What Drives the International Bond Risk Premia?

What Drives the International Bond Risk Premia? Guofu Zhou Washington University in St. Louis Xiaoneng Zhu 1 Central University of Finance and Economics First Draft: December 15, 2013; Current Version: January 28, 2014 1 Zhou: Olin School of Business, Washington University in St. Louis, e-mail: zhou@wustl.edu.cn; and Zhu: The Chinese Academy of Finance and Development, Central University of Finance and Economics, Beijing, China, e-mail: xiaonengz@gmail.com. We thank seminar participants at Washington University in St. Louis, Central University of Finance and Economics, Southwest University of Finance and Economics for helpful comments.

Abstract This paper nds that the global leading economic indicator, which is a measure of the overall state of the world economy published by the OECD, can strongly predicts international bond risk premia, with out-of-sample R 2 s up to 25:9%. In contrast, local leading economic indicators generally generate mixed results for predicting international bond risk premia. Moreover, the forecasting power of the global leading economic indicator is above and beyond Cochrane-Piazzesi (2005) forward-rate predictor and well as the principle components extracted from a large set of macroeconomic variables. Theoretically, the predictive ability of the global leading economic indicator is consistent with rational asset pricing models in an integrated world market of government bonds. JEL Classi cations: G1, E4, F3. Keywords: Bond risk premia, economic value, global common factor, leading economic indicator, return predictability.

1 Introduction One of the more important empirical ndings in bond studies is that the risk premia are time-varying, similar to the equity market. To explain the economic forces that drive the time-varying risk premia, numerous predictors of future US government bond returns have been proposed. Fama and Bliss (1987), Stambaugh (1988) and Fama (2006) nd forward-spot spreads have signi cant predictive power, while Mankiw (1986), Keim and Stambaugh (1986) and Fama and French (1989) and Campbell and Shiller (1991), among others, show the term spread is useful. Additional variables, real bond yields (Ilmanen, 1995), the output gap (Cooper and Priestley, 2009), inverse relative wealth (Ilmanen, 1995), in ation (Joslin, Priebsch, and Singleton, 2010), option prices (Almeida, Gravelineb, and Joslin, 2011), variance risk premia (Muller, Vedolin, and Zhou, 2011), net bond issues (Baker, Greenwood, and Wurgler, 2013), return jumps (Wright and Zhou, 2009), principle components extracted from a large set of macro variables (Ludvigson and Ng, 2009, 2010), and technical indicators (Goh, Jiang, Tu, and Zhou, 2013) are found to have predictive power too. To date, Cochrane and Piazzesi s (2005, 2008) forward rate predictor seems the single most powerful predictor that has by far the largest out-of-sample R 2 s. While these studies provide mainly analysis on the United States, Ilmanen (1995), Zhu (2013), and Dahlquist and Hasseltoft (2013), among others, show that international bond risk premia are predicted by various predictors. This paper uncovers a new and powerful predictor of international bond returns: the global leading economic indicator, which is a measure of the overall state of the world economy published by the OECD, Rational asset pricing models (see, for example, Buraschi and Jiltsov, 2007; Wachter, 2006; Piazzesi and Schneider, 2007) provide the theoretical basis for the state of the economy as a predictor of bond risk premia. Intuitively, a leading economic indicator may capture changing investment opportunities, as suggested by the classic Merton (1971) model. Hence, the global leading economic indicator, which may capture time-varying risk aversion to economic recessions or booms and may vary inversely with excess returns, can predict world bond 1

risk premia. An overall measure of the economy provides a bird s eye view on the economy. However, it may not be easy to construct such a measure. Fortunately, the leading economic indicators of the organization for economic co-operation and development (OECD) are designed for this purpose, which are available to investors from Datastream. OECD provides not only country-sepci c leading economic indicators (LEI) for leading bond markets such as US, UK, Japan, and Germany, but also o ers a leading economic indicator (LEI4) for measuring the overall level of the state of the four major economies: US, UK, Japan, and Germany. In other words, LEI4 is the available best proxy for the world economy of state as far as bonds in the four countries are concerned. Hence, LEI4 is our global leading economic indicator. Although LEI type of predictors have been used in earlier equity studies of Perezquiros and Timmermann (2000), Lamont, Polk, and Saá-Requejo (2001), Ozoguz (2009), and Lee (2012), they seem new in the bond literature. Why is it important to investigate the predictive ability of LEI4 in addition to the predictive power of local LEIs? The motivation is the recent works of Kose, Otrok, and Whiteman (2003, 2008) and Canova, Ciccarelli, and Ortega (2007), who demonstrate the presence of a signi cant world business cycle and show that country speci c indicators play a much smaller role than the global indicator does. In light of this, LEI4 is likely to better predict the future overall state of the global economy than country-speci c LEIs do. Empirically, our investigation focuses on two questions: (1) Does LEI4/LEI predict bond risk premia out-of-sample? (2) What is the economic value of LEI4/LEI? We have a few interesting ndings. First, our empirical results show that the predictive power of country-speci c leading economic indicators are mixed. Speci cally, the local LEI predicts excess bond returns in the Japan and Germany, with out-ofsample R 2 ranging between 0.6% and 19.3%. These out-of-sample R 2 s are statistically signi cant. However, the local LEI does not forecast bond risk premia in the U.S. and the U.K., with the average out-of-sample R 2-9.3% and -12.1%, respectively. 2

Second, in contrast with the mixed results from the local LEIs, the global common LEI4 strongly predicts international excess bond returns across the countries, with out-of-sample R 2 ranging between 0.85% and 25.9%. The average out-of-sample R 2 is 13.6%. Broadly speaking, the empirical results are consistent with Harvey (1991) and Ilmanen (1995) who nd that global factors can predict international asset returns better than local factors do. As emphasized by these two studies, the better forecasting performance of global factors is in line with an integrated global market. Moreover, it is worthwhile to emphasize that the predictive power of the LEI4 is above and beyond that contained in the Cochrane-Piazzsi (2005)forward rate predictor and the principle components extracted from a large set of macro variables (Ludvigson and Ng, 2009, 2010). In addition, the predictive ability of the LEI4 is robust to the subsample analysis and to multiple-step-ahead forecasting analysis. Since statistical signi cance does not necessarily imply economic signi cance, the economic value of LEI4 is still an open question. To assess the economic value of the out-of-sample bond risk premium forecasts, following Campbell and Thompson (2008), Thornton and Valente (2013) and many others, we investigate the utility gains from an asset allocation problem. Speci cally, we assume that mean-variance investors allocates a portfolio between a long-term bond and the one-year risk-free Treasury bill. The average utility gain is the utility di erence between two di erent investing strategies: the strategy using LEI4/LEI to dynamically rebalance bond portfolios and the strategy using the expectation hypothesis (the empirical benchmark) to form bond portfolios. Our third set of results is related to the economic values of LEI4 and LEI. Though local LEIs often delivers negative out-of-sample R 2 in the prediction of excess bond returns, they usually generate positive economic value. More importantly, the LEI4 delivers systematic economic value. Indeed, all excess bond return forecasts deliver positive economic value. The average utility gain is respectively 0.58%, 1.0%, 0.10%, and 0.14% for the United States, the United Kingdom, Japan, and Germany. Overall, our ndings suggest that the global LEI4 has economically and statistically meaningful 3

predictive power for forecasting international bond risk premia. The remainder of this article is organized as follows. In the next section, we outline the methodology for predicting excess bond returns and discuss criteria for evaluating predictive power. The out-of-sample forecasting results for the LEI4 and local LEIs are reported in Section 3. Section 4 conducts the robustness checks and reports empirical results. In Section 5, we compare the forecasting performance of the LEI4 with the forecasting performance of principle components extracted from a large set of macroeconomic variables. Section 6 concludes. 2 Methodology In this section, we describe our methodology. First, we discuss the predictive regression model framework. Then, we discuss the criteria we use to evaluate the out-of-sample forecasts. Finally, in the spirit of Campbell and Thompson (2008), Welch and Goyal (2008), Rapach, Strauss, and Zhou (2009), we discuss how to assess the economic value of predictive regressions. 2.1 Predictive Regressions In line with Cochrane and Piazzesi (2005), we use the following notation for the (log) yield of n-year bond where p (n) t = ln P (n) t y (n) t 1 n p(n) t, is the log bond price of an n-year zero-coupon bond at time t. A forward rate at time t for loans between time t + n 1 and t + n is de ned as f (n) t p (n 1) t p (n) t. (1) 4

The log holding period return from buying an n-year bond at time t and selling it as an n 1 year bond at time t + 1 is r (n) t+1 = p (n 1) t+1 p (n) t. (2) Naturally, the excess return of an n-year discount bond is the di erence between the holding period return of an n-year bond and the holding period return of a 1-period bond rx (n) t+1 r (n) t+1 y (1) t. (3) For assessing whether excess bond returns are predictable by some variable, a standard predictive regression is estimate rx (n) t+1=12 = + X t + " t+1 (4) by least squares. A natural candidate predictor is leading economic indicators. In this paper, we propose leading economic indicators as the predictor of excess bond returns. Economic theories generally imply that rational economic agents should be compensated for bearing macroeconomic risk. For example, the classic work of Merton (1971) indicates that the state of the economy represents changing investment opportunities and drive time-varying risk premia. In term of time-varying bond risk premia, Buraschi and Jiltsov (2007) and Wachter (2006) link term structure dynamics to economic fundamentals and show that bond risk premia should vary with macroeconomic shocks. In a recursive utility framework, Piazzesi and Schneider (2007) suggest that investors may require a premium to hold nominal bonds due to the fear of stag ation. In the spirit of this strand of literature, we use leading economic indicators to predict excess bond returns. While it is intuitively straightforward to predict excess bond returns in market i using the country-speci c leading economic indicator, Kose, Otrok, and Whiteman 5

(2003, 2008) and Canova, Ciccarelli, and Ortega (2007) suggest that world economic business cycles are very likely to be driven by some global common factors. As such, the LEI4 may better capture time-varying risk aversion and changing investment opportunities. Hence, we also use the LEI4 to predict excess bond returns in international bond markets. To show that the predictive ability of leading economic indicators is above and beyond that contained in the in uential and powerful Cochrane and Piazzesi (2005, CP hereafter) factor, we also predict excess bond returns out-of-sample by estimating the following two predictive regressions rx (n) t+1=12 = + CP t + " t+1=12, (5) rx (n) t+1=12 = + 1X t + 2 CP t + " t+1=12, (6) where CP t denotes the Cochrane-Piazzesi factor. If the predictive ability of regression (6) is above the predictive power of regression (5), it means that the predictive ability of a leading economic indicator is not consumed by the CP factor. To construct the CP factor, we regress average excess returns across maturity at each time t on the one-year yield and four forward rates f t [y (1) t f (2) t f (3) t f (4) t f (5) t ] T : rx t+1 = 0 + T f t + " t+1, (7) where average excess log return across the maturity spectrum is de ned as rx t+1 1 4 X 5 n=2 rx(n) t+1. (8) The CP factor is CP t+1 = 0 + T f t. (9) The CP factor is built upon the fact that the same function of forward rates predicts holding period returns at all maturities. 6

To avoid look-ahead bias and the use of future data, we generate one-month-ahead out-of-sample forecasts of excess bond returns using a recursive expanding estimation method. In the out-of-sample exercise, the CP factor is recursively constructed, using only information upon time t. All predictive regression parameters estimated just using information available up to the month of forecast formation. More speci cally, we estimate and forecast recursively, using data from the rst observation 1 to the time that the forecast is made, beginning in 1990:01 and extending through 2011:12. 2.2 Forecast Evaluation A natural empirical benchmark for assessing the predictive ability of leading economic indicators is the expectations hypothesis of interest rates. According to this theory, excess bond returns are unpredictable, and the historical average is the optimal forecast of excess bond returns. Any predictability in bond risk premia is a violation of the expectations hypothesis of the term structure. In light of the fundamental role of the expectations hypothesis, we choose the expectations hypothesis as the most straightforward benchmark. Speci cally, the historical average of excess bond returns over the out-of-sample period is rx (n) t+1 = 1 T X T j=1 rx(n) j. (10) Indeed, when a predictor contains no useful information for predicting bond risk premia ( = 0 in regression (4)), the predictive regression becomes the historical average forecast. A popular measure of out-of-sample predictive ability is the out-of-sample R 2 statistic, ROS 2, proposed by Campbell and Thompson to compare the forecasting power of various regressions. Let crx (n) t+1 denote the forecast of excess bond returns generated by a predictive regression, the R 2 OS statistic is akin to the familiar in-sample R2 statistic 1 The starting period varies across markets. 7

and is given by R 2 OS = X T X T j=1 (rx(n) j j=1 (rx(n) j crx (n) j ) rx (n) j ). (11) The R 2 OS statistic measures the reduction in mean square prediction errors (MSPE) for the predictive regression model relative to the expectations hypothesis. It is clear from the de nition of the R 2 OS statistic that R2 OS > 0 (R2 OS < 0) implies that the crx (n) t+1 forecast statistically outperforms (underperforms) the historical average forecast according to the MSPE metric. We further test whether leading economic indicators have a signi cantly lower MSPE than the expectations hypothesis benchmark. Statistically, this is equivalent to testing the null hypothesis that R 2 OS R 2 OS 0 against the alternative hypothesis that > 0. For this purpose, Clark and West (2007) develop the MSPE-adjusted statistic, which is an adjusted version of the Diebold and Mariano (1995) and West (1996) statistic. In contrast with the Diebold-Mariano test, the MSPE-adjusted test generates asymptotically valid inference when comparing forecasts from nested linear models. 2 Hence, the MSPE-adjusted test can be applied to compare the relative forecasting performance of two nested models. Since the historical average of excess bond returns is a restricted predictive regression (4) with = 0, we use the the MSPE-adjusted method to test the statistical signi cance of R 2 OS statistic is conveniently calculated by rst de ning statistics. Speci cally, the MSPE-adjusted f t+1 = (rx (n) t+1 rx (n) t+1) 2 [(rx (n) t+1 crx (n) t+1) 2 (rx (n) t+1 crx (n) t+1) 2 ]. (12) By regressing ff t+1 g T 1 t=1 on a constant and calculating the t-statistic corresponding to the constant, a p-value for a one-sided (upper-tail) test is obtained with the standard normal distribution. Clark and West (2007) also demonstrate that the MSPE-adjusted statistic performs reasonably well in terms of power and size properties. 2 The Diebold and Mariano (1995) and West (1996) method generates a nonstandard distribution for comparing nested models. 8

2.3 Economic Value Since statistical signi cance does not mechanically imply the economic signi cance of a predictive regression, it is important to assess the economic value of predictors. Following Campbell and Thompson (2008), Welch and Goyal (2008), and Rapach, Strauss, and Zhou (2009), we calculate realized utility gains for a mean-variance investor on a real-time basis. The method we employ explicitly account for the risk borne by an investor over the out-of-sample period. Speci cally, we rst calculate the average utility for a mean-variance investor with relative risk aversion parameter who allocates his or her portfolio monthly between a long-term bond and a one-year short-term Treasury bond using forecasts of excess bond returns based on the expectations hypothesis. This exercise requires the investor to forecast the variance of excess bond returns. In the spirit of Campbell and Thompson (2008), we assume that the investor estimates the variance using a ten-year rolling window of annual returns. A mean-variance investor who predicts excess bond returns using the historical average will decide at the end of period t to allocate the following share of his or her portfolio to the long-term bond in period t + 1: t+1 w t = ( 1 )(rx(n) ), (13) where ^ 2 t is the ten-year rolling-window estimate of the variance of excess returns. 3 Over the out-of-sample period, the investor realizes an average utility level of ^ 2 t+1 v = ( 1 2 )2, (14) where and 2 are the sample mean and variance, respectively, over the out-of-sample period for the return on the benchmark portfolio formed using forecasts of excess bond returns based on the historical average. We then calculate the average utility of the trading strategy based on the predictive 3 w 0;t is restricted to be positive and less than 150% at maximum so that extrement investments are prevented, as in Campbell and Thompson (2008), Goyal and Welch (2008), and Rapach, Strauss, and Zhou (2010). 9

regression in Equation (4). Similarly, the investor will choose a long-term bond share of and realizes an average utility level of c;t+1 ^w t = ( 1 )(crx(n) ^ 2 t+1 ), (15) ^v = ^ ( 1 2 )^2, (16) where ^ and ^ 2 are the sample mean and variance, respectively, over the out-of-sample period for the return on the portfolio formed using the predictive regression (4). The utility gain of using predictive variables is the di erence between Equation (16) and Equation (14): = ^v v. (17). The utility gain can be interpreted as the portfolio management fee that an investor is willing to pay to have access to the additional information available in a predictive regression model. 3 Empirical Results This section reports the summary statistics for international bond yields and brie y discusses the construction of composite leading economic indicators. This section also reports the out-of-sample forecasting results. 3.1 Data For our empirical analysis, we study excess bond returns in four largest bond market in the world: the United States, the United Kingdom (UK), Japan (JP), and Germany (GM). These markets are very liquid. As such, our study on the predictability of excess bond returns is less subject to the e ect of illiquidity. In addition, for these currencies, 10

almost all foreign exchange risk can be hedged. So, our study is less subject to the e ect of exchange rate exposure. The data set of international interest rates is made up of end-of-month observations of the one- to ve-year zero-coupon Treasury bond yields. The data samples respectively range from 1962:01 to 2011:12 for US, from 1970:01 to 2011:12 for UK, from 1980:01 to 2011:12 for JP, and from 1975:01 to 2011:12 for GM. The standard point of data availability determines the starting period of the data. 4 The US data are obtained from the Fama-Bliss discount bond le in the Center for Research in Securities Prices (CRSP). We collect the UK data from the Bank of England. The Japanese data are obtained from the Ministry of Finance Japan. The German observations are obtained from the Bundesbank, the central bank of Germany. [Insert Figure 1 about Here] [Insert Table 1 about Here] Figure 1 plots the Treasury bond yields for maturities of 1-, 2-, 3-, 4- and 5-year. Typically, bond yields increase as the maturity of bonds increases in all four bond markets. In addition, bond yields in the international bond markets appear to be volatile. A striking feature of bond yields is the persistence of interest rates. The gure clearly suggests these features of bond yields. In addition, bond yields in these major bond markets show a tendency of comovement. To illustrate the point, Table 1 reports the correlation coe cients between the average of bond yields in each market over the period 1980:01-2011:12. It is evident that international bond yields are highly correlated. The evidence is clearly indicative that some global common factors may predict international excess bond returns. [Insert Table 2 about Here] 4 The US leading economic indicator is available since 1962:01. 11

Excess returns on long-term bonds are calculated from bond yields as describe in Section 2. The summary statistics of the international excess bond returns are reported in Table 2. We nd that excess bond returns of di erent maturities in each market are highly correlated. To look at the level of bond risk premia, we nd that the mean of excess bond returns ranges between 0.48% and 2.21%. However, we want to emphasize that excess bond returns are very volatile, as indicated by the volatility of excess bond returns. Though the mean of excess bond returns is small, excess bond returns vary a lot over the sample period. All excess bond returns, except the US bond risk premia, are found to be signi cant at the 1% signi cance level. We also report the autocorrelation coe cients of order 1 and 12 for international excess bond returns. The results suggest that excess bond returns are highly serially correlated. [Insert Figure 2 about Here] The economic leading indicators for US, UK, JP, and GM are compiled by OECD and obtained from Datastream. In addition to the leading indicator for each market, OECD also compiles a leading economic indicator (LEI4) for all four countries (G4). The OECD leading indicators are designed to provide early signals of turning points in business cycles. In our out-of-sample forecasting exercise, instead of directly using LEIs to predict excess bond returns, we use the year-over-year log changes in the LEIs to forecast excess bond returns. Figure 2 plots the changes in the LEIs for US, UK, JP, GM, and G4. The intuition for using the change in LEI is straightforward: log changes in the LEIs remove the trend in the LEIs. Moreover, as emphasized by Ilmanen (1995), relative changes in economic situation can better capture investors relative risk aversion. 3.2 Out-of-Sample Forecasting Results This section examines the out-of-sample predictability of excess bond returns in four industrialized countries the United States, the United Kingdom, Japan, and Germany. 12

Our analysis of bond risk premium predictability in international markets proceeds in three steps. First, we assess whether excess bond returns can be forecast using country-speci c local LEIs. Second, we investigate whether excess bond returns can be predicted using the global common LEI4. Third, we examine whether the predictive ability of the LEI4 is subsumed by the CP factor. [Insert Table 3 about Here] Panel A of Table 3 reports the out-of-sample forecasting results using the countryspeci c LEIs to predict international bond risk premia. The results are mixing. While the LEI can predict excess bond returns in Japan and Germany, it underperforms the historical average in US and UK. In the GM bond market, the LEI generates R 2 OS statistics ranging between 12.5% and 19.3%. When assessed using the Clark and West (2007) MSPE-adjusted statistics, the ROS 2 statistics are statistically signi cant at the 1% level. In the JP bond market, the LEI also consistently delivers positive R 2 OS statistics ranging between 0.6% and 4.97%, which are statistically signi cant. For US and UK, the forecasts based on the LEI consistently have negative ROS 2 statistics, ranging between -8.81% and -13.8%. Given the statistical evidence, an open question is whether the statistical signi - cance is of economic signi cance. To assess the economic value of the out-of-sample bond risk premia forecasts, Panel A of Table 3 also reports the utility gains from an asset allocation perspective by setting = 3. The results are qualitatively similar for other reasonable values. In line with the statistical results, we nd that the LEI usually delivers positive utility gains in the GM bond market. In contrast, though the LEI delivers positive ROS 2 statistics in the JP bond market, it cannot generate positive utility gains for a mean-variance investor. 5 In the US and UK bond market, the opposite holds: The ROS 2 statistics are consistently negative, but the economic value of the LEI is generally positive, suggesting that investors are better o when using 5 When a portfolio weight of greater than 1.5 and less than 0 is allowed, the LEI does have positive economic value. 13

information contained in the LEI to predict bond risk premia. Overall, the results from predicting bond risk premia using the local LEIs are mixing. We turn next to the detailed results for out-of-sample predictions of excess bond returns using the global LEI4. Panel B of Table 1 reveals that the LEI4 outperforms consistently the historical average in terms of ROS 2 statistics. Indeed, when we predict international bond risk premia using only the global LEI4, the ROS 2 statistics range between 0.85% and 24%. The average ROS 2 statistics for the US, UK, JP, and GM are respectively 22.2%, 22.7%, 1.05%, and 8.3%. These results contrast substantially to the evidence from the LEI regressions. We also use the Clark and West (2007) MSPE-adjusted statistics to assess the signi cance of the better out-of-sample forecasting performance of LEI4, the results suggest that the ROS 2 statistics are consistently signi cant at the 5% level. [Insert Figure 3 about Here] To provide a visual impression of the consistency of the LEI4 s predictive ability over time, Figure 3 presents time-series plots of the di erences between the cumulative square prediction error (CSPE) for the historical average benchmark and the predictive model based on the LEI4. When the curve in each panel of Figure 3 increases, the LEI4 predictive model outperforms the historical average, while the opposite holds when the curve decreases. The plots conveniently illustrate whether a predictive model beat competitors for any particular out-of-sample period by redrawing the horizontal zero line to correspond to the start of the out-of-sample period. The gure suggests that the LEI4 generally performs well in the US, UK, and GM bond markets. It is noteworthy that the LEI4 perform extremely well during the nancial crisis of 2007-2008. The evidence is consistent with those from the stock market, as reported in Huang and Zhou (2012). These results provide evidence on the consistency of the out-of-sample predictive power of the LEI4. In contrast, the forecasting performance of the LEI4 in the JP bond market appears unstable. 14

Furthermore, Panel B of Table 3 presents the utility gains of the LEI4. In portfolio management, we set = 3. The evidence indicates that the LEI4 can generate systematic economic value. The average utility gains are respectively 0.58%, 1.0%, 0.10%, and 0.14%. Though the LEI4 does not outperform the JP LEI when predicting Japanese bond risk premia, we nd that the economic value of LEI4 is higher than the economic value of the JP LEI. These results are largely robust to the risk-averse parameter. If we set the values of the relative risk-aversion coe cient to be 1 or 5, the conclusions are unchanged. As such, it is safe to say that the LEI4 is statistically and economically signi cant in the prediction of international excess bond returns. Though the LEI4 generates high ROS 2 statistics, we nd the economic value of the LEI4 is only comparable to that from the stock market (see, for example, Rapach, Strauss, and Zhou, 2009). Our results are consistent with those reported in Zhu (2013) and Goh, Jiang, Tu, and Zhou (2013). The economic value assessment is interesting in understanding why bond risk premia are much more predictable than excess stock returns in terms of ROS 2 statistics. As emphasized by Goh, Jiang, Tu, and Zhou (2013), although the bond market is much more predictable than the stock market in terms of out-of-sample ROS 2 statistics, the economic value from predicting stock returns and bond returns are comparable, suggesting across nancial markets, the economic value of forecasting is likely to be the same due to probably across market arbitrage or intermarket e ciency. More interestingly, our results indicate that the global LEI4 is usually a better predictor of international bond risk premia than the country-speci c LEIs. Indeed, Ilmanen (1995) nd that some global common factors are better predictors of international excess bond returns than local instruments. In the stock market, Harvey (1991) nds that global factors outperform local factors in the forecasting exercise. Our results are consistent with those of Ilmanen (1995) and Harvey (1991). Our ndings may re ect the integrated nature of international bond markets. Naturally, bonk risk premia are driven by some global factors rather than local factors in an integrated market. 15

Given the predictive ability of the LEI4, we conduct a model comparison. Specifically, we compare the out-of-sample forecasting performance of speci cation (6) that includes the LEI4 and local CP factor to the benchmark model (5) that includes just the country-speci c Cochrane-Piazzesi factor. This comparison allows us to assess the incremental predictive power of the global factor above and beyond the predictive power in the Cochrane-Piazzesi factor. [Insert Table 4 about Here] Table 4 reports the results from out-of-sample forecast comparisons of log excess bond returns. Panel A presents the forecasting results of the CP-factor only model. Consistent with Ludvigson and Ng (2009, 2010), Zhu (2013) and Goh, Jiang, Tu, and Zhou (2013), we nd that the CP factor does strongly predict bond risk premia, with the ROS 2 statistics ranging between 22.1% and 31.7%. Statistically, all R2 OS statistics are signi cant at the 5% level. Panel B reports the out-of-sample forecasting results of the two-factor model (the LEI4 and the local CP factor). The results show that the twofactor model performs very well. The ROS 2 statistics are large, ranging between 24.1% and 45.8%. All ROS 2 statistics are statistically signi cant at the 1% level. Indeed, the two-factor model outperforms consistently the CP-factor only model in terms of ROS 2 statistic. To test the signi cance of the better performance of the two-factor model, we conduct the Clark-West (2007) test. The testing results, indicated in Panel B, suggest that the better forecasting performance of the two-factor model are consistently signi cant at the 5% level. Overall, the ndings seem to suggest that the LEI4 contains important information about future bond risk premia, above and beyond that contained in the Cochrane-Piazzesi factor. In addition to statistical signi cance, we also study whether the observed predictability patterns are economically signi cant. Table 4 reports the economic gains of the two-factor model and the CP-factor only model. For the United Kingdom, Japan, and Germany, our empirical analysis reveals that the two-factor model delivers higher 16

utility gains than the CP-factor only model, suggesting the economic signi cance of the LEI4. For the US, the economic value of the two-factor model are only comparable to that of the CP-factor only model. [Insert Table 5 about Here] To further shed light on the predictive power of the CP factor and LEI4, we regress the LEI4 on the four country-speci c factors. Table 5 reports the empirical results. It is evident that the CP factor and LEI4 are largely orthogonal. Hence, it is not surprising that the LEI4 contains additional information for predicting international bond risk premia, above and beyond that contained in the Cochrane-Piazzesi. 4 Robustness Checks This section checks the robustness of the baseline results. In light of the predictability of international excess bond returns, a natural concern is "data-snooping bias". We address this concern from two perspectives: (1) we test whether our results are robust to subsamples; (2) we conduct the 3- and 6-month-ahead forecasting analysis. 4.1 Subsample Analysis This section conducts a subperiod analysis. Speci cally, the full sample period is 1975:01-2011:12 for US and 1985:01-2011:12 for UK, JP, and GM. Statistical and economic performance measures are calculated for the out-of-sample period 2000:01-2011:12 assuming = 3 in line with the value used in previous studies (see, for example, Rapach, Strauss, and Zhou, 2009, 2013; Zhu, 2013). The out-of-sample forecasting procedure involves fully recursive parameter estimation using data only through time t for forecasting at time t + 1. [Insert Table 6 about Here] 17

Panel A of Table 6 reports R 2 OS statistics comparing the historical average and the predictive regression based on the country-speci c LEI. We nd that the countryspeci c LEIs cannot predict international excess bond returns. Indeed, we generally nd negative R 2 OS statistics, which are statistically signi cant at the 5% level. Only two R 2 OS statistics are positive. However, these positive R2 OS insigni cant. statistics are statistically Table 6 also reports the economic value of the country-speci c LEIs. It seems that the country-speci c LEIs do not deliver meaningful economic value. Overall, our empirical analysis reveals that the LEIs have no power in predicting bond risk premia. Panel B of Table 6 reports the out-of-sample forecasting results for the predictive regression based on the LEI4. In sharp contrast with the results presented in Panel A, we nd that the LEI4 does predict excess bond returns. Indeed, all R 2 OS statistics are signi cantly positive when forecasting excess bond returns in the US, UK, and GM bond markets. Though the R 2 OS statistics are negative in the JP bond market, they are statistically insigni cant. The economic value analysis provides further evidence on the predictive power of the LEI4. The average utility gain of the LEI4 is respectively 0.41%, 1.38%, and 0.66% in US, UK, and GM. Our empirical analysis therefore suggests that the LEI4 has predictive power on international excess bond returns. There is a natural concern about the additional predictive power of the LEI4 since the predictive ability of the CP factor has been well-documented. To provide insights on this issue, we conduct a model comparison. Speci cally, we compare the out-ofsample forecasting performance of speci cation (6) based on the LEI4 and CP factor to the benchmark model (5) based on the Cochrane-Piazzesi factor. This analysis allows us to assess the incremental predictive power of the LEI4 above and beyond the predictive power in the Cochrane-Piazzesi factor. [Insert Table 7 about Here] Table 7 shows the results of the model comparison. Panel A presents the outof-sample forecasting results of the predictive model based on the CP factor. We nd 18

that the CP factor can predictive excess bond returns in US, UK, and GM. In addition, the CP factor deliver systematic economic values in these markets. Though the CP factor delivers negative ROS 2 statistics in the Japanese bond market, the R2 OS statistics are statistically insigni cant. Roughly speaking, our analysis provides evidence on the predictive power of the CP factor. Given the predictive power of the CP factor, Panel B reports the forecasting results of the predictive model based on both the LEI4 and the CP factor. It reveals that in 16 out of 16 forecasts, the two-factor model consistently beats the CP-factor only model in terms of ROS 2 statistics, suggesting that the LEI4 has incremental forecasting power for predicting international excess bond returns. More importantly, the Clark-West testing analysis indicates that the better forecasting performance of the two-factor model is consistently statistically signi cant at the 5% level. The subsample results are broadly consistent with the full sample results, thus providing further evidence on the key implications of our analysis: (1) the predictive ability of local LEIs varies across markets; (2) the global common LEI4 factor can consistently predict international bond risk premia, suggesting that a large fraction of international bond risk premia may be driven by some global factors; (3) the predictive power of the LEI4 is above and beyond that contained in the CP factor. 4.2 6-Month-Ahead Forecasting Results Up to now, we consider the one-month-ahead forecasts. It leaves open to the question of the forecasting performance at longer horizons. It is well established that long-horizon forecasting exercises may be more informative than their shorter-horizon counterparts (see, for example, Lo and MacKinlay, 1989). To shed light on the robustness of the forecasting results reported in Table 3, we conduct the 6-month-ahead forecasting analysis. The full sample period for the 6-month-ahead forecasting exercise is respectively 1962:01 to 2011:12 for US, from 1970:01 to 2011:12 for UK, from 1980:01 to 2011:12 for JP, and from 1975:01 to 2011:12 for GM. Statistical and economic performance 19

measures are calculated for the out-of-sample period 1990:01-2011:12 assuming = 3 in line with the value used in previous studies (see, for example, Rapach, Strauss, and Zhou, 2009, 2013, Zhu, 2013). The out-of-sample forecasting procedure involves fully recursive parameter estimation using data only through time t for forecasting at time t + 1. [Insert Table 8 about Here] Table 8 reports the 6-month-ahead forecasting results. In contrast to the 1-monthahead results, we nd that at the 6-month horizon, the country-speci c LEI generally deliver positive R 2 OS statistics. Indeed, the US/GM LEI can signi cantly predict US/GM bond risk premia. The Japanese bond market provides mixing results: While the JP LEI delivers signi cantly negative R 2 OS bond returns of the 2- and 3-year Treasury bonds, the R 2 OS statistics when predicting the excess statistics are signi cantly positive when forecasting the bond risk premia of the 4- and 5-year discount bonds. In UK, the R 2 OS insigni cant. statistics are consistently positive. However, they are statistically While the country-speci c LEIs appear to weakly predict international bond risk premia in terms of R 2 OS statistics, the economic value analysis suggests that the economic value of the country-speci c LEIs are usually small. In summary, we conclude that the country-speci c LEIs may contain some information about future bond risk premia, however, the predictive power of these LEIs are very weak. Panel B of Table 8 reports the 6-month-ahead forecasting results for the predictive model based on the global common LEI4 factor. The LEI4 consistently delivers statistically signi cant R 2 OS statistics. More importantly, 14 out of the 16 excess bond return forecasts are positive, suggesting that the global LEI4 generally predict international bond risk premia. In addition, our economic value analysis reveals that the LEI4 deliver systematic economic value. Indeed, all utility gains are positive, though some gains are economically small. 20

We also conduct the 3-month-ahead forecasting exercise. For saving space, we do not report the results here. Indeed, the 3-month-ahead forecasting results are generally quantitatively more favorable to the predictive power of the LEI4 than the 6-monthahead forecasting results are. In addition, we also conduct the 6-month-ahead forecasting exercise using the subsample, the conclusions are invariant to the subsample analysis. 5 LEI4 and Macro Factors in Bond Risk Premia Ludvigson and Ng (2009, 2010) show that the movements in bond risk premia are intimately related to cyclical macroeconomic activity. Speci cally, Ludvigson and Ng extract a few principle components from a large set of macroeconomic variables and reveal that these principle components have predictive power for future bond risk premia. The important work of Ludvigson and Ng provides direct evidence on rational asset pricing models, which suggest a link between business cycle activity in macro variables and risk premia in bond markets. Since the LEI4 is a leading indicator for aggregate business cycle activity, one may argue that the predictive power of the LEI4 overlaps the information contained in principle components extracted from a large set of macro indicators. To provide insight on the issue of whether the LEI4 has forecasting power for future excess bond return, above and beyond that contained in a large set of macro variables, this section compare the forecasting power of the LEI4 with the predictive ability of the Ludvigson and Ng regression. The principle components are extracted from a balanced panel of 132 monthly US economic series, each spanning the period 1964:01 2011:12. 6 originally used in Stock and Watson (2002a, 2002b, 2005). The economic series are The series are selected to provide a bird s eye view on business cycle activity because they include broad categories of macroeconomic time series. Ludvigson and Ng (2009) provide a detailed description of the data series and their sources. 6 We thank Sydney Ludvigson for updating the data set and make the data available at http://www.econ.nyu.edu/user/ludvigsons/. 21

Ludvigson and Ng (2009, 2010) use a subset of principle components to predict excess bond returns out-of-sample. We follow their tradition and use a ve-factor subset F! 5 t = ( ^F 3 1t, ^F 1t, ^F3t, ^F4t, ^F8t ) to predict future bond risk premia. Speci cally, the Ludvigson and Ng regression is rx (n) t+1=12 = + 0! F 5 t + " t+1=12. We compare the results from the Ludvigson and Ng regression with the forecasting regressions with both the LEI4 and! F 5 t factors. 7 To avoid look-ahead bias, we recursively extract! F 5 t in the out-of-sample analysis, using only information up to the month of forecast made. For predicting excess bond returns in the UK, JP, and GM! bond markets using macro factors, we also use the information content of F 5 t extracted from the US macro variables since! F 5 t may capture some common uctuations in world business cycle (see, for example, Kose, Otrok, and Whiteman 2003, 2008). In addition, we also include local industrial production growth rate and in ation rate in each market to predict excess bond returns in the corresponding bond market. 8 local factors are used to capture country-speci c uctuations in economic activity. 9 The data samples respectively range from 1970:01 to 2011:12 for UK, from 1980:01 to 2011:12 for JP, and from 1975:01 to 2011:12 for GM. The out-of-sample period is consistently 1990:01-2011:12. The [Insert Table 10 about Here] The forecasting results are reported in Table 10. Panel A of Table 10 presents the forecasting performance of the Ludvigson and Ng regression. It shows that macro factors extracted from a large set of macro indicators have predictive power for international excess bond returns. These results are consistent with those presented in 7 For US, the forecasting results of the LEI4-only regression are very similar to those reported in Panel B of Table 4. For UK, JP, and GM, the forecasting results of the LEI4-only regression are all the same as those reported in Panel B of Table 4 since the samples are all the same in these markets. 8 To keep notation as simple as possible, we still use! F 5 t to denote the set of predictors. 9 Our conclusions are robust to the exclusion of US factors or local factors. 22

Ludvigson and Ng (2009, 2010). The economic value analysis further suggests that macroeconomic factors generally deliver positive economic value, suggesting the importance of macro factors in predicting excess bond returns. Panel B of Table 10 presents the results of the forecasting regression with both the LEI4 and F! 5 t factors. The results indicate that the regression with both the LEI4 and F! 5 t factors consistently beat the Ludvigson and Ng regression in terms of out-ofsample R 2. The Clark and West statistics further suggest that the better forecasting performance of the regression with both the LEI4 and F! 5 t factors is generally signi cant at the 5% level. In addition, the regression with both the LEI4 and F! 5 t factors usually deliver higher utility gains. These results are largely robust to the subsample analysis over the period 1975:01-2011:12 for US and 1985:01-2011:12 for UK, JP, and GM. These results are also largely robust to the 3- and 6-month-ahead forecasting exercise. Overall, our empirical analysis suggests that the LEI4 has predictive power for international excess bond returns, above and beyond the predictive power contained in principle components extracted from a large set of macro factors. 6 Conclusions This paper investigates an important theoretical and practical question as to what factors that drive the international bond risk premia. We contribute to the literature on bond time-varying risk premia by showing that the global leading economic indicator, which measures the aggregate state of the economy, have important predictive power for international excess bond returns. Interestingly, country-speci c leading economic indicators provide mixed results for predicting bond risk premia. Our results seem to suggest that international bond markets are highly integrated, and the same global factor(s) may largely be responsible for the dynamics of bond risk premia. While statistical signi cance does not mechanically imply economic signi cance in the out-of-sample exercise, we conduct the economic value analysis to examine the economic signi cance of the global leading economic indicator. Speci cally, we assess 23

the economic value of the predictive power of the LEI4 by exploring the utility gains accrued to investors who use the predictive model based on the LEI4 to forecast bond risk premia. Our economic value analysis con rms the statistical evidence, suggesting that the global LEI4 has economically and statistically meaningful forecasting power for predicting international bond risk premia. We emphasize two aspects of our ndings. First, we nd that a global aggregate measure of the state of the economy can predict international bond risk. This is important because economic theories generally imply that risk-averse economic agents should be compensated for bearing macroeconomic risks. The predictive power of the LEI4 is consistent with the economic theories in a global integrated bond market. Second, the predictive power of the LEI4 is above and beyond the information contained in the famous Cochrane-Piazzesi (2005) forward rate predictor and Ludvigson and Ng s (2009, 2010) principle component predictors extracted from a large set of macro variables. For future research, it will be of interest to investigate the role of the global leading economic indicator in term structure models. References [1] Almeida, C., J. J. Gravelineb, and S. Joslin. 2011. Do Interest Rate Options Contain Information about Excess Returns? Journal of Econometrics 164, 35-44. [2] Ang, A., M. Piazzesi, and M. Wei. 2006. What Does the Yield Curve Tell Us about GDP Growth? Journal of Econometrics 131, 359-403. [3] Baker, M., R. Greenwood, and J. Wurgler. 2003. The Maturity of Debt Issues and Predictable Variation in Bond Returns. Journal of Financial Economics 70, 261 291. [4] Bansal, R., and A. Yaron. 2004. Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles. Journal of Finance 59, 1481 1509. 24

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