger causality tests is that there seemsto be more evidence, on a bivariate basis, suggesting that commodity prices are drivenby currency movements rather than the other way around. The hypothesis that theAustralia dollar does not Granger cause the non-energy commodity return is rejectedat the 5% level of signi…cance. The same is true for the Canadian dollar with the oilprice return, and the New Zealand dollar with the non-energy commodity return. Thebivariate test also suggests causality from the Swiss franc to the non-energy commodityreturn. Conversely, when the tests of Granger causality from commodity returns tocurrency returns are performed, only the null hypothesis of the non-energy commodity9


Table 3: Lag Selection Criteria of a VAR of the Demeaned Currency, Commodity andEquity ReturnsLag LogL LR AIC SC HQ1 -8647.3 n.a. 52.44 53.69 52.94 2 -8588.5 110.27 52.69 55.08 53.643 -8533.8 99.22 52.96 56.49 54.374 -8450.6 146.00 53.06 57.74 54.9211 -7904.6 113.96 53.98 66.65 59.0312 -7793.5 141.65 53.91 67.72 59.42 indicates lag order selected by the criterionMax lag length is 12.The LR test for lags 5 to 10 are not reported to conserve spaceprice not Granger causing the New Zealand dollar is rejected. These preliminary resultssuggest that, among the currencies, the New Zealand dollar is best described as acommodity currency and that treating commodity prices as exogenous in a model maygive rise to a misspeci…cation error.Causality between the currency and equity returns assists in assessing the uncoveredequity parity condition based on the portfolio rebalancing motive. The bivariate testsshow little evidence of Granger causality between the currency and the equity returns.It is of interest to test if this is true when the system is modelled jointly.Lastly, causality between the equity and commodity returns is examined. Thebivariate tests reveal that the oil price Granger causes the New Zealand and the Swissequity market. The return in the equity markets of Australia, Canada and SwitzerlandGranger causes the non-oil commodity return.To summarise, there seems to be evidence of linkages between the currency, commodityand equity markets based on the bivariate Granger causality tests. An obviousnext step is to examine cross-market linkages in a system in which all the asset returnsare jointly modelled rather than on a bivariate basis. Many empirical papers studya unidirectional commodity-currency relationship by assuming that commodity pricesare exogenous and “commodity currencies” are a function of these prices. Clementsand Fry (2008) examine the possibility of the opposite case of “currency commodities”whereby the value of an exchange rate of a commodity-exporting country can have10


Table 4: Bivariate Granger Causality from Currency Returns to Currency, Commodityand Equity ReturnsCurrency to currency Currency to commodity Currency to equityHypothesis p-Value Hypothesis p-Value Hypothesis p-ValueFrom To From To From toAUD CND 0.162 AUD nonoil 0.001 AUD au 0.309NZD 0.000 oil 0.167 cn 0.961SW F 0.518 nz 0.151sw 0.369CND AUD 0.258 CND nonoil 0.208 CND au 0.530NZD 0.011 oil 0.050 cn 0.348SW F 0.101 nz 0.904sw 0.471NZD AUD 0.205 NZD nonoil 0.014 NZD au 0.016 CND 0.589 oil 0.206 cn 0.288SW F 0.682 nz 0.314sw 0.222SW F AUD 0.336 SW F nonoil 0.007 SW F au 0.464CND 0.086^ oil 0.225 cn 0.519NZD 0.013 nz 0.534sw 0.132^ and denote statistical signi…cance at 10% and 5% level, respectively11


Table 5: Bivariate Granger Causality from Commodity Returns to Currency, Commodityand Equity ReturnsCommodity to currency Commodity to commodity Commodity to equityHypothesis p-Value Hypothesis p-Value Hypothesis p-ValueFrom To From To From tononoil AUD 0.467 nonoil oil 0.071^ nonoil au 0.754CND 0.585 cn 0.859NZD 0.094^ nz 0.783SW F 0.612 sw 0.360oil AUD 0.608 oil nonoil 0.597 oil au 0.131CND 0.468 cn 0.435NZD 0.559 nz 0.014 SW F 0.608 sw 0.001 ^ and denote statistical signi…cance at 10% and 5% level, respectivelyan impact on the world prices of commodities. Their empirical approach of a latentfactor model allows the speci…cation of bidirectional causality between the currencyand commodity returns. This paper aims to contribute to the asset pricing literatureby considering an additional linkage with the equity market which is motivated bythe portfolio balance model of exchange rates. Multidirectional causality amongst thecurrency, commodity and equity returns are examined in a factor model framework inthe next section.3 A Latent Factor Model of Currency, Commodityand Equity ReturnsThe analytical framework employed here is a latent factor model where currency, commodityprice and equity price returns are jointly determined as a function of a set ofindependent latent factors. A single time series (factor) which is likely to be a functionof more than one observable variables is extracted from information that is commonto each subset of variables. The joint impact of the three types of returns are assessedby examining the spillovers across each market, allowing insight into the portfolio rebalancinghypothesis which gives rise to the uncovered equity parity condition. Themodel provides a decomposition of the importance that each factor plays in contribut-12


Table 6: Bivariate Granger Causality from Equity Returns to Currency, Commodityand Equity ReturnsEquity to currency Equity to commodity Equity to equityHypothesis p-Value Hypothesis p-Value Hypothesis p-ValueFrom To From To From toau AUD 0.888 au nonoil 0.012 au cn 0.876CND 0.473 oil 0.101 nz 0.007 NZD 0.999 sw 0.006 SW F 0.155cn AUD 0.962 cn nonoil 0.003 cn au 0.026 CND 0.206 oil 0.136 nz 0.056^NZD 0.795 sw 0.000 SW F 0.035 nz AUD 0.436 nz nonoil 0.687 nz au 0.996CND 0.722 oil 0.147 cn 0.413NZD 0.775 sw 0.004 SW F 0.682sw AUD 0.173 sw nonoil 0.080^ sw au 0.220CND 0.333 oil 0.330 cn 0.520NZD 0.189 nz 0.058^SW F 0.298^ and denote statistical signi…cance at 10% and 5% level, respectively13


ing to volatility in the returns of each asset. The advantage of this approach is thatobservable variables do not have to be identi…ed and modelled which is convenient asit implicitly takes into account shocks a¤ecting all markets simultaneously. The modelis estimated using maximum likelihood and the Kalman …lter.The factor model describing the data in (1) can be separated into a commoditycurrency (CE i;t ) returns component, an additional noncommodity currency (NCE j;t )return component, the commodity price (P C k;t ) returns component and the equityprice (EQ l;t ) returns component. The following provides the speci…cation for eachcomponent.Commodity-currency returns speci…cationEquation (2) shows the factor model for the commodity-currency returns:CE i;t = i V t + ' i CF t + i P CF t 1 + i QF t 1 + i U i;t ; (2)where i = AUD; CND; NZD.The commodity currency returns (CE i;t ) are a function of a common or world factor(V t ), which is included in all equations of the system, a commodity-currency returnsfactor (CF t ), the lagged commodity price factor (P CF t 1 ) term, the lagged equity pricefactor (QF t 1 ) term and an idiosyncratic term (U i;t ), with loading i ; ' i , i , i and irespectively.The inclusion of data for Switzerland which is not a commodity-exporting country(described in the noncommodity currency return and equity returns speci…cationsection) and the implicit inclusion of the U.S. dollar as the numeraire currency shouldprovide su¢ cient information to identify the common factor (V t ).The lagged commodity price factor (P CF t 1 ) term and the lagged equity pricefactor (QF t 1 ) term are included to capture, respectively, the spillovers from the commodiymarket and the equity market to the currency market. The commodity pricefactor at time t is speci…c only to the commodity returns series. Likewise, the equityprice factor at time t is speci…c only to the equity returns series. They are describedin more detail below.Following the lag speci…cation tests in the preliminary data analyis in the previoussection, the common and the currency returns factors are modelled as AR(1) processes14


with loading Vand CF whereV t = V V t 1 + " V;t ; (3)andCF t = CF CF t 1 + " CF;t : (4)The idiosyncratic factors that capture the components of each return series not explainedby the other factors are assumed not to exhibit autocorrelation.Noncommodity-currency return speci…cationThe additional noncommodity currency, that is the Swiss franc is included in themodel to help identify the common factor and to separate movements in the commoditycurrencies from the currency market in general. The speci…cation of the noncommoditycurrency returns is:NCE j;t = j V t + j U j;t ; (5)where j = SW F: The return is a function of the world factor (V t ) and the idiosyncraticfactor, with loadings j and j . No additional linkages are considered.Commodity price returns speci…cationThe commodity returns equation isP C k;t = k V t + k P CF t + ' k CF t 1 + k QF t 1 + k U k;t ; (6)where k = nonoil; oil. Commodity returns are a function of the common factor (V t ),the commodity price factor (P CF t ), spillovers from the lagged commodity currencyreturns factor (CF t 1 ), spillovers from the lagged equity price factor (QF t 1 ) and anidiosyncratic factor (U k;t ) with loadings k ; k ; ' k ; k and k : Two restrictions are imposed,i.e. ' oil = oil = 0. That is, the oil price return is a function of the worldfactor, the commodity price factor and the idiosyncratic factor and not a¤ected byspillovers from the currency market or the equity market. This is to re‡ect the realitythat OPEC plays a role in consciously altering supply and hence the price of oil. Thecommodity price factor is also an AR(1) processP CF t = P CF P CF t 1 + " P CF;t : (7)15


Equity returns speci…cationThe equity returns of the commodity-exporting countries are speci…ed as:EQ l;t = l V t + l QF t + ' l CF t 1 + l P CF t 1 + l X t + l U l;t ; (8)where l = au; cn; nz. The equity returns of Australia, Canada and New Zealand, whichare the commodity exporting countries, are a function of the common factor (V t ),the equity price factor (QF t ), spillovers from the lagged commodity-currency factor(CF t 1 ), spillovers from the lagged commodity price factor (P CF t 1 ), an exogenousvariable (X t ) and an idiosyncratic factor (U l;t ) with loadings l ; l ; ' l ; l ; l and l . Theexogenous variable (X t ) is the stock market crash dummy variable taking the value ofone at the crash period in October, 1987. The equity price factor is also an AR(1)processQF t = QF QF t 1 + " QF;t : (9)The equity return of Switzerland, which is a noncommodity-exporting country, isincluded in the model for the same reason as the Swiss franc. That is to help identify thecommon factor (V t ) and to separate movements in equity markets of the commodityexportingcountries from the equity market in general. In other words, it is assumedthat the equity factor speci…ed in the model captures information that is speci…c tothe equity markets of the commodity-exporting countries. The equity return of thenoncommodity-exporting countries is speci…ed as:EQ l;t = l V t + l X t + l U l;t ; (10)where l = sw: The Swiss equity return is a function of the common factor (V t ), theexogenous stock market crash dummy variable (X t ) and the idiosyncratic factor, withloadings l ; l and l . No additional linkages are considered.The complete factor modelDe…ne the latent factor F t asF t = fV t ; CF t ; P CF t ; QF t ; U i;t ; U j;t ; U k;t ; U l;t g; (11)for i = AUD; CND; NZD; j = SW F ; k = nonoil, oil and l = au; cn; nz; sw.16


The model can be expressed in matrix form asY t = F t + F t 1 + X t + W t ; (12)F t+1 = F t + t ; (13)where Y t in (1) is a function of the latent factor contained in F t with parameter loadings, spillovers, which are modelled through the lag of the latent factor F t1 withparameter loadings and the exogenous dummy variable X t with parameter loading. The state equation in (13) shows that the factor F t+1 is an autoregressive processwith loading . The error matrices W t and t are vector of white noise processes suchthatandE( t 0 ) =E(W t W 0 ) = Q for t = 0 otherwise ; (14) R for t = 0 otherwise : (15)Here, W t = 0 and hence, R = 0. The error matrix E( t 0 ) is speci…ed as in (14) tore‡ect an assumption that the factors are independent of each other. 5 This assumptionenables the results to be interpreted in terms of the contribution of each factor to theoverall volatility of each asset. The volatility of currency, commodity and equity returnscan be decomposed in terms of the factors by squaring both sides of (2), (5), (6), (8) and(10) and taking expectations. The decomposition of the variances for the commoditycurrencies isE[CE 2 i;t] =2 i1 2 V+ '2 i1 2 CF 2 i+1 2 P CF+ 2 i1 2 QF+ 2 i ; (16)for i = AUD; CND; NZD, where 2 i =(1 2 V ) represents the contribution of the commonfactor to the volatility of commodity currency i, ' 2 i =(1 2 CF ) represents the contributionof the currency factor, 2 i =(1from the commodity factor, 2 i =(1 2 QF ) is the contribution of spillovers from the equityfactor, and 2 i 2 P CF ) represents the contribution of spilloversis the contribution of the idiosyncratic factor. The decompositionof the additional currency, the commodity price and the equity price series is computedanalogously.5 The model in (12)-(15) is estimated using maximum likelihood and the Kalman …lter. Thelikelihood function is maximised using the procedure MAXLIK in Gauss 8.0 with the BFGS iterativegradient algorithm and numerical derivatives. For details on the Kalman …lter algorithm, see Hamilton(1994, Chapter 13).17


The extent of cross-market linkages are assessed by considering the volatility decompositionand the statistical signi…cance of the individual spillover parameters. Inaddition, hypotheses of cross-market linkages among the currency, commodity and equitymarkets are tested formally using the likelihood ratio (LR) test. There are six nullhypotheses of interest, namely;Hypothesis 1: There is no spillover from the currency market to the commoditymarket,H 0 : ' nonoil = 0; (17)Hypothesis 2: There is no spillover from the currency market to the equity market,H 0 : ' au = ' cn = ' nz = 0; (18)Hypothesis 3: There is no spillover from the commodity market to the currency market,H 0 : AUD = CND = NZD = 0; (19)Hypothesis 4: There is no spillover from the commodity market to the equity market,H 0 : au = cn = nz = 0; (20)Hypothesis 5: There is no spillover from the equity market to the currency market,H 0 : AUD = CND = NZD = 0; (21)Hypothesis 6: There is no spillover from the equity market to the commodity market,H 0 : nonoil = 0: (22)A joint test of each null hypothesis in (17) to (22) that the parameter loadings ofthe spillover e¤ects in question are zero is tested using the likelihood ratio (LR) test.Under the null hypothesis, the LR statistic is2[L( b ) L( e )] 2 (m); (23)where L( b ) denotes the value of the log likelihood function at the unrestricted estimate,L( e ) denotes the value of the log likelihood function at the restricted estimate, the LRstatistic has a chi-square distribution with the degree of freedom (m) equal to thenumber of restrictions.18


4 ResultsThe likelihood ratio tests of the joint signi…cance of the spillover e¤ects followingHypothesis 1 to Hypothesis 6 in (17) to (22) are summarised in Table 7 for the monthyreturns model and 8 for the quarterly returns model. Tables 9 and 10 present thevolatility decompositions of the monthly returns data and the parameter estimates of(2)-(10). The volatility decomposition of the quarterly returns data and the parameterestimates are presented in Tables 11 and 12.The results are discussed in the following order. Firstly, the extracted latent worldcommon factor is discussed. Secondly, the e¤ects of each asset’s own-market andidiosyncratic factors are then discussed. Thirdly and most importantly, the spillovere¤ects across the asset markets are attended to. The focus of the cross-market linkagesdiscussion is on two issues. First is the nature of linkages between the currency andequity markets, in particular under investigation is if the two asset markets are linkedin a fashion consistent with the uncovered equity parity condition. Second is the roleof the commodity market in interconnecting the currency and equity markets of thecommodity-exporting countries which helps to explain why the uncovered equity paritybased on the portfolio rebalancing hypothesis tends not to hold in the data for thesecountries.4.1 The common factorThe common factor is speci…ed in the model as a factor that has an in‡uence on thecomplete set of the asset returns. Table 9 and Table 11 show that a substantial proportionof the movements in these assets returns, especially the equity returns of the fourcountries is captured by the common or world factor. The common factor explains43%, 60%, 19% and 40% of the volatility of the monthly returns of the Australian,Canadian, New Zealand and Swiss equities, respectively. The contribution of the commonfactor to the volatility of the currency returns, especially the Canadian dollar isalso large, accounting for 22% and 15% of the volatility of the monthly and quarterlyCanadian dollar returns, respectively. As shown in Tables 10 and 12, the estimatesof the parameter loadings of the common factor are statistically signi…cant at the 5%or the 10% level for all asset returns, except for the oil price and the Swiss franc atthe monthly frequency and the oil price and the New Zealand dollar at the quarterly19


frequency. All of the estimated parameters have a positive sign, except for the Swissfranc. This indicates that all markets excluding the Swiss franc are a¤ected in the sameway by the common factor, though the e¤ect on the oil market is small and statisticallyinsigni…cant.The importance of the world factor in accounting for the volatility of most assetreturns, especially the Canadian dollar and the Canadian equity return prompts usto relate this factor to the U.S. economy which is known to have a strong in‡uenceon the economy of Canada given their close proximity and trade ties. Also since thecommon factor seems to capture much of the movements in the four equity markets,the estimated common factor is compared to the U.S. equity return in Figure 2 andFigure 3 for the monthly and quarterly frequency, respectively. 6The …gures showthat the dynamics of the estimated common factor closely mimic those of the U.S.equity returns over the sample. Given that the United States is a large economy witha highly traded equity market, the estimated common factor may be appropriatelyinterpreted as representing the global economic conditions. Under the model set uphere, it is speci…ed as a latent unobservable factor. An alternative speci…cation is toinclude the U.S. equity returns as an observable world factor a¤ecting the completeset of currency, commodity and equity returns.comparison in Section5.4.2 Factors speci…c to each marketThis speci…cation is explored as aAs shown in Tables 9 and 11 for each of the asset return series in both the monthlyand quarterly cases, the factor speci…c to its own market or its idiosyncratic factorsexplains the majority of its volatility over the sample. Tables 10 and 12 also showthat the parameters loading of the own market factors and the idiosyncratic factorsare statistically signi…cant at the 5% or the 10% level, with a few exceptions.The commodity currency factor a¤ects the Australian dollar, the Canadian dollarand the New Zealand dollar returns in the same direction, as shown in Tables 10 and12 where the parameter loadings on the factor have the same (positive) sign. Theestimated commodity currency factor tends to capture more of the movements in theAustralian dollar and the New Zealand dollar than that of the Canadian dollar. At6 In Figures 2 and 3, the U.S. equity returns are standardised by their standard deviation to makethem comparable to the estimated common factor.20


Figure 2: The Estimated Common Factor (solid line) and the U.S. Equity MonthlyReturn (dashed line)6420­2­4­61985 1990 1995 2000 2005Figure 3: The Estimated Common Factor (solid line) and the U.S. Equity QuarterlyReturn (dashed line)420­2­41985 1990 1995 2000 200521


the monthly frequency, the currency factor accounts for 75%, 14% and 40% of thevolatility of the Australian dollar, the Canadian dollar and the New Zealand dollarreturns, respectively as shown in Table 11. This re‡ects that the Australian dollar andthe New Zealand dollar move more closely with each other than with the Canadiandollar.The commodity price factor explains roughly more than half of the volatility of thenon-oil commodity price monthly and quarterly returns, i.e. 47% and 83%, respectively.The factor captures more than 15% of the oil price volatility at both monthly andquarterly frequency while the rest is captured by the idiosyncratic factor. This resultre‡ects that although the non-oil commodity and oil prices are driven by some commonin‡uences, the oil price is still largely a¤ected by its own idiosyncratic factor such asthe OPEC decision to expand or contract its oil supply. The world factor has a smallin‡uence on the volatility of the oil price.The factor common to the equity returns of the three commodity-exporting countriesis extracted. It is well known that international equity markets tend to positivelycomove and that large equity markets like the U.S. market can in‡uence equity marketsworldwide (see, for example, Eun and Shim, 1989; Hamao et al, 1990; Masih and Masih,2001; Brook and Del Negro, 2002 and Ibrahim and Brzeszcynski, 2009). To the extentthat the world factor represents movements in the U.S. equity market, the equity factorextracted here can be thought of as domestic in‡uences, such as an increase in productivityand pro…tablity of listed domestic …rms. All three equity returns respond to theequity price factor in the same direction, as the parameter loadings on the factor areof the same (positive) sign. These parameter estimates are also statistically signi…cantat the 5% level, except for the Canadian equity quarterly return. The equity factorexplains more of the volatility in the Australian and New Zealand equity returns thanthat of the Canadian equity return. Less than 2% of the volatility of the Canadianequity return is accounted for by the equity factor speci…c to the commodity-exportingcountries. On the other hand, more than 50% of the Canadian equity return volatiltityis explained by the common factor which is shown to track closely movements in theU.S. equity market. This …nding re‡ects that the structure of the Canadian economyis less simlar to that of the Australian and the New Zealand economies, probably beingmore closely related to the U.S. economy.22


Table 7: Likelihood Ratio Tests of Cross-Market Linkages Among the Monthly Currency,Commodity and Equity ReturnsHypothesis Statistics p-value1. No spillover from currency to commodity markets 5.26 0.02 2. No spillover from currency to equity markets 5.12 0.163. No spillover from commodity to currency markets 1.94 0.594. No spillover from commodity to equity markets 1.45 0.695. No spillover from equity to currency markets 1.11 0.786. No spillover from equity to commodity markets 0.69 0.411. H 0 : ' nonoil = 02. H 0 : ' au = ' cn = ' nz = 03. H 0 : AUD = CND = NZD = 04. H 0 : au = cn = nz = 05. H 0 : AUD = CND = NZD = 06. H 0 : nonoil = 0* and ** denote signi…cance at the 10% and 5% level, respectively4.3 Cross-market linkagesThere is not much evidence of cross-market linkages among the currency, commodityand equity markets at the monthly frequency. The joint test of spillover e¤ects inTable 7 can only reject the null hypothesis of no spillover from the currency marketto the commodity price returns (Hypothesis 1) at the 5% level. When considering thestatistical signi…cance of individual parameters in Table 10, only the spillover fromthe commodity currency factor to the non-oil commodity price return is statisticallysigni…cant at the 5% level.More evidence of cross-market linkages are found at the quarterly frequency. Thejoint test of spillover e¤ects in Table 8 shows that the null hypotheses of no spilloverfrom the currency market to the commodity market (Hypothesis 1); no spillover fromthe currency market to the equity market (Hypothesis 2) and no spillover from thecommodity market to the equity market (Hypothesis 4) are rejected with p-values of0.02, 0.02 and 0.07, respectively. The …nding of more spillovers from the currencymarket to other asset markets than the opposite direction supports the view stressedin the more recent literature on exchange rate determination that the exchange rate23


Table 8: Likelihood Ratio Tests of Cross-Market Linkages Among the Quarterly Currency,Commodity and Equity ReturnsHypothesis Statistics p-value1. No spillover from currency to commodity markets 5.61 0.02 2. No spillover from currency to equity markets 9.73 0.02 3. No spillover from commodity to currency markets 4.46 0.224. No spillover from commodity to equity markets 7.08 0.07 5. No spillover from equity to currency markets 2.07 0.566. No spillover from equity to commodity markets 1.27 0.261. H 0 : ' nonoil = 02. H 0 : ' au = ' cn = ' nz = 03. H 0 : AUD = CND = NZD = 04. H 0 : au = cn = nz = 05. H 0 : AUD = CND = NZD = 06. H 0 : nonoil = 0* and ** denote signi…cance at the 10% and 5% level, respectivelyis a forward looking variable which embodies information about future fundamentalsand has robust forecasting power (Engle and West, 2005; Bacchetta and van Wincoop,2006; and Chen, Rogo¤ and Rossi, 2008). The nature of these linkages found providesa key to the answer of why the uncovered equity parity condition based on the portfoliorebalancing hypothesis are less evident among the commodity-exporting countries.a) The currency market and the equity marketEvidence of the spillover e¤ect from the currency market to the equity market of thethree commodity-exporting countries is found. The joint test of the hypothesis that theparameter loadings of the commodity-currency factor in the quarterly equity returns iszero, Hypothesis 2 in (18), is rejected with a p-value of 0.02, as shown in Table 8. Themagnitude of the linkage is relatively large, with the exception of the spillover from thecurrency market to the Canadian equity return. Table 11 shows that the commoditycurrencyfactor explains about 4.6% of the volatility of the Australian equity quarterlyreturn and 2.7% of the volatility of the New Zealand equity quarterly return series.Further, Table 12 shows that the estimated parameter loadings of the currency factor24


in the equity returns have a sign consistent with the uncovered equity parity conditionfor Australia and New Zealand.The commodity-currency factor which appreciates the Australian dollar and theNew Zealand dollar decreases the returns of the Australian and New Zealand stockmarkets in the next period. That is, when a lag is allowed and conditional on a shockoriginating in the exchange rate market, the relationship between the exchange ratereturns and the equity returns of Australia and New Zealand follows the predictionof uncovered equity parity. These results suggest that the failure to …nd the negativerelationship between exchange rate and equity returns for the commodity-exportingcountries in previous empirical studies may partly be attributable to the lack of a lagstructure in their empirical model. Recall that Hau and Rey (2006) use a measure ofunconditional contemporaneous correlations and Chaban’s (2009) model is based onconditional contemporaneous correlations.Less evidence of the spillover e¤ect from the equity market to the currency marketis found. Although the estimated parameter loadings of the equity factor in the currencyreturns have a sign inconsistent with the uncovered equity parity condition butconsistent with previous empirical studies, the joint test of the hypothesis that theyare jointly zero (Hypothesis 5) cannot be rejected with p-value of 0.78 and 0.56, whenthe monthly returns and the quarterly returns are considered, respectively.b) The currency market and the commodity marketEvidence of the spillovers from the currency market to the commodity market is oneof the most robust …ndings in this paper. The hypothesis that the parameter loadingsof the commodity-currency factor in the commodity price returns is zero, Hypothesis1 in (17), is rejected at both the monthly and quarterly frequency with a p-value of0.02, as shown in Tables 7 and 8. The commodity-currency factor captures 1.5% and4.6% of the volatility of the non-oil commodity price monthly and quarterly returns asshown in Tables 9 and 11.As for the spillovers in the opposite direction, that is from the commodity marketto the currency market, less evidence is found. Tables 7 and 8 show that the joint testof the hypothesis that the parameter loadings of the commodity factor in the currencyreturns of the three commodity-exporting countries is zero, Hypothesis 3 in (18), cannotbe rejected with a p-value of 0.59 for the monthly returns and a p-value of 0.22 for the25


quarterly returns. The most supportive case of the commodity-to-currency causality isfound for the New Zealand dollar. The parameter loading of the commodity factor inthe New Zealand currency quarterly return series is statisticaly signi…cant at the 10%level, as shown in Table 12 and 2.7% of the volatility in the New Zealand currencyquarterly return series is captured by the commodity factor, as shown in Table 11.These results suggest that there is a bidirectional causality between commodityprices and the currencies of commodity-exporting countries. This …nding is contradictoryto an assumption often made in the literature that commodity prices are thedrivers of the commodity currencies, but not vice versa. However, it is consistent withClements and Fry (2008) who also …nd that commodity prices are more a¤ected by thespillovers from the commodity-currency factor than currency returns are a¤ected bythe commodity price factor. The New Zealand dollar is found to exhibit the strongestattribute of commodity currencies among the three currencies considered in this paper.The terms of trade theory provides a theoretical justi…cation for the commodityto-currencycausality. Since Australia, Canada and New Zealand are commodityexportingcountries, their terms of trade are closely linked to the movements of theworld commodity prices (see, for example, Chen and Rogo¤, 2003). Booming commodityprices represent terms of trade improvements which can be viewed as a transfer ofwealth from commodity-importing to commodity exporting economies, which in turnincreases the relative price of these countries and appreciates their currencies (Neary,1988 and Engel, 2005). The positive relationship between the commodity price andcurrency returns predicted by the terms of trade theory is found here. Tables 10 and12 show that the factor that increases the price of commodities also has the e¤ect ofincreasing (i.e. an appreaciation) the Australian, Canadian and New Zealand exchangerates.The result obtained in this paper also suggests a positive and in fact strongercurrency-to-commodity causality. Tables 10 and 12 show that the currency factorwhich appreciates the exchange rates of the commodity-exporting countries also hasa positive e¤ect on the price of the non-oil commodity. A conceptual explanation ofthis bidirectional causality is given in Clements and Fry (2008). In short, a commodityboom appreciates the currency of a commodity-exporting country through the terms oftrade e¤ect mentioned above. The appreciated currency in turn squeezes its exporters.26


If the country has some degree of power over the world market, the reduced volume ofexports also has the e¤ect of increasing the world prices further. The empirical resultfrom the model presented in this paper lends support to the existence of market power,which implies that models that fail to account for endogeneity between currency andcommodity returns may be misspeci…ed.c) The commodity market and the equity marketThere is evidence of spillovers from the commodity market to the equity market. Thejoint test of the hypothesis that parameter loadings of the commodity factor in theequity quarterly returns of the commodity-exporting countries is zero, Hypothesis 4 in(20), is rejected with a p-value of 0.07, as shown in Table 8. The extent of the spilloverfrom the commodity market is particularly important for the Australian equity returnseries. Table 11 shows that 4.5% of the volatility of the Australian equity quarterlyreturn is captured by the commodity price factor. Considering the sign of the estimatedparameters in Table 12 reveals that the commodity price factor has a positive e¤ect onthe return of the equity markets of the three commodity-exporting countries.It is discussed above that the commodity-currency factor has a positive (and statisticallysigni…cant) spillover e¤ect on the commodity price returns. The commodityprice factor is also found to, in turn, have a positive (and statistically signi…cant)spillover e¤ect on the equity returns of the commodity-exporting countries. It is thisrole of the commodity price in connecting the currency market and the equity marketthat may produce the positive relationship between the currency and equity returnsof the commodity-exporting countries in the data. That is, even though it is foundthat the currency factor has a negative (and statistically signi…cant) spillover e¤ecton the equity returns of Australia and New Zealand, consistent with the prediction ofthe uncovered equity parity; the interconnection of the currency market, commoditymarket and the equity market in this fashion can taint the way equity returns appearto respond to an exchange rate shock for the commodity currencies, especially when asimple unconditional correlation measure is used.In summary, the results obtained from the factor model of currency, commodity andequity returns considered in this section suggest the existence of linkages among thethree asset markets. The most robust and strongest linkage is found for the spilloversfrom the currency market to the commodity price returns. This implies the impor-27


tance of allowing for a bidirectional causality between the commodity prices and thecurrencies of commodity-exporting countries in empirical modelling. Lastly, the roleof the commodity market in interconnecting the exchange rate and the equity marketprovides an explanation as to why a positive relationship between the exchange rateand the equity returns of the commodity-exporting countries is observed in the data.5 The U.S. equity return as an observable worldfactorThis section considers an alternative speci…cation of the factor model to the one consideredin the previous section. The U.S. equity return is included in the model insteadas an exogenous variable a¤ecting all the asset returns in the data set. The factormodel in equations (12) - (13) above is re-speci…ed such that the latent common factorV t in the vector F t in equation (11) is omitted and the U.S. equity return is includedin the exogenous variable vector X t in equation (12) as an observable common factor.The re-speci…cation implies that the decomposition of the variances for the commoditycurrencies is'2 iE[CEi;t] 2 = 2 i V ar(EQ U:S: ) +1 2 CF 2 i+1 2 P CF+ 2 i1 2 QF+ 2 i ; (24)for i = AUD; CND; NZD, where 2 i V ar(EQ U:S: ) represents the contribution of U.S.equity return as the proxy of the common factor to the volatility of commodity currencyi, ' 2 i =1 2 CF represents the contribution of the currency factor, 2 i =1 2 P CF representsthe contribution of spillovers from the commodity factor, 2 i =1 2 QFis the contributionof spillovers from the equity factor, and 2 i is the contribution of the idiosyncratic factor.The decomposition of the additional currency, the commodity price and the equity priceseries is computed analogously. The model of quarterly asset return data is estimated.Table 13 and 14 present the volatility decompositions of the quarterly return data andthe parameter estimates of the re-speci…ed factor model.Overall, the key results remain as the factor model is re-speci…ed to include the U.S.equity return as a proxy for the world factor. There is still evidence of the bi-directionalcausality between the commodity and the currency markets. The results also suggestthat the role of the commodity market in interconnecting the currency and the equitymarkets helps to explain the positive relationship between the currency and the equity28


eturns of the commodity-exporting countries, which is against the prediction of theuncovered equity parity condition.The most noticeable di¤erence that results from the re-speci…cation is the smallerspillovers from the equity factor to the currency and commodity returns. Only thespillover from the equity factor to the New Zealand dollar return is statistically signi…cantat the 10% level, where about 3% of the volatility of the New Zealand dollarreturn is explained by the equity factor.Although the U.S. equity return is shown to display a close relation with the estimatedlatent world factor in Section 4, the world factor is likely to be a functionof more than one observable variable. The U.S. equity return may be one dominantcomponent of the factor but not all. Explicitly replacing the latent common factorwith the observable U.S. equity return decreases the importance of domestic equityin‡uences on other assets.Another minor di¤erence is that the e¤ect of the latent world factor on the oil priceis estimated to be positive whereas the e¤ect of the U.S. equity return on the oil priceis negative. However, both estimates are statistically insigni…cant, suggesting that themost important determinant of the oil price is its idiosyncratic factor.6 ConclusionThis paper analysed the nature of the interconnection among the currency, commodityand equity markets in a latent factor model framework. Its central focus is to seek anexplanation as to why previous empirical studies …nd that an “uncovered equity parity”condition based on the portfolio rebalancing hypothesis (that is, a higher relative equityreturn is associated with a currency depreciation) tends to hold in the data for mostcountries but not the commodity-exporting countries. The role of the commoditymarket in interconnecting the currency and equity markets provides a key to the answer.Currency and equity returns of Australia, Canada and New Zealand as the commodityexportingcountries and Switzerland as the noncommodity-exporting country weremodelled jointly with the non-oil and oil commodity price returns. Spillovers amongthe commodity-currency market, equity market and commodity market were allowedthrough a lagged e¤ect. The empirical results obtained suggest that an uncovered equityparity condition based on the portfolio rebalancing motive is less evident among29


commodity currencies due to a stronger (and o¤setting) in‡uence of world commodityprices on the dynamics of these currencies.It is important to note that the portfolio rebalancing hypothesis concerns bothasset returns and equity ‡ows. The relationship of the asset returns, which is onlyone aspect of the portfolio rebalancing hypothesis, is considered in this paper. Hence,the empirical results obtained here should not be taken as a conclusive validation orinvalidation of the portfolio rebalancing hypothesis.30


Table 9: Volatility Decomposition of Currency, Commodity and Equity Monthly Returns (Percentages)Variable Common Commodity Commodity Equity Spillovers from Idiosyncraticfactor currency factor factor factor currencies commodities equities factorAUD 14.42 74.57 0.29 0.05 10.67CND 21.53 14.44 0.51 0.01 63.51NZD 6.35 40.11 0.82 0.35 52.36SW F 0.53 - - - 99.47nonoil 5.04 46.61 1.51 1.80 46.66oil 0.30 23.11 - - 76.59au 42.79 56.50 0.63 0.08 0.01cn 59.63 1.36 0.09 0.50 38.42nz 19.32 5.86 0.70 0.07 74.05sw 40.32 - - - 59.6831


Table 10: Parameters Estimates for Currency, Commodity and Equity Monthly Returns (P-values in Parentheses)Variable Common Commodity Commodity Equity Spillovers from Idiosyncratic Dummyfactor currency factor factor factor currencies commodities equities factor variableAUD 1.135 (0.000) 2.696 (0.000) 0.124 (0.513) 0.072 (0.758) 1.029 (0.066)^CND 0.793 (0.000) 0.679 (0.000) 0.095 (0.370) 0.013 (0.944) 1.436 (0.000) NZD 0.827 (0.000) 2.170 (0.000) 0.231 (0.241) 0.205 (0.399) 2.502 (0.000) SW F -0.237 (0.630) - - - 3.432 (0.001) nonoil 0.498 (0.016) 1.174 (0.000) 0.285 (0.024) 0.099 (0.409) 1.598 (0.000) oil 0.438 (0.739) 2.991 (0.000) - - 7.407 (0.000) au 2.723 (0.000) 3.295 (0.000) -0.345 (0.160) 0.089 (0.698) 0.002 (0.997) -53.423 (0.000) cn 3.289 (0.000) 0.523 (0.116) 0.132 (0.586) 0.233 (0.323) 2.784 (0.000) -23.246 (0.000) nz 2.167 (0.000) 1.257 (0.000) -0.430 (0.164) -0.102 (0.750) 4.473 (0.000) -32.215 (0.000) sw 2.473 (0.000) - - 3.173 (0.000) -26.436 (0.000) V 0.317 (0.000) CF 0.134 (0.062)^ P CF 0.678 (0.000) QF -0.058 (0.480)Log-likelihood -9025.72C-currency and NC-currency denote commodity currency and noncommodity currency, respectively^ and denote statistical signi…cance at 10% and 5% level, respectively32


Table 11: Volatility Decomposition of Currency, Commodity and Equity Quarterly Returns (Percentages)Variable Common Commodity Commodity Equity Spillovers from Idiosyncraticfactor currency factor factor factor currencies commodities equities factorAUD 2.98 67.66 0.95 16.22 12.19CND 14.73 19.62 2.37 8.71 54.57NZD 0.72 29.67 2.73 16.40 40.49SW F 6.29 - - - 93.71nonoil 5.22 83.21 4.62 6.94 0.01oil 0.01 15.26 - - 84.72au 49.64 22.05 4.57 4.53 19.20cn 65.88 1.76 0.79 0.23 31.34nz 19.97 18.01 2.68 0.58 58.76sw 58.32 - - - 41.6933


Table 12: Parameters Estimates for Currency, Commodity and Equity Quarterly Returns (P-values in Parentheses)Variable Common Commodity Commodity Equity Spillovers from Idiosyncratic Dummyfactor currency factor factor factor currencies commodities equities factor variableAUD 0.951 (0.075)^4.627 (0.000) 0.540 (0.319) 1.863 (0.009) 1.964 (0.012) CND 1.185 (0.000) 1.396 (0.000) 0.477 (0.108) 0.765 (0.037) 2.328 (0.000) NZD 0.510(0.408) 3.882 (0.000) 1.001 (0.084)^2.053 (0.011) 3.922 (0.000) SW F -1.554 (0.034) - - - 6.113 (0.001) nonoil 1.235 (0.025) 4.954 (0.000) 1.187 (0.024) 1.197 (0.120) 0.006 (0.972)oil 0.155 (0.928) 7.098 (0.000) - - 16.996 (0.000) au 5.548 (0.000) 3.107 (0.000) -1.719 (0.010) 1.684 (0.014) 3.524 (0.997) -58.124 (0.000) cn 6.961 (0.000) 0.955 (0.255) 0.780 (0.292) 0.413 (0.571) 4.904 (0.000) -21.410 (0.009) nz 4.044 (0.000) 3.227 (0.036) -1.513 (0.092)^0.693 (0.441) 7.084 (0.000) -68.837 (0.000) sw 6.318 (0.000) - - 5.456 (0.000) -42.292 (0.000) V 0.203 (0.122) CF 0.002 (0.989) P CF 0.181 (0.106) QF 0.568 (0.006) Log-likelihood -3661.28C-currency and NC-currency denote commodity currency and noncommodity currency, respectively^ and denote statistical signi…cance at 10% and 5% level, respectively34


Table 13: Volatility Decomposition of Currency, Commodity and Equity Quarterly Returns (percentages): With an ObservableU.S. Equity ReturnVariable U.S. equity Commodity Commodity Equity Spillovers from Idiosyncraticfactor currency factor factor factor currencies commodities equities factorAUD 4.78 87.89 1.11 1.87 4.35CND 17.91 21.34 3.85 0.79 55.81NZD 3.05 44.46 3.03 2.91 46.55SW F 3.18 - - - 96.82nonoil 2.37 71.91 4.63 0.49 20.61oil 1.43 21.07 - - 77.50au 39.17 47.75 6.41 6.67 0.01cn 62.11 2.95 0.11 1.32 33.52nz 13.21 19.51 2.57 0.54 64.17sw 56.08 - - - 43.9235


Table 14: Parameters Estimates for Currency, Commodity and Equity Quarterly Returns (P-values in Parentheses): With anObservable U.S. Equity ReturnsVariable U.S. equity Commodity Commodity Equity Spillovers from Idiosyncratic Dummyfactor currency factor factor factor currencies commodities equities factor variableAUD 0.178 (0.009) 5.079 (0.000) 0.596 (0.379) 0.775 (0.149) 1.181 (0.462)CND 0.191 (0.000) 1.399 (0.000) 0.616 (0.180) 0.280 (0.287) 2.347 (0.000) NZD 0.151 (0.043) 3.850 (0.000) 1.049 (0.134) 1.030 (0.076)^4.117 (0.000) SW F -0.162 (0.053)^- - - 6.223 (0.001) nonoil 0.115 (0.099)^4.425 (0.005) 1.076 (0.032) 0.365 (0.456) 2.373 (0.365)oil -0.317 (0.233) 8.448 (0.001) - - 16.234 (0.000) au 0.723 (0.000) 5.561 (0.000) -1.949 (0.002) 2.075 (0.005) 0.006 (0.976) -57.160 (0.000) cn 0.986 (0.000) 1.495 (0.003) 0.281 (0.632) 0.997 (0.344) 5.043 (0.000) -23.206 (0.009) nz 0.481 (0.000) 4.070 (0.000) -1.412 (0.123) 0.678 (0.620) 7.380 (0.000) -66.921 (0.000) sw 0.908 (0.000) - - 5.599 (0.000) -44.380 (0.000) CF -0.010 (0.944) P CF 0.291 (0.220) QF 0.061 (0.554)Log-likelihood -3586.51C-currency and NC-currency denote commodity currency and noncommodity currency, respectively^ and denote statistical signi…cance at 10% and 5% level, respectively36


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Figure 4: Percentage Demeaned Currency, Commodity Price and Equity Price QuarterlyReturns (1980Q2 - 2008Q4)Australian dollarCanadian dollarNew Zealand dollarSwiss franc20202020101010100000­10­10­10­10­20­20­20­20­301985 1990 1995 2000 2005­301985 1990 1995 2000 2005­301985 1990 1995 2000 2005­301985 1990 1995 2000 2005Non­oil commodity price indexOil price indexAustralian equity price indexCanadian equity price index75752020502550250000­20­20­25­25­40­40­50­75­50­75­60­601985 1990 1995 2000 20051985 1990 1995 2000 20051985 1990 1995 2000 20051985 1990 1995 2000 2005New Zealand equity price indexSwiss equity price index202000­20­20­40­40­60­601985 1990 1995 2000 20051985 1990 1995 2000 2005AppendixPreliminary data analysis of the quarterly returns39


Table 15: Descriptive statistics of currency, commodity and equity quarterly returns(1980M2-2008M12)Currencies Commodities EquitiesAUD CND SW F GBP nonoil oil au cn sw ukMean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00Max 10.44 8.10 17.46 14.18 16.12 81.03 17.01 19.43 13.31 19.92Min -18.16 -14.42 -17.38 -7.42 -32.01 -87.29 -23.34 -15.02 -23.58 -7.42Std.dev. 5.48 3.11 6.42 4.61 5.59 18.46 6.67 5.45 5.76 4.61Jarque-Berra 13.02 60.16 1.34 17.81 376.32 303.02 5.19 10.33 18.68 62.88Prob. 0.00 0.00 0.51 0.00 0.00 0.00 0.07 0.01 0.00 0.00Table 16: Correlations (upper diagonal), variances (diagonal), and covariances (lowerdiagonal) of currency, commodty and equity quarterly returns (1980M2-2008M12)Currencies Commodities EquitiesAUD CND SW F GBP nonoil oil au cn sw ukCurrenciesAUD 29.76 0.56 0.22 0.39 0.36 0.23 0.07 0.14 -0.13 -0.06CND 9.40 9.59 0.10 0.36 0.29 0.30 0.02 0.20 -0.20 -0.14SW F 7.64 1.98 40.88 0.61 0.14 0.09 0.01 0.09 -0.30 -0.24GBP 11.50 6.07 21.35 29.89 0.40 0.31 0.04 0.13 -0.24 -0.29Commoditiesnonoil 10.87 5.01 5.12 12.11 30.98 0.43 -0.08 0.16 -0.10 -0.15oil 23.47 17.33 10.18 31.17 44.01 337.76 0.12 0.19 -0.12 -0.05Equitiesau 2.61 0.44 0.39 1.45 -2.94 14.20 44.14 0.22 0.21 0.16cn 4.24 3.34 3.27 3.72 4.86 18.81 7.78 29.41 0.05 0.10sw -4.06 -3.47 -11.14 -7.65 -3.05 -13.13 7.84 1.44 32.86 0.25uk -1.51 -1.93 -7.07 -7.33 -3.95 -4.22 4.83 2.43 6.68 21.1040

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