Government Bond Market Seasonality, Diversification, and Cointegration: International Evidence

The Journal of Financial Research • Vol. XXV, No. 2 • Pages 203–221 • Summer 2002

GOVERNMENT BOND MARKET SEASONALITY, DIVERSIFICATION,AND COINTEGRATION: INTERNATIONAL EVIDENCE

Kenneth L. SmithPittsburg State University

Abstract

Using government bond market data for the United States, Canada, theUnited Kingdom, Germany, France, and Japan, I investigate several hypotheses.Market efficiency is investigated by testing for seasonality and cointegration. Theseasonality results are mixed. In regression tests, a January effect is detected inseveral markets (United States, Germany, France, United Kingdom, and Canada)using local currencies. However, in a nonparametric test, the January effect is sup-ported only for France. When U.S. dollar returns are used, regression results alsoreveal a January effect for several markets (United States, Germany, France, andUnited Kingdom). These results are not confirmed by a nonparametric test. Cor-relation analysis shows considerable diversification opportunities for short-terminvestors. Cointegration tests indicate that several of the markets share cointegrat-ing vectors, increasing the possibilities of using other endogenous bond marketsto better predict movements in a particular market.

JEL Classifications: F30, G12

I. Introduction

World bond and equity markets provide liquidity for growing world trade.However, less research focuses on correlations among international bond marketsthan on correlations among international equity markets (e.g., Smith 1999; Darbarand Deb 1997; Theodossiou and Lee 1993). In the literature, several hypothesesrelated to market efficiency, international portfolio diversification, and equilib-rium relations are tested using international equity market data. A January effect iswell documented for major equity markets (Gultekin and Gultekin 1983). Solnik,Boucrelle, and Fur (1996) demonstrate correlations between the United States andthe United Kingdom and between the United States and Japan, and French andGerman equity markets are trending upward. Also, multivariate tests are performedto test long-run equilibrium relations among major equity markets (Kasa 1992).

The author would like to thank Carol Sabia of Salomon Smith Barney for providing the data for thisstudy and an anonymous referee for helpful comments.

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204 The Journal of Financial Research

There is a gap in the literature regarding these hypotheses as they relate to govern-ment bond markets.

I apply these same tests to six major world government bond markets(United States, Japan, Germany, France, United Kingdom, and Canada). A sea-sonal anomaly in government bond returns would indicate market inefficiency inthat information would exist to help investors earn abnormal returns. Increasingcorrelation would indicate that information from other government bond marketscan be used to predict bond returns in a particular market. Increasing correlationwould also imply that gains from international diversification have diminished. Evi-dence of equilibrium relations among these markets would show the markets arenot independent, indicating one or more markets may be helpful in predicting othermarkets.

The January effect, first identified by Rozeff and Kinney (1976) for stocks,is shown to exist in several international stock markets. Evidence of a January effectin government bonds across countries is mixed. Clayton, Delozier, and Ehrhardt(1989) find that among longer maturities, U.S. government bonds have lowerJanuary returns. Using U.S. data, Schneeweis and Woolridge (1979) do not finda January effect in ten-year government bonds. Similarly, Smirlock (1985) findsno evidence of seasonality in U.S. government bonds. All of these tests employU.S. government bond data alone. In this article I test whether seasonality existsin several government bond markets across the major industrial countries. The re-sults are mixed. When bond returns are regressed on monthly dummy variables, astatistically significant January effect is identified for U.S., U.K., German, French,and Canadian government bond markets when measured in local currencies. Theseresults are duplicated for the same markets using excess returns measured in U.S.dollar returns with one exception—Canada does not exhibit this anomaly in U.S.dollar terms. A January effect is not found for the Japanese market in either localcurrencies or U.S. dollars. Nonparametric tests fail to detect a January effect, re-gardless of which unit of measure is used, except for the French government bondmarket (local currency).

Levy and Lerman (1988) find that low correlations among world bondmarkets make international diversification of bond market portfolios beneficial.Iben and Litterman (1994) show that, except for Japan, correlations among theG-7 countries have increased, although they conclude that benefits to internationaldiversification are still possible. Solnik, Boucrelle, and Fur (1996) report increasingcorrelations among several major world bond markets. Greater correlations amongthe markets reduce benefits of international bond portfolio diversification. Resultsreported here suggest correlation may be low, or even negative, for the short-terminvestor. For buy-and-hold investors, correlations are consistently high and positive.

Kasa (1992) investigates the long-term interaction of U.S., Japanese,German, French, and Canadian equity markets using tests of cointegration. No suchtests exist for international bond market movements. Those tests are performed here

Government Bond Market 205

using the familiar Johansen (1988) and Johansen and Juselius (1990) technique,which relies on the multivariate likelihood ratio test applied to nonstationary se-ries. The common objective of these studies is to determine whether internationaldiversification of bond portfolios is beneficial to investors. To benefit internationalinvestors, tests should reject cointegration. If the six bond markets are cointegratedthey may be part of a mean-reverting equilibrium system. If they are found to sharea common equilibrium each market may be thought of as part of an endogenous(“common”) system; in which case, to the extent that the endogenous variablesare predictable, market efficiency is rejected and benefits of diversification are re-duced. Chung and Liu (1994) perform these tests on major equity markets. Resultsindicate, with one exception, the markets are part of a “common” region.

II. Method

Johansen (1988) and Johansen and Juselius (1990) set out a method toestimate cointegrating relations within a multivariate context such that

Xt = A1Xt−1 + · · · + AkXt−k + εt t = 1, . . . , T , (1)

where Xt is a p × 1 vector of endogenous variables and εt is an independent andidentically distributed (i.i.d.) Gaussian process. The test for cointegration involvesestimating the following vector error correction model:

∆Xt =Γ1∆Xt−1 + · · · + Γk−1∆Xt−k+1 + ΠXt−k + εt , (2)

where

Γi = −I + A1 + · · · + Ai , (3)

and

Π= I − A1 − · · · − Ak . (4)

It is well known that simply first differencing data to induce stationarity in a vectorautoregression (VAR) when the variables of the model are cointegrated leads tomisleading results. Thus, the model used here, which includes the level information(Xt ), as well as the first-differenced data, must be estimated. The data in the Xt

matrix contain information (deviations from long-run equilibrium) excluded fromthe VAR specification. Accordingly, the estimated coefficients in Π capture long-run information lost when estimating a VAR of a system of cointegrated variables.The estimated coefficients on the first differenced terms (Γi ) in equation (2) arethe parameters from a conventional VAR.

The matrix Π is decomposed as Π = αβ′, where α and β are both p × rmatrices. To test for cointegration, first the rank of Π is determined; second, theestimated number of characteristic roots (λ) is used to form β′; and third, α is


estimated. The vector β captures the distance from long-run equilibrium, and thevector α captures speed of adjustment to equilibrium. Rank can range from zeroto the number of variables in the system (p) minus one. Thus, a system of twovariables may have at most one cointegrating vector. The rank of Π is equal to thenumber of its statistically significant characteristic roots. If r = 0 (where r is thenumber of cointegrating vectors), the variables in Xt are not cointegrated andthe traditional VAR may be estimated. If r = 1, the cointegrating vector is unique.The number of cointegrating vectors can range up to p – 1.

This method relies on one or both of the following two statistics to test therank of Π.

λtrace(r ) = −Tn∑

i=r+1

ln(1 − λ̂i ), (5)

λ(r, r + 1)max = −T ln(1 − λ̂r+1) (6)

where λi is the estimated value of the characteristic roots (eigenvalues) of the Πmatrix. Equation (5) can be used to test the rank of Π in the following manner. Thenull hypothesis of r = 0 is tested against the alternative hypothesis of r > 1. If thisnull is rejected, the researcher then tests the null of r ≤ 1 against the alternativethat r > 1. If this null is rejected, the null becomes r ≤ 2, tested against r > 2.

In addition, equation (6) can be used to test for the rank of Π. Using theλmax statistic the null, r = 0, is tested against the alternative hypothesis r = 1. If thisnull is rejected, the null becomes r = 1 and is tested against r = 2.

Once the model is estimated, the Johansen procedure allows a test of restric-tions on β. If a market’s cointegration estimated coefficients are zero, the marketmay be considered excluded from a common system. Where a test is conducted todetermine whether the U.S. bond market is part of a common system, the test of

β = Hς , (7)

where H is a p × m (= 6 – 1 restriction) matrix, and ς is an m × r matrix, such that

H =

∣∣∣∣∣∣∣∣∣∣∣∣

0 0 0 0 01 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1

∣∣∣∣∣∣∣∣∣∣∣∣

.

The restriction that the U.S. bond market is not part of a common systemis tested by performing the cointegration test with only zeros in the first row of H.Likewise, Japan is tested by restricting the second row of H to zeros. Other marketsare tested by similar restrictions to the appropriate rows.


III. Data and Unit Root Tests

These cointegration hypotheses are tested using the Johansen method onmonthly government bond market data supplied by Salomon Smith Barney. Testsare also conducted for common trends among bond markets for February 1985through March 1999. Indexes are constructed of weighted (by market capitalization)fixed-rate sovereign debt and include securities with a minimum maturity of oneyear. A single maturity (e.g., ten years) may be the most suitable when testingfor correlation. In this case, ideally, each index would be composed of a singlematurity. However, when testing for cointegration and seasonal factors, an indexcomposed of a single maturity may miss the hypothesized relation because the indexis narrowly defined. The Salomon Smith Barney bond indexes are constructed suchthat maturities range from one year to whatever maturity may be outstanding in themarket in question, ensuring that tests are more likely to capture any cointegratingvectors and January effects that are present. The average maturities fall withina fairly narrow range: 10.44 years for the United Kingdom, 8.96 years for theUnited States and Canada, 7.24 years for Germany, 7.17 years for France, and6.13 years for Japan. Corresponding modified durations are even more narrowlymeasured: 6.92 years for the United Kingdom, 5.9 years for Canada, 5.6 years forthe United States, 5.54 years for Japan, 5.11 years for France, and 4.93 years forGermany. Returns are first differences of logs.1

The six markets studied constitute approximately 85% of world bond mar-ket value. As mentioned earlier, research has not been conducted using internationalgovernment bond data. The Salomon data allow tests of seasonality across countriesfor the first time.

The risk-free rates are ninety-day government securities from each country.These data have been supplied by the Organization of Economic Cooperation andDevelopment. Tests are conducted in both local currency and U.S. dollars. Multi-national investors should be interested in U.S. dollar results, given that hedgingof exchange rate risk makes the results in local currencies of interest as well. Thepurpose is to begin to fill the gap in the literature about the relations among worldbond markets.

Typically, Dickey-Fuller tests are conducted to ensure the absence of unitroot in the series tested. Kwiatkowski et al. (1992) show that the Dickey-Fullertests have low power, making it likely that, without strong evidence against it, the

1Salomon Smith Barney constructs the monthly bond indexes to ensure that: (a) the indexes are relevantto investors; (b) the bond markets are realistically available to market participants; (c) investors can replicatethe results; (d) the indexes do not change composition very often; (e) the indexes do not contain significantbarriers to entry; (f) expenses are well understood by market participants and are not excessive; and (g) theselection criteria to be included in the indexes are simple and objective. The maturities are mixed, exceptthat maturity must be at least one year.


null hypothesis is accepted. Kwiatkowski et al. propose a complementary test, analternative method in which the null hypothesis of stationarity is tested (against thealternative of unit root). This test is based on whether a random walk has a varianceof zero. Both tests are conducted. The Dickey-Fuller and augmented Dickey-Fullertests cannot reject unit roots for the level series while rejecting unit roots for thereturns series at the 1% significance level. This is true whether the data are measuredin local currencies or in U.S. dollars. The Kwiatkowski et al. test statistic rejectsstationarity for the bond level data in both local currencies and U.S. dollars when thelag is 0. When the lag is extended to 10 using dollar terms, stationarity is rejectedfor the level series for the United States and the United Kingdom at the 1% level.Stationarity is only rejected at the 10% level for the Japanese and French bondlevels. Stationarity is not rejected for the German and Canadian U.S. dollar bonddata. In each returns series (local or U.S. dollar) for lags of 0 or 10, stationarity isnot rejected.2

IV. Bond Market Summary Statistics and Volatility

Panel A of Table 1 reports the summary statistics for the bond markets in lo-cal currencies. Except for Japan (both skewness and kurtosis), Germany(skewness), and the United Kingdom (kurtosis), the data do not depart from normal-ity. The Japanese bond data exhibit a fair amount of negative skewness (−0.60996)and kurtosis (1.372813). The German data are also negatively skewed (−0.61807),whereas the U.K. data indicate kurtosis (1.231679). Panel B shows the summarystatistics for the data measured in U.S. dollars. These data are not skewed. How-ever, there is kurtosis in the excess returns for Japan (1.21292), Germany (1.14504),France (1.04603), and the United Kingdom (1.00543).

The question of bond market volatility is important in light of the volatilityfound in world equity markets. The ten-month moving standard deviations areplotted in Figures I and II. When measured in local currencies (Figure I), thereappears to be a downward trend over the sample period for each of the series, witha minimum volatility of 0.005. These same results are even more pronounced whenthe excess returns are measured in dollar terms. Figure II indicates that there isgreater volatility in the moving ten-month standard deviation in dollar terms, withdecreasing trend. These results are in sharp contrast to Iben and Litterman (1994).They find that government bond market volatilities increased in the most recentperiod compared with historical periods. However, their government bond data arecomposed solely of one maturity: the ten-year government bond. The Salomon dataare indexes that cover a fairly narrow range of maturities (and durations) and thusare more representative of the total market.

2 To conserve space, the table reporting unit root tests is omitted. However, it is available from theauthor.


TABLE 1. Summary Statistics of Excess Returns.

U.S. Japan Germany France U.K. Canada

Panel A. Local Currencies: 1985:2 Through 1999:3

Average 0.002851 0.002183 0.001537 0.002175 0.001660 0.002645Std. dev. 0.014209 0.013874 0.009952 0.012803 0.019351 0.018294Skewness 0.013846 −0.60996∗∗∗ −0.61807∗∗∗ −0.12995 −0.26588 −0.20619Kurtosis −0.00365 1.37283∗∗∗ 0.290242 −0.08577 1.231679∗∗∗ 0.370261

Panel B. U.S. Dollars: 1985:2 Through 1999:3

Average 0.002851 0.002826 0.001887 0.002620 0.002104 0.003152Std. dev. 0.014209 0.034073 0.029933 0.028248 0.031591 0.022249Skewness 0.013846 −0.12721 −0.02492 0.017235 −0.07372 −0.15982Kurtosis −0.00365 1.21292∗∗∗ 1.14504∗∗∗ 1.04603∗∗∗ 1.00543∗∗∗ 0.53359

Note: Both skewness and kurtosis are tested against the null of zero.

∗∗∗Significant at the 1% level.

V. Bond Market Correlations

Panel A of Table 2 shows the correlations among the bond markets whenmeasured in local currencies. The correlations range from 0.3082 (Japan/France) to0.7814 (United States/Canada). The second highest correlation is 0.7464 (Germany/France). This is not surprising given the cultural and geographical links betweenthese countries. On the other hand, correlations with Japan are relatively high,ranging from 0.3082 (France) to 0.4684 (Germany). This is surprising given thecultural and geographical dispersions. Panel B of Table 2 shows the correlations

TABLE 2. Correlation of Monthly Bond Returns.

U.S. Japan Germany France U.K.


Japan 0.4109Germany 0.5207 0.4684France 0.5212 0.3082 0.7464U.K. 0.4562 0.3661 0.6280 0.5866Canada 0.7814 0.3560 0.4539 0.4323 0.4868


Japan 0.2341Germany 0.3422 0.6526France 0.4116 0.6863 0.8847U.K. 0.3510 0.6321 0.5762 0.6614Canada 0.6151 0.4183 0.2797 0.4109 0.6260


Figure I. Ten-Month Moving Standard Deviations of Excess Returns in Local Currencies.


Figure II. Ten-Month Moving Standard Deviations of Excess Returns in U.S. Dollars.


among the bond markets when measured in U.S. dollars. These correlations rangefrom 0.2341 (United States/Japan) to 0.8847 (Germany/France). The correlationbetween the United States and Canada is 0.6151. In dollar terms, the correlationsof Japanese bond returns with Germany, France, and the United Kingdom are againrelatively high. Both the local currency and U.S. dollar data suggest that there mightbe a long-run relation among these markets.

Figure III plots the ten-month moving correlations of excess returns (be-ginning with January 1986) in local currencies among the markets using the U.S.market for comparison. This is assumed to represent the time horizon for a short-term investor interested in timing the market. There is a great deal of short-termvariation in these moving correlations. The estimated correlations are strictly pos-itive, with a few exceptions. Correlations turned negative for the U.S./Japanese,U.S./German, U.S./French, and U.S./U.K. combinations in the early to mid-1990s(they also decreased for the U.S./Canadian correlations, although they remainedpositive). This was a period—following the Gulf War, a U.S. recession, and a slowrecovery—where long-term government bond rates were decreasing fairly rapidly.Given the construction of the data (i.e., ten-month moving correlations), the nega-tive correlations may be explained by these movements in U.S. interest rates duringthis period. Otherwise, these ten-month moving correlations are volatile, rangingup to 0.8 or 0.9. The U.S./Canadian correlations exhibit the same pattern, except ata higher level.

Figure IV shows the recursive correlations of excess returns in local curren-cies (beginning with January 1986). The plots begin with the ten-month correlation,followed by the eleven-month correlation, and so on, throughout the entire sample.Buy-and-hold investors may find information on these correlations useful in judg-ing the merits of international diversification over long horizons. After about twentyobservations the correlations for the United States/Japan, United States/Germany,United States/France, United States/United Kingdom stabilize at about 0.5. TheU.S./Canadian correlations are much higher, but appear to be decreasing. Thissuggests that long-term gains from international diversification between U.S. andCanadian government bonds are increasing, although other countries’ markets mayprovide more benefit.

The ten-month moving correlations in U.S. dollars are shown in Figure V.Again, considerable variation in the short-term correlation is evident. These cor-relations are low and frequently negative for the U.S./Japan combination, indi-cating opportunity for diversification. Although the estimated correlations for theU.S./German, U.S./French, and U.S./U.K. correlations are for the most part positive,they are generally low, providing diversification benefits. They are frequently low, ifnot negative. There appears to be much less benefit from short-term diversificationbetween the U.S. and Canadian bond markets.

The recursive correlations in U.S. dollars are graphed in Figure VI. Afterthe first few observations, the correlations are fairly stable. Each of the four markets


Figure III. Ten-Month Moving Correlations of Excess Returns in Local Currencies.


Figure IV. Recursive Correlations of Excess Returns in Local Currencies.


Figure V. Ten-Month Moving Correlations of Excess Returns in U.S. Dollars.


Figure VI. Recursive Correlations of Excess Returns in U.S. Dollars.


(Japan, Germany, France, and United Kingdom) exhibit about the same amount ofcorrelation, between about 0.25 and 0.40. Canada’s correlations are higher, but adecreasing trend is again apparent.

VI. Seasonality Results

The results of regressing excess government bond returns on monthlydummy variables and a dummy variable for October 1987 are shown in Table 3.Panel A reports the results when measured in local currencies. A January effectis detected in five of the G-6 countries using the regression. The United King-dom exhibits the strongest effect at 1.25%. Germany has the smallest effect at0.66%. Only the Japanese bond market fails to exhibit this seasonal effect. Anegative October effect is detected for the U.S. market (–1.01% at the 6% signifi-cance level). This is equivalent in size to the positive January effect. The October1987 crash period indicates that as stock markets were declining, investors were

TABLE 3. Regression of Returns on Monthly and October 1987 Dummies and Wilcoxon Rank Test.



January 0.0100 — 0.0066 0.0074 0.0125 0.0109(2.7234) (2.5190) (2.0944) (2.3300) (2.3649)

October −0.0101 — — — — —(1.9372)

October 1987 0.0283 0.0283 — — — 0.0420(1.9668) (1.9580) (2.3449)

Durbin-Watson 1.69 1.52 1.68 1.50 1.67 1.83Wilcoxon rank 68 46 73 85∗∗ 67 54


January 0.0100 — 0.0198 0.0208 0.0197 —(2.7234) (2.1407) (2.4239) (1.8976)

August — — −0.0295 −0.0267 — —(−2.2115) (−2.1506)

October −0.0101 — — — — —(1.9372)

October 1987 0.0283 0.076 0.0731 0.0646 0.0972 —(1.9668) (1.7461) (2.0264) (1.9245) (2.4038)

Durbin-Watson 1.69 1.76 1.93 1.92 1.70 1.98Wilcoxon rank 68 28 27 35 22 42

Note: Local currencies are reported in returns. U.S. dollar currencies are reported in excess returns. Onlystatistically significant coefficients are reported. The t-values are in parentheses.

∗∗Significant at the 5% level.


shopping for safety in the government bond markets. An October 1987 effect isfound for the United States, Japan, and Canada. Canada shows the strongest ef-fect, 4.2%, although both the U.S. and Japanese effects were also strong, both at2.83%.

Panel B of Table 3 reports the same results in U.S. dollar terms. A Januaryeffect is apparent in four of the G-6 countries, with Canada and Japan being theexceptions. The strongest positive January effect is found for France, 2.08%; theweakest for the United States, 1.0%. A negative August effect of approximatelyequal magnitude is found for two markets, Germany and France. A positive October1987 effect is reported for five of the markets—the United States, Japan, Germany,France, and the United Kingdom—ranging from 2.83% for the United States to9.72% for the United Kingdom.

The regression results must be viewed with caution. Table 3 also reportsthe Durbin-Watson statistic for each equation. These statistics for both local cur-rency and U.S. dollar returns indicate possible serial correlation in the residu-als. This raises the possibility of biasedness and reducing the reliability of theestimates. As a consequence, a nonparametric test of the January effect is con-ducted. The Wilcoxon rank tests are also reported in Table 3. Given that the sam-ple period contains fourteen January returns, the test compares the mean Januaryreturns with the mean of the other eleven months. If there is no differ-ence between mean January returns and mean non-January returns, the expectedrank statistic is 52.5 (= n(n + 1)/4). When applying this test in local currencies,the January effect is only confirmed for the French bond market. When mea-sured in U.S. dollar terms, the January effect is not confirmed for all marketstested.

Thus, the results are mixed. As mentioned earlier, there is a dearth ofinternational bond market data with which to conduct these tests. Future researchshould focus on alternative data sets from various countries, and weekly, or evendaily, data in an effort to further investigate the questions regarding seasonality.

VII. Cointegration Results

Caution must be used in determining lag length when conducting cointegra-tion tests. Both the normality and absence of serial correlation in the residuals arecritical issues. Additionally, longer lags are more likely to detect mean-reverting re-lations, with care taken to conserve degrees of freedom. Consequently, lag length isselected only after multivariate tests for the normality and lack of serial correlationin the residuals are conducted.

Panel A of Table 4 reports the trace and max statistics for the bond marketsin local currencies. Tests for normality and serial correlation confirm that at lagsof 15, neither nonnormality nor autocorrelation in the residuals appears to be a


TABLE 4. Johansen Tests for Cointegration Among Government Bond Markets.

Trace 10% Max 10%Trace H0: Trace Statistics Critical Value Max H0: Max Statistic Critical Value


r = 0 161.06 89.37 r = 0 67.18 24.63r ≤ 1 93.88 64.74 r = 1 44.95 20.90r ≤ 2 48.93 43.84 r = 2 21.94 17.15r ≤ 3 26.98 26.70 r = 3 17.53 13.39r ≤ 4 9.45 13.31 r = 4 5.97 10.60r ≤ 5 3.48 2.71 r = 5 3.48 2.71


r = 0 134.99 89.37 r = 0 48.17 24.63r ≤ 1 86.82 64.74 r = 1 34.90 20.90r ≤ 2 51.93 43.84 r = 2 24.70 17.15r ≤ 3 27.23 26.70 r = 3 15.03 13.39r ≤ 4 12.20 13.31 r = 4 7.70 10.60r ≤ 5 4.49 2.71 r = 5 4.49 2.71

problem.3 Both the trace and L-max statistics indicate there are three cointegratingvectors among the six bond markets. Panel B shows these same results for the bondmarkets measured in dollars.

The efficient markets hypothesis implies that no information from othermarkets can be used to forecast the endogenous variables. Thus, these marketscannot be described as efficient if they share three cointegrating vectors. Threecointegrating vectors, in a system of six endogenous variables, increase the oppor-tunities to predict future movements in the bond markets. This begs the question:Are these six markets part of a “common region”? If so, there must be some com-mon factors driving the markets. This raises questions for future research. Can thecommon factors be identified? Are there mean-reverting relations among worldbond and equity markets?

Additional tests are conducted to determine whether any one of the marketsis not part of a common region. This is accomplished by testing equation (7), thatis, the restriction that each market does not enter the cointegration space. Theseresults are shown in Table 5. In terms of local currencies, only the U.K. marketappears to be separate from a common region. For U.S. dollar investors, all markets

3Each model is tested to ensure that the residuals were normally distributed and that serial correlationis absent. For the test in local currencies, the test for normality yielded a statistic of 12.515 ( p-value of0.41). The Lagrangian multiplier tests for 1 and 4 lags for the absence of serial correlation yielded statisticsof 34.89 ( p-value of 0.52) and 42.34 ( p-value of 0.22), respectively. For the test in U.S. dollars, the test fornormality yielded a statistic of 10.21 ( p-value of 0.60). The tests for absence of serial correlation resultedin statistics of 39.96 ( p-value of 0.30) and 31.89 ( p-value of 0.66), respectively.


TABLE 5. Likelihood Ratio Tests of Restriction That Each Market Is Not Part of a CommonRegion.


Local currencies 44.41 7.56 21.07 20.86 5.02 11.96(0.00) (0.06) (0.00) (0.00) (0.17) (0.01)

U.S. dollars 18.95 9.66 13.88 10.99 8.58 18.23(0.00) (0.02) (0.00) (0.01) (0.04) (0.00)

Note: The p-values are in parentheses. The statistics are distributed χ2 with 3 degrees of freedom.

are part of a common region. These results indicate not only that the markets sharethree cointegrating vectors, but that all of the markets (in U.S. dollar terms) are partof a common system. The conclusion is that international diversification is not asbeneficial as if these equilibrium relations did not exist among the markets.

VIII. Summary and Conclusions

Less academic attention has been focused on world government bond mar-kets than on world equity markets. Questions of seasonal anomalies, increasingcorrelation, and cointegration in equity markets are familiar research topics. In thisarticle I investigate these questions for world government bond markets.

Several hypotheses have been offered to explain the January effect in worldstock markets. None of these seems completely satisfactory in explaining a poten-tial January effect in government bonds (either measured in local currencies or inU.S. dollars). The data show that world equity markets are increasingly correlated.Correlation results reported here indicate that the comovements among governmentbond markets are decreasing, leading to the conclusion that international diversi-fication is becoming more beneficial to investors. Finally, cointegration tests forequity markets show that major world equity markets share common factors thatdrive these markets. Results reported here confirm that this is also the case forgovernment bond markets, indicating that international diversification potential islower and that this information can be used to better predict government bondmarket movements than if markets are not cointegrated.

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Documents

Government Bond Market Seasonality, Diversification, and Cointegration: International Evidence