Risk and Expectations in Exchange Rates: Evidence from Cross-Country Yield Curves*

Transcription

1 Risk and Expectations in Exchange Rates: Evidence from Cross-Country Yield Curves* Yu-chin Chen Byunghoon Nam Kwok Ping Tsang University of Washington University of Washington Virginia Tech June 2016 Abstract. This paper examines the empirical relevance of expectations about future macroeconomic conditions and perceived risk in determining currency movements. While the theoretical distinction and policy implications between risk and expectations is wellunderstood, empirical assessments of their relative importance have been less conclusive. To decompose the two, we rely on the observation that the term structure of interest rates contains information about both expected future policy paths and time-varying term premiums. Postulating that term risk in bond markets is also priced in foreign exchange markets, we aim to connect expectations and risk premiums extracted from bond yields across countries to currency movements. Using monthly data between 1995 and 2016 for eight major country pairs, we construct measures of term premiums under several well-known term structure models, including augmented Nelson-Siegel(1987) model, affine Gaussian dynamic model, and the Cochrane and Piazzesi (2005) model. We first find strong evidence of structural breaks around 2008, and see that overall, both expectations (about future yields or macroeconomic conditions) and risk premiums can explain up to 30% 40% of the variations in quarterly currency movements individually. Comparing the two, we find that expectations play a stronger and more consistent role over the full sample period, while risk measures pick up their significance post Finally, we construct a joint macro-yield model for the exchange rate and demonstrate the importance of capturing both time-varying risk and expectations about future macroeconomic conditions in modeling exchange rate dynamics. J.E.L. Codes: E43, F31, G12, G15 Keywords: Exchange Rate, Yield curve, Macro Fundamentals, Term Premiums * First draft: August We thank Charles Nelson, Richard Startz, and conference participants at the Asian Meeting of the Econometric Society, for helpful comments. This work is partly undertaken while Chen and Tsang were visiting scholars at Academia Sinica and Hong Kong Institute of Monetary Research respectively, whose support and hospitality are gratefully acknowledged. Chen: Department of Economics, University of Washington, Box , Seattle, WA 98195; yuchin@washington.edu. Nam: Department of Economics, University of Washington, Box , Seattle, WA 98195; nambh@washington.edu. Tsang: Department of Economics, Virginia Tech, Box 0316, Blacksburg, VA, 24061; byront@vt.edu.

2 1 Introduction This paper proposes to model nominal exchange rates by incorporating both macroeconomic determinants and latent financial risks, bridging the gap between two important strands of recent research. First, against decades of negative findings in testing exchange rate models, recent work by Engel, Mark and West (2007), Molodtsova and Papell (2009) among others, shows that models in which monetary policy follows an explicit Taylor (1993) interest rate rule deliver improved empirical performance, both in in-sample fits and in outof-sample forecasts. 1 These papers emphasize the importance of expectations, in particular about future macroeconomic dynamics, and argue that the nominal exchange rate should be viewed as an asset price embodying the net present value of its expected future fundamentals. 2 While generally recognizing the presence of risk, this literature largely ignores risk in empirical testing and renders it an unobservable. 3 On the finance side, research shows that systematic sources of financial risk, as captured by latent factors, drive excess currency returns both across currency portfolios and over time. 4 These papers firmly establish the role of risk but are silent on the role of macroeconomic conditions, including monetary policy actions, in determining exchange rate. They thus fall short on capturing the potential feedback between macroeconomic forces, expectations formation, and perceived risk in exchange rate dynamics. This paper argues that the macro and the finance approaches should be combined, and proposes a joint framework to capture intuition from both bodies of literature by incorporating information from the term structures of interest rates. We present an open economy model where central banks follow a Taylor-type interest rate rule that stabilizes expected inflation, output gap, and the real exchange rate. 5 1 This approach works well for modeling exchange rates of countries that have credible inflation control policies. 2 Since the Taylor-rule fundamentals measures of inflation and output gap affect expectations about future monetary policy actions, changes in these variables induce nominal exchange rate responses. 3 Engel, Mark, and West (2007), for example, establish a link between exchange rates and fundamentals in a present value framework. After explicitly recognizing the possibility that risk premiums may be important in explaining exchange rates, they do not explore that avenue in this paper, but treat it as an unobserved fundamental. Molodstova and Papell (2009), show that Taylor rule fundamentals (interest rates, inflation rates, output gaps and the real exchange rate) forecast better than the commonly used interest rate fundamentals, monetary fundamentals and PPP fundamentals. Again, they explain exchange rate using only observed fundamentals and do not account for risk premium. This is an obvious shortcoming in modeling short-run exchange rate dynamics. Faust and Rogers (2003) for instance argue that monetary policy accounts for very little of the exchange rate volatility. 4 See Lustig et al. (2011), and Farhi et al. (2009), and references therein for the connection between risk factors and currency portfolio returns. Bekaert et al. (2007), for instance, point out that risk factors driving the premiums in the term structure of interest rates may also drive the risk premium in currency returns. In addition, Clarida and Taylor (1997) uses the term structure of forward exchange premiums to forecast spot rates. de los Rios (2009) and Krippner (2006) connect the interest rate term structure factors and exchange rate behavior. These papers do not examine the role of macroeconomic fundamentals or monetary policy. 5 Note that following Clarida, Gali, and Gertler (1999), the incorporation of the exchange rate term to an otherwise standard Taylor rule has become commonplace in recent literature, especially for modeling The 1

3 international asset market efficiency condition - the risk-adjusted uncovered interest rate parity (UIP) - implies that nominal exchange rate is the net present value of expected future paths of interest differentials and risk premiums between the country pair. This framework establishes a direct link between the exchange rate and its current and expected future macroeconomic fundamentals; it also allows country-specific risk premiums over different horizons to affect exchange rate dynamics. Since exchange rate in this formulation relies more on expectations about the future than on current fundamentals, properly measuring expectations and time-varying risk becomes especially important in empirical testing. Previous papers largely fail to address this appropriately. 6 We propose to use information from cross-country yield curves to separately identify and test the importance of expectations about future macroeconomic conditions and systematic risk in driving currency behavior. We also combine the latent yield curve factors with monetary policy targets (unemployment and inflation rates) to study their dynamic interactions with bilateral exchange rate changes. 7 The joint macro-finance strategy has proven fruitful in modeling other financial assets such as the yield curves themselves. 8 As stated in Diebold, Piazzesi and Rudebusch (2005), the joint approach captures both the macroeconomic perspective that the short rate is a monetary policy instrument used to stabilize the economy, and the financial perspective that yields of all maturities are risk-adjusted averages of expected future short rates. exchange rate model is a natural extension of this idea into the international context. First, the no-arbitrage condition for international asset markets explicitly links exchange rate dynamics to cross-country yield differences at the corresponding maturities and a time-varying currency risk premium. Yields at different maturities - the shape of the yield curve - are in turn determined by the expected future path of short rates and perceived future uncertainty (the term premiums). The link with the macroeconomy comes from noticing that the short rates are monetary policy instruments which react to macroeconomic fundamentals. Longer yields therefore contain market expectations about future macroeconomic conditions. the other hand, term premiums in the yield curve measure the market pricing of systematic monetary policy in non-us countries. See, for example, Engel and West (2006) and Molodtsova and Papell (2009). 6 Previous literature often ignores risk or makes overly simplistic assumptions about these expectations, such by using simple VAR forecasts of macro fundamentals as proxies for expectations. For instance, Engel and West (2006) and Mark (1995) fit VARs to construct forecasts of the present value expression. Engel, Mark and West (2007) note that the VAR forecasts may be a poor measure of actual market expectations and use surveyed expectations of market forecasters as an alternative. See discussion in Chen and Tsang (2013). 7 Chen and Tsang (2013) show that the Nelson-Siegel factors between two counties can help predict movements in their exchange rates and excess returns. It does not, however, consider the dynamic interactions between the factors and macroeconomic conditions. 8 Ang and Piazzesi (2003), among others, illustrate that a joint macro-finance modeling strategy provides the most comprehensive description of the term structure of interest rates. Our On 2

4 risk of various origins over different future horizons. 9 Under the reasonable assumption that a small number of underlying risk factors affect all asset prices, currency risk premium would then be correlated with the term premiums across countries. From a theoretical point of view, the yield curves thus serve as a natural measure to both the macro- and the financeaspect of the exchange rates. From a practical standpoint, the shape and movements of the yield curves have long been used to provide continuous readings of market expectations; they are a common indicator for central banks to receive timely feedback to their policy actions. Recent empirical literature, such as Diebold, Rudebusch and Aruoba (2006), also demonstrates strong dynamic interactions between the macroeconomy and the yield curves. These characteristics suggest that empirically, the yield curves are also a robust candidate for capturing the two asset price attributes of nominal exchange rates: expectations on future macroeconomic conditions and perceived time-varying risks. For our empirical analyses, we look at monthly exchange rate changes for eight country pairs - Australia, Canada, Denmark, Japan, New Zealand, Sweden, Switzerland, and the UK relative to the US - over the period from January 1995 to March each country pair, we extract three Nelson-Siegel (Nelson and Siegel, 1987) factors from the zero-coupon yield differences between them, using yield data with maturities ranging from three months to ten years. For These three latent risk factors, which we refer to as the relative level, relative slope, and relative curvature, capture movements at the long, short, and medium part of the relative yield curves between the two countries. The Nelson-Siegel factors are well known to provide excellent empirical fit for the yield curves, providing a succinct summary of both expectations about future macroeconomic dynamics as well as the systematic sources of risk that may underlie the pricing of different financial assets. Taking into account the possibility of structural breaks, we first confirm results established in Chen and Tsang (2013) that these yield curve factors indeed have robust explanatory power for subsequent exchange rate behavior. We then proceed to examine the specific role of risk versus expectations in these results. In order to decompose the yield curves into expectations and risk, we employ four alternative methods based on different concepts of terms structure modeling that are wellknown in the literature. These include the Nelson-Siegel latent factor model, the Nelson- Siegel latent factor model which allows interaction with macro fundamentals as discussed in Diebold, Rudebusch and Aruoba (2006), Ang and Piazzesi (2003) s discrete-time affine Gaus- 9 Kim and Orphanides (2007) and Wright (2011), for example, provide a comprehensive discussion of the bond market term premium, covering both systematic risks associated with macroeconomic conditions, variations in investors risk-aversion over time, as well as liquidity considerations and geopolitical risky events. 10 We present results based on the dollar cross rates, though the qualitative conclusions extend to other pair-wise combinations of currencies. 3

5 sian term structure model and also the Cochrane and Piazzesi (2005) approach. 11 Based on these alternative and admittedly all incomplete measures of expectation and risk, we demonstrate that both expectations and risk contained in the yield curves act as important determinants for quarterly exchange rate changes, providing empirical support for the present value models of exchange rate determination. This also provides support for the view that a same set of country-specific time-varying latent risks is priced into both the bond and the currency markets. We view this result as a clear indication that neither the macro nor the finance (risk) side of exchange rate determination should be ignored. Given the above findings, we investigate which of expectations and risk play ore important role in determining exchange rate changes. We test for the joint significance of each determinant by the Wald test and compare the portion explained by each determinant by the Hodrick s partial R 2 (Hodrick, 1992). Finally, we propose a joint macro-finance model to capture the joint dynamics of exchange rates, the macroeconomy, and the relative yield curve factors which embody both risk and expectations. yield curve factors and macro fundamentals. We also examine the joint significance and explanatory power of Since our short sample size and overlapping observations preclude accurate estimates of long-horizon regressions, we evaluate the performance of our macro-finance model in predicting exchange rate at various horizons by way of the rolling iterated VAR approach, as in Campbell (1991), Hodrick (1992) and Lettau and Ludvigson (2001). 12 We iterate the full-sample estimated VAR(1) to generate exchange rate predictions at horizons beyond one month, and compare the mean squared prediction error of our model to that of a random walk. Our main results are as follows: 1) empirical exchange rate equations based on only macro-fundamentals or only latent risk factors can miss out on the two crucial elements that drive currency dynamics: risk and expectations; 2) decomposing the yield curves into expectations for future macrodynamics versus term premiums, we show that both are important and can explain up to 30%-40% of the variations in subsequent excess currency returns and quarterly exchange rate changes individually; 3) expectations play a stronger and more consistent role over the full sample period, while risk measures pick up their significance 11 As an example for the Nelson-Siegel model augmented with macro variables, we use an estimated VAR that allows for dynamic interactions between macro fundamentals and the yield curve factors, to construct measures of expected yields, which is average of expected short yields, for different maturities for each country. We then take the difference between the fitted yields from the model and the expected yields to separate out the time-varying bond term premiums. The relative expected yields and the relative term premiums are defined as the difference in expected yields and term premiums between each country-pair. 12 While it is more common in the macro-exchange rate literature to compare models using out-of-sample forecasts (Meese and Rogoff 1983), we adopt this iterated VAR procedure used in recent finance literature to evaluate long horizon predictability. Out-of-sample forecast evaluation can be an unnecessarily stringent test to impose upon a model. For both theoretical and econometric reasons, it is not the most appropriate test for the validity of a model (see Engel, Mark and West 2007). 4

6 post-2008; 4) yield factors explain currency movement more than macro variables before 2008, and macro variables also becomes important in explaining the variation in exchange rates after 2008; 5) even though the yield curves contain information about future macro dynamics, macro fundamentals themselves are still important in exchange rate modeling. Their dynamics should be jointly modeled with the yield curve and currency behavior; 6) our macro-finance model delivers improved performance over the random walk, with the yield curve factors playing a bigger role in the shorter-term, and the macro fundamentals becoming increasingly relevant in longer horizons such as a year. Overall, these findings support the view that exchange rates should be modeled using a joint macro-finance framework. 2 Theoretical Framework 2.1 Exchange Rate Determination in a Present Value Framework We present the basic setup of a Taylor-rule based exchange rate model below while emphasizing our proposal for addressing the issues previous papers tend to ignore. Consider a standard two-country model where the home country sets its interest rate, i t, and the foreign country sets a corresponding i t. we designate the United States as the foreign country. To be consistent with our empirical results below, We assume that the central bank follows a standard Taylor rule, reacting to inflation and output (or unemployment) deviations from their target levels, but the home country targets the real exchange rate, or purchasing power parity, in addition. This captures the notion that central banks often raise interest rates when their currency depreciates, as discussed in Clarida, Gali, and Gertler (1999) and previous work. 13 The monetary policy rules can be expressed as: i t = µ t + β y ỹ t + β π π e t + δq t + u t (1) i US t = µ US t + βy US ỹt US + βπ US π US,e t + u US t where ỹ t is the output gap, πt e is the expected inflation, and q t (= s t (p t p US t )) is the real exchange rate, defined as the nominal exchange rate, s t, adjusted by the CPI-price level difference between home and abroad, p t p US t. µ t absorbs the inflation and output targets and the equilibrium real interest rate, and the stochastic shock u t represents policy errors, which we assume to be white noise. The corresponding foreign or US variables are denoted with superscript U S and all variables except for the interest rates in these equations are in logged form. For notation simplicity, we assume the home and US central banks to have 13 It is common in the literature to assume that the Fed reacts only to inflation and output gap, yet other central banks put a small weight on the real exchange rate. See Clarida, Gali, and Gertler (1999), Engel, West, and Mark (2007), and Molodtsova and Papell (2009), among many others. 5

7 the same policy weights, and that β y = βy US time-invariant. > 0, δ > 0, β π = β US π > 1, and µ t and µ US t Under rational expectations, efficient market condition equates cross-border interest rate differentials of maturity m, i R,m t, with the expected rate of home currency depreciation and the currency risk premium over the same horizon. 14 This is the risk-adjusted uncovered interest rate parity condition (UIP): i R,m t = i m t i m,us t = E t s t+m + ρ m t, m (2) Here s t+m s t+m s t, and ρ m t denotes the risk premium associated with holding home relative to US investment between time t and t + m. A key assumption we make (and test) is that ρ m t depends on the general latent risk factors associated with asset-holding within each country over the same period, and that these latent risks are also embedded in the term premiums at home and in the US. Approximating the policy rules, eqs.(1), with m = 1, we can express the exchange rate in the following differenced expectation equation by combining them with eq.(2): s t = γf T R t + κρ 1 t + ψe t s t+1 + v t (3) where ft T R = [p t p US t, ỹ t ỹt US, πt e π US,e t ] ; v t is a function of policy error shocks u t and u US t ; and coefficient vectors, γ, κ, and ψ, are functions of structural parameters defined above. 15 Iterating the equation forward, the Taylor-rule based model can deliver a net present value (NPV) equation where exchange rate is determined by the current and the expected future values of cross-country differences in macro fundamentals and risks: s t = λ j=0 ψ j E t (f T R t+j I t ) + ζ are ψ j E t (ρ 1 t+j I t ) + ε t (4) where ε t incorporates shocks, such as that to the currency risk (ζ t ), and is assumed to be j=0 uncorrelated with the macro and bond risk variables. This formulation shows that the exchange rate depends on both expected future macro fundamentals and differences in the perceived risks between the two countries over future horizons. From this standard present value expression, we deviate from previous literature by making an attempt to find proxies for both terms. We derive our exchange rate estimation equations by emphasizing the use of latent factors extracted from the yield curves to proxy the two present-value terms on the right-hand side of eq.(4). We show in the 14 By assuming rational expectations, we do not explore role of systematic expectations errors in ρ. 15 Since these derivations are by now standard, we do not provide detailed expressions here but refer readers to e.g. Engel and West (2005) for more details. 6

8 next subsection that the Taylor-rule fundamentals are exactly the macroeconomic indicators the yield curves appear to embody information for, and of course, the term premiums θ t are by definition a component of each country s yield curves. Exploiting these observations, we do not need to make explicitly assumptions about the statistical processes driving the Taylor-rule macro fundamentals to estimate eq.(4), as previous papers tend to do. Instead, we use the information embedded in the yield curves and allow macro variables to interact dynamically with the latent yield curve factors. 16 Since nominal exchange rate is best approximated by a unit root process empirically, we focus our analyses on exchange rate change, s t+m, as well as excess currency returns, which we define as: XR t+m = i m t i m,us t s t+m (= ρ m t ) (5) Note that XR measures the excess return from home investment. 2.2 The Yield Curve: Proxy for both Expectation and Risk The yield curve or the term structure of interest rates describes the relationship between yields and their time to maturity. Traditional models of the yield curve posit that the shape of the yield curve is determined by the expected future paths of interest rates and perceived future uncertainty. According to the expectations hypothesis (EH), a long yield of maturity m can be written as the average of the current one-period yield and the expected one-period yields for the coming m 1 periods, plus a term premium: i m t 1 m m 1 j=0 E t [ i 1 t+j ] + θ m t (6) where θt m represents the term premium perceived at t associated with holding a long bond until t + m. So, the yield curve, which consists of short to long yields, provides information about both expected future paths of short-term interest rates and term premiums. In this subsection, we discuss how the yield curve can proxy for the first and the second summation in eq.(4) Capturing the Expectations about Future Macro Fundamentals A large body of research over the past decades has convincingly demonstrated that the yield curve contains information about expected future economic conditions such as output 16 The use of the yield curves to proxy expectations about future macro dynamics and risks makes our model differ from the traditional approach in international finance, which commonly assume that the macrofundamentals evolve according to a univariate VAR (e.g. Mark (1995) or Engel and West (2005), among others). See Chen and Tsang (2013) for a more detailed discussions. 7

9 gap and inflation. The recent macro-finance yield curve literature connects the observation that the short rate is a monetary policy instrument with the idea that yields of all maturities are risk-adjusted averages of expected short rates. This structural framework offers deeper insight into the relationship between the yield curve and macroeconomic dynamics. As shown in eq.(6), longer-term yields reflect the expected path of future short-term interest rates, which in turn are set by monetary policy rules, eqs.(1). Theoretically, it is therefore clear that the yield curve reflects market expectations about future macroeconomic fundamentals, the first summation on the right hand side of eq.(4). Two empirical strategies are typically adopted in the literature to test this macrofinance view of the yield curve, and both utilize a small number of factors to summarize the shape of the yield curve, which are typically referred to as level, slope and curvature factors. The first, more atheoretical approach does not provide structural modeling of the macroeconomic fundamentals and the yield curve, but capture their joint dynamics using a general VAR. Ang, Piazzesi and Wei (2006), for example, estimate a VAR model for the US yield curve and GDP growth. By imposing no-arbitrage condition on the yields, they show that the yield curve predicts GDP growth better than an unconstrained regression of GDP growth on the term spread. 17 Another body of studies model the macroeconomic variables structurally. For instance, using a New Keynesian framework, Rudebusch and Wu (2007, 2008) find that the level factor incorporates long-term inflation expectations, and the slope factor captures the central bank s dual mandate of stabilizing the real economy and keeping inflation close to its target. They provide macroeconomic underpinnings for the factors, and show that when agents perceive an increase in the long-run inflation target, the level factor will rise and the whole yield curve will shift up. They model the slope factor as behaving like a Taylor-rule, reacting to the output gap and inflation. When the central bank tightens monetary policy, the slope factor rises, forecasting lower growth in the future. 18 The above body of literature demonstrates the dynamic connection between latent yield curve factors and macroeconomic indicators both theoretically and empirically, thereby justifying their potential usefulness for proxying the expectated future paths of macro fundamentals. Since exchange rate fundamentals are in cross-country differences, we propose to use the relative 17 More specifically, they find that the term spread (the slope factor) and the short rate (the sum of level and slope factor) outperform a simple AR(1) model in forecasting GDP growth 4 to 12 quarters ahead. Diebold, Rudebusch and Aruoba (2006) took a similar approach using the Nelson-Siegel framework instead of a no-arbitrage affine model. 18 Dewachter and Lyrio (2006) and Bekaert, Cho and Moreno (2010) are two other examples taking the structural approach. Dewachter and Lyrio (2006), using an affine model for the yield curve with macroeconomic variables, find that the level factor reflects agents long run inflation expectation, the slope factor captures the business cycle, and the curvature represents the monetary stance of the central bank. Bekaert, Cho and Moreno (2010) demonstrate that the level factor is mainly moved by changes in the central bank s inflation target, and monetary policy shocks dominate the movements in the slope and curvature factors. 8

10 expected yields, which are the differences in the averages of expected one-period yields for the current and coming m 1 periods across countries, to proxy the first discounted sum in eq.(4): E t i R,m t = E t [ i m t ] i m,us t = 1 m 1 [ ] E t i 1 t+j i 1,US t+j m Linking Term Premiums to Currency Risk Premium The yield curve is linked to the exchange rate not only through the monetary policy and macro expectations channel, but also through the term premiums. j=0 (7) The second summation on the right hand side of eq. (4) shows that the term premiums embedded in the yields may also capture another important determinant of exchange rate dynamics and excess currency return: risk. Empirically, both the currency market and the bond market exhibit significant deviations from their respective risk-neutral efficient market conditions - the UIP and the EH - with the presence of time-varying risk being the leading explanation for both empirical patterns. 19 Assuming that a small number of underlying risk factors affect all asset prices, the bond term premiums would then be correlated with the currency risk premiums. relationship can be shown with simple modification of eq.(2) and eq.(6). Rearranging and iterating forward eq.(2) with m = 1 from t to t + m, the UIP relationship can be modified to: This E t s t+m = i m t i m,us t ρ m t (8) = 1 m 1 [ ] E t i 1 t+j i 1,US t+j 1 m 1 E t ρ 1 t+j m m (9) j=0 Using eq.(6), the cross-border interest rate differentials of maturity m can be expressed as: j=0 i m t i m,us t = 1 m m 1 j=0 [ ] E t i 1 t+j i 1,US t+j + (θ m t θ m,us t ) (10) Substituting eq.(10) into eq.(8) and comparing it with eq.(9), we can say the relative term premiums of maturity m is correlated with the currency risk premiums of the same maturity: ρ m t = (θt m θ m,us t ) 1 m 1 E t ρ 1 t+j (11) m 19 Fama (1984) and subsequent literature documented significant deviations from uncovered interest parity. In the bond markets, the failure of the expectation hypothesis is well-established; Wright (2011) and Rudebusch and Swanson (2012) are recent examples of research that studies how market information about future real and nominal risks are embedded in the bond term premiums. j=0 9

11 The typically upward-sloping yield curves reflect the positive term premiums required to compensate investors for holding bonds of longer maturity. These risks may include systematic inflation, liquidity, and other consumption risks over the maturity of the bond. While previous research has documented these premiums to be substantial and volatile (Campbell and Shiller, 1991; Wright, 2011), there appears to be less consensus on their empirical or structural relationship with the macroeconomy. 20 For our purposes, we use the relative term premiums across countries to measure the difference in the underlying risks perceived by investors over different investment horizons: 21 θ R,m t = θ m t θ m,us t (12) 3 Background Empirics 3.1 Data Description The main data we examine consists of monthly observations from January 1995 to March 2016 for Australia(AU), Canada(CA), Denmark(DK), Japan(JP), New Zealand(NZ), Sweden(SE), Switzerland(CH), the United Kingdom(UK) and the United States(US) of the following series: 1) yield data: zero-coupon bond yields include maturities of 3, 6, 12, 24, 36, 48, 60, 72, 84, 96, 108 and 120 months, where the yields are computed using the curved stripping method. The data set is from Bloomberg. 22 The yields are from the last trading day of each month; 2) macroeconomic data: We obtain headline CPI and unemployment rate from the OECD main economic indicators. Unemployment rate for Switzerland is from Swiss Federal Statistical Office. Inflation rate is defined as 12-month percentage change of the CPI. Unemployment gap is obtained by detrending the unemployment rate using the Hodrick-Prescott filter; 3) exchange rate data: End-of-period monthly exchange rates are obtained from the FRED database. We use the logged exchange rate, measured as the perdollar rates. Exchange rate change from t to t + m is expressed as s t+m = s t+m s t and annualized. Tables 1A-1C report the summary statistic of the data. Considering potential 20 A common view among practitioners is that a drop in term premium, which reduces the spread between short and long rates, is expansionary and predicts an increase in real activity. Bernanke (2006) agrees with this view. However, based on the canonical New Keynesian framework, movements in the term premium do not have such implications. For example, Rudebusch, Sack, and Swanson (2007) point out that only the expected path of short rate matters in the dynamic output Euler equation, and the term premium should not predict changes in real activity in the future. 21 The linkage between the bond and currency premiums is also explored in Bekaert et al (2007), though one of our model further incorporates dynamics of the macroeconomic fundamentals into the expectation formation process. 22 Please refer to Kushnir(2009) for details on the construction of the data. 10

12 structural breaks due to the Great Recession, the sample period is divided by the break date, May For three-month exchange rate change s t+3 in the top panel of Table 1A, a positive mean value indicates that averaged over the sample, the country s currency experienced a quarterly depreciation against the US dollar. We see that all currencies except the Japanese Yen and Swiss Franc have appreciated before the break, but depreciated after the break. The volatility of exchange rate has been increased after the break except for Japan and Switzerland, as standard deviations indicate. The two commodity currencies (Australian and New Zealand dollars) are not especially volatile, though certainly have the widest swings. Turning to excess returns, XR t+3, with the exception of Japan and Switzerland, we see that all currencies on average offer excess quarterly returns relative to US dollar investment before the break. But, after the break, all currencies except New Zealand and Switzerland cause loss to this investment. This would be consistent with the idea that the US dollar (along the Swiss Franc) is commonly considered safe haven currencies. Excess currency returns are also more volatile after the break. In both exchange rate changes and excess currency returns, we observe large fluctuations at orders that are atypical for other macro-fundamentals. From Figures 1A and 1B, we see episodes of exchange rate volatility, with the recent financial crisis period being especially noticeable in all currencies except Japan and Switzerland. 24 Table 1B presents statistics on the yields. In order to describe the shape of the yield curves across countries over time, we use the Nelson-Siegel (1987) exponential components framework to distill the entire relative yield curves, period-by-period, into a three relative factors that evolves dynamically. Specifically, assuming symmetry and exploiting the linearity in the factor-loadings, we extract three factors of relative level (L R t ), relative slope (S R t ), and relative curvature (C R t ) as follows: 25 i R,m t = i m t i m,us t = L R t + S R t ( ) 1 exp( λm) + Ct R λm ( 1 exp( λm) λm ) exp( λm) + ɛ m t As the number of yields is larger than the number of factors, eq.(13) cannot fit all the yields perfectly, so an error term ɛ m t of fit. 26 (13) is appended for each maturity as a measure of the goodness 23 The break date is arbitrary in the summary statistic. But, the structural break test in the later sections reports May 2008 as a most common break date across countries. 24 The absence of drastic changes in the value of these latter two currencies relative to the USD is likely due to the fact that all three are viewed to some degree as safe haven currencies. 25 See Appendix A for further discussion. The interpretation of the relative factors extends readily from their single-country counterparts. For example, an increase in the relative level factor means the vertical gap between the entire home yield curve and the U.S. one becomes more positive (or less negative). 26 The parameter λ, is set to , in accordance with the literature such as Diebold and Li (2006). It controls the particular maturity the loading on the curvature is maximized. 11

13 We see that Australia and New Zealand have a higher level factor than the US while Japan and Switzerland have a lower level factor than the US on average. For Canada, Denmark and Sweden, the level factor is higher than the US before the break, but lower than the US after the break. Since the level factor represents the long yield, the positive relative level factor implies that the inflation rate of home country is expected to be higher than that of the US. It is not surprising that we see Japan s average level to be lower in the US, given its deflationary spiral that started in the early 1990s. We see a dramatic change in the relative slope factor before and after the break. For all countries except New Zealand and the UK, the slope factor changes its sign from negative to positive. Noting that the slope factor represents the short minus long yield, the positive relative slope factor means that the yield curve of home country is relatively flat compared to that of the US, expecting relatively lower economic growth or severe economic downturn. For the relative curvature, we see a large increase after the break with the exception of the UK, reflecting relatively more humped shape of home country s yield curve. 27 Relative Nelson-Siegel factors are more volatile before the break. This reflects the fact that the yield curve is a leading indicator of business cycle, so that it has fluctuated more right before the recession started. 28 Figure 2A shows the monthly average of relative yields, i R,m t = i m t i m,us t, before and after the break. As discussed above, the relative yield curve after the break is more negatively sloped, which means that the yield curve of home country is flatter than that of the US. Figure 2B shows the time-varying relative Nelson-Siegel factors. Table 1C reports the summary statistics for two macro variables we use: the relative unemployment gap and inflation rate between each of the eight countries to those of the US. 29 Relative unemployment gaps have been higher before the break but lower after the break, implying severe job loss and slow recovery in the U.S. labor market. Australia has higher inflation rate, while Japan, Sweden and Switzerland have lower inflation rate, compared to the US. For Canada, Denmark, New Zealand and the UK, relative inflation rate is lower before the break but higher after the break. Table 1D shows the correlation between quarterly exchange rate changes and each of the relative Nelson-Siegel factors. Again, considering the possibility of structural breaks in their correlations, sample period is divided by the break date, May As we can see from the table, correlation of exchange rate change with the relative level and slope factors switches its sign after the break in most of the countries. The correlation of exchange rate 27 See Chen and Tsang (2013) for a more complete discussion of the relative factors. 28 One measure of the yield curve slope is included in the Financial Stress Index published by the St. Louis Fed and the Index of Leading Economic Indicators published by The Conference Board. 29 We use unemployment gap to measure the output gap since monthly data is easily obtained. Monthly industrial productin index is also available, but the choice of variables for the output gap does not make big difference for our empirical analysis. 12

14 change with the relative level becomes stronger after the break, but the opposite is true for the correlation with the relative curvature. We further show correlation coefficients with rolling window, as in Figures 3A, 3B and 3C. From the summary statistics, we can say that structural breaks are potentially detected and should not be ignored when estimating the econometric models. 3.2 Explaining the Currency Movements with Bond Yields In this sub-section, we confirm findings in Chen-Tsang (2013) that relative Nelson-Siegel yield curve factors have predictive power for subsequent quarterly exchange rate changes and excess currency returns and justify the role of yield curves as a candidate for capturing both expectation and risk in explaining the exchange rate dynamics. Compared to the previous work, we cover a larger set of country-pairs, and the data sample covers the recent financial crisis. As such, we put an emphasis on possible structural breaks in the yield curve-exchange rate relation. For each of the eight country pairs, we run the following regressions and report the results in Tables 2A and 2B: s t+3 = β 0 + β 1 L R t + β 2 S R t + β 3 C R t + ɛ t+3 (14) XR t+3 = α 0 + α 1 L R t + α 2 S R t + α 3 C R t + ɛ t+3 (15) To address possible parameter instabilities, we test for endogenous structural breaks in the regression. These tables report results based on Bai and Perron (2003) multiple break tests(with 15% trimming and 5% significance level), which identify one to three breaks. In order to capture the common behavior changes across countries, one or two breaks are chosen to identify the Great Recession period. The first break date is around 2008, when the Global Financial Crisis has been triggered. The second break date is around For economic interpretation, we categorize three phases identified by break dates as Pre-Crisis (from January 1995 to the first break), During Crisis (from the first break to the second break) and Post-Crisis (from the second break to March 2015). The first break date is consistent with casual observations in summary statistics, as discussed earlier. 30 From Tables 2A and 2B, we first note that with the exception of Canada and Switzerland, the predictive power of the relative yield curve is apparent. Contrary to results typical in the empirical exchange rate literature which tend to find essentially no explanatory power, especially at the monthly or quarterly frequency, we see that the regressions here can produce adjusted R 2 on the order of 20% or 30%. We also note that the Pre-Crisis coefficients are consistent with prior findings: an increase in the relative level 30 We also tested for a structural break using the Quants and Andrews (1993) test. In all cases, Quants and Andrews test identified one of breaks we have chosen. 13

15 and slope factors in a country tends to lead to subsequent appreciation of the currency as well as higher excess return. The During Crisis data indicates a significant change in the coefficients to a sign reversal. During the Crisis, higher relative level and slope factors result in depreciation of the currency and negative excess return. however, do not show consistent results across countries. The Post-Crisis coefficients, We conjecture that this may be due to different speed of recovery and path of inflation. We then test the joint significance of relative factors in explaining currency behavior. Again, with the exception of Switzerland, the p-values from the Wald test are all below 1%, indicating strongly rejections of the hypothesis that yield curves contain no information about subsequent currency behavior. These results establish the predictive power of the relative factors, and show that information in the cross country yield curves are important for understanding currency behavior. Although we do not explicitly test for any specific macroeconomic models, our results nevertheless have intuitive economic interpretations. As discussed in Section 2, the exchange rate is determined by expectations about future macro fundamentals and time-varying risk premiums and the relative yield curves contain information about both determinants. In this regard, the coefficients on relative yield factors are joint results from both expected macro conditions and risk premiums. Expectation channel is well explained by the Taylor-rule type monetary policy. When home country s economy has an inflationary gap and the market expects higher inflation in the future, its central bank raises the interest rate, resulting in appreciation of its currency. and even more downturn is expected. exchange rate rises. On the other hand, suppose the economy is in the recession Then, the central bank lowers its policy rate and Since the relative level reflects the expected inflation, higher relative level factor before the crisis results in its currency appreciates. However, during the Crisis, as higher relative slope factor or equivalently flatter yield curve implies deeper recession or slower recovery, the home country experiences depreciation of its currency. Turning to risk premium channel, we refer to recent empirical evidences about the carry-trade strategy. 31 This line of research says that when the volatility of exchange rate is low, the currency with higher risk appreciates as investors require compensation for holding risky currency. However, under high volatility, abrupt withdrawal of investment causes loss to the currency with higher risk. Since the country of which economy is expected to have higher inflation and lower economic growth embodies higher underlying risk, this currency appreciates when the volatility is low and depreciates when the volatility is high. Therefore, combining 31 The carry-trade is a strategy under which investors take long positions on high-yield currency and short positions on low interest rate currency. Lustig and Verdelhan (2007) find that the portfolios constructed by the carry-trade strategy yield high returns. Clarida et al.(2009) show that returns to the carry trade depend on the volatility of exchange rate. That is, when the volatility is low, the carry-trade gives gain. And when the volatility if high, it causes loss. Kohler (2010) also mention that under adverse financial market, as the carry-trades are unwound, dramatic depreciation happens for the high interest rate currency. 14

16 the expectation channel and risk premium channel together, the sign-switching property of coefficients on the relative level and slope factor from our regression can be intuitively established. 4 Decomposing the Yield Curve: Expectation vs Risk 4.1 Decomposition Results We showed in Section 2 that the yield curves relate to the exchange rate via two channels: 1) they embody expectations about future macroeconomic variables, and 2) they capture perceived risk about future periods (the two discounted sums in eq.(4)). Since there are alternative methods based on different concepts of term structure modeling and one is not necessarily considered as superior to the others, we adopt four models in the literature to decompose the yield curves: 1) the Nelson-Siegel latent factor model (hearafter, NS model), 2) the Nelson-Siegel latent factor model which allows interaction with macro fundamentals as discussed in Diebold, Rudebusch and Aruoba (DRA 2006) (hearafter, NSM model), 3) Ang and Piazzesi (2003) s discrete-time affine Gaussian term structure model (hearafter, Affine model) and 4) the Cochrane and Piazzesi (2005) approach (hearafter, CP model). With these models, we first estimate expected yields, which are averages of expected short yields, and use them as a proxy for expected future paths of macro fundamentals, taking into account of the observation that the short rate is a monetary policy instrument. 32 then take the difference between the fitted yields from the model and the expected yields to separate out the time-varying bond term premiums. 33 We While the general perceived risk is not observable, we use partial measures of perceived risk from the yield curves based on the concept of bond market term premiums as a proxy. 34. The NS model decompose the yield curve into expected yields and term premiums as follows: assuming that the factors follow a VAR(1) (as in DRA, 2006), we simultaneously fit the yield curve at each point in time and estimate the underlying dynamics of Nelson- Siegel factors by employing the state-space and Kalman filter approach. 35 the VAR(1) to obtain in-sample forecasts of the factors. Then, we iterate Using the Nelson-Siegel formula (13), we can obtain the predicted 1-month yield for any horizon. Averaging the expected 32 For Affine model, we use risk-neutral yields as a proxy for expected yields 33 For CP model, the term premiums are estimated first and the expected yields are defined as the difference between the actual yields and term premiums. 34 Here, we briefly explain how we construct expected yields and term premiums based on each model. For details, please refer to Appendix 35 This one-step approach improves upon the two-step estimation procedure of Diebold and Li (2006). See DRA (2006) for discussion. 15

17 1-month yields over each maturity, we obtain the expected yields and subtracting the expected yields from the fitted yield of the same maturity, we obtain the term premiums. For our cross-country analysis, relative expected yields and relative term premiums are defined as the difference in expected yields and term premium between each country-pair. The estimation procedure for the NSM model is the same as that for the NS model except the underlying dynamics of factors. While in the NS model, expected yields and term premiums are calculated based on yields only, in the NSM model we take a macrofinance approach. We posit that longer-term yields embody not only expected future short yields but also expected future macroeconomic conditions such as inflation and output and unemployment conditions. This reflects the idea that if, based on current macroeconomic condition, inflation is expected to be high over the coming year, the one-year yield will be higher than otherwise, to take into account this expected high inflation. DRA (2006) formalized this idea that yield curve factors and macro dynamics are jointly determined in a VAR system. One justification is that future short yields are determined by macroeconomic conditions via monetary policy actions such as a Taylor type rule. The Affine model has different representation of the yield curve, compared to the Nelson-Siegel type approach, since it assumes the stochstic discount factor that prices all assets under the absence of arbitrage. Here, we follow the discrete-time Affine Gaussian dynamic term structure model based on Ang and Piazzesi (2003). Furthermore, in order to avoid small sample bias due to high persistence of interest rate, we adopt the bias correction estimation method proposed by Bauer, Rudebusch and Wu (2012). Estimating the model, we can obtain the risk-neutral yields, which would prevail if investors were risk-neutral, and the model-implied yields. Risk-neutral yields reflect policy expectations over the lifetime of the bond, as such it represents expected yields, and term premiums are defined as the difference between the model-implied yields and the risk-neutral yields. Motivated by Cochrane and Piazzesi (2005), we introduce the CP model to estimate term premiums and expected yields. Specifically, we estimate excess long returns, which is the holding period returns from buying an n-year bond and selling it as an n 1 year bond one year later net of one-year yield, in a VAR(1) system with forward rates at 1- to 10-year maturities. Iterating the estimated VAR(1) forward, in-sample forecasts of excess long returns are calculated and using the relationship between excess long returns and term premiums, term premiums are obtained. Then, expected yields are calculated by subtracting the term premiums from the actual yields of the same maturity. Figures 4A, 4B, 4C and 4D show the the monthly averages over the sample period of relative yields, relative expected yields and relative term premiums, estimated by four alternative models. We first note that the sum of relative expected yields and relative term premiums of each maturity is equal to relative yields of the same maturity. The relative 16

18 term premiums are very small close to zero in the shortest maturity and departs from zero over longer maturities, as it can be interpreted as the extra compensation of holding longer maturity bond. model-dependent. We also see that the shape of decomposed yield curve is country- and Figures 5A and 5B explicitly compare estimated relative expected yields and relative term premiums across models. The Affine model shows the different shape of decomposed curves, while the NS, NSM and CP models share similar patterns for most of the countries. We conjecture that this unique characteristics of the Affine model is due to imposition of no-arbitrage condition and correction of small sample bias. We do not evaluate in this paper which term structure model is better in decomposing the yield curves because each model has its pros and cons. Rather, the focus of our research is to decompose the yield curves into expectations and risk and show both expectations and risk contribute to explaining exchange rate and excess currency return behavior, no matter which term structure model is employed. In order to describe the shape of relative expected yields and relative term premiums at all maturities, we summarize them with three factors: level, slope and curvature. 36. Tables 3A, 3B, 3C and 3D and Tables 4A, 4B, 4C and 4D report summary statistics for relative expected yield factors and relative term premiums factors. Again, considering possible structural breaks, the sample period is divided by an arbitrary break date, May, First, factors of relative expected yields and relative term premiums are less volatile than those of the entire relative yield curve. Second, slope factors of relative expected yields and relative term premiums from NS, NSM and CP models have smaller means than those of entire relative yields. This observation is consistent with the idea that the yields reflect both expectations and risk and the gap between the zero-coupon yield and expected yield represents the term premium. Third, the correlation between level and slope of relative term premiums is close to negative unity since the term premiums at the shortest maturity is almost zero. So, when estimating the model with relative term premiums in the later sections, we use only slope and curvature factors in order to avoid the multi-collinearity problem. Lastly, there seems to exist a structural break. As shown in the tables, the means of factors, especially slope factor, have different values before and after the break date. We also see clearly from Figures 6A, 6B, 6C and 6D and Figures 7A, 7B, 7C and 7D that pre and post, the expectation and perceived riskiness of various sovereign bonds at different horizons shifted significantly in May, The choice of three factors is consistent with the idea of three Nelson-Siegel factors. Recall the definition of relative expected yields of maturity m, E t i R,m t = E t i m t E t i m,us t and relative term premium of maturity m, θ R,m t = θt m θ m,us t. The level, slope and curvature factors of the relative expected yields are constructed as follows: L(E t i R t ) = E t i R,120 t, S(E t i R t ) = E t i R,3 t E t i R,120 t, C(E t i R t ) = 2E t i R,24 t (E t i R,3 t + E t i R,120 t ). The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θt R ) = θ R,120 t, S(θt R ) = θ R,3 t θ R,120 t, C(θt R ) = 2θ R,24 t (θ R,3 t + θ R,120 t ) 17

19 4.2 Explaining the Currency Movement with Expectations or Risk In this sub-section, we examine if either expectations or risk perceived at the particular point in time can individually explain subsequent quarterly exchange rate changes and excess currency returns. After separate regressions, we investigate further which of expectations and risk explain more, by putting them together in the same regression in the next sub-section. We first show that expectation about future macro fundamentals, measured by relative expected yield factors, have considerable explanatory power for currency movements. We run the following regressions with structural breaks for each currency: 37 s t+3 = β 0 + β 1 L(E t i R t ) + β 2 S(E t i R t ) + β 3 C(E t i R t ) + ɛ t+3 (16) XR t+3 = α 0 + α 1 L(E t i R t ) + α 2 S(E t i R t ) + α 3 C(E t i R t ) + ɛ t+3 (17) Tables 5A and 5B present the p-values from the joint Wald test and adjusted R shown in the tables, the p-values from the joint Wald test are all below 5% (except Japan, all below 1%). The hypothesis that the relative expected yields, equivalently the expected future paths of macro fundamentals, have no information about exchange rate changes or excess currency returns is strongly rejected. The goodness of fit measures (adjusted R 2 ) say that the relative expected yields can explain at least 13% up to 41% except Japan. As This is quite an impressive portion in light of the near-zero R 2 typical in this literature. Interestingly, the adjusted R 2 s are even higher than those from the relative yield factor model in Section 3 for most of the countries. We guess that more information from macro variables or no-arbitrage condition imposition help improve the explanatory power. Another interesting feature is that for Japan, the goodness of fit is worst when regressed with the factors from NSM model, which allow the interaction between yield factors and macro variables. Intuitively, since Japan has experienced a prolonged deflation pressure since early 1990s, macro variables seem to have no additional information about currency movements. Looking at the p-values in sub-periods, expectation is significant determinants during the Crisis, but less significant before and after the Crisis for some countries. explain. Now we explore how much of currency movements the relative term premium factors This is same as to test the idea that the same systematic latent risk is priced in 37 we test for endogenous structural breaks in the regression, based on Bai and Perron (2003) multiple break tests(with 15% trimming and 5% significance level). As explained in Section 3, one or two breaks, out of at most three breaks, are chosen to identify the common behavior changes across countries. The first break date is around 2008 and the second one is around We do not report the coefficients on relative expected yield factors or on relative term premium factors. Since we argue that both expectation and risk matter for currency movements, regression with only expectation or only risk may suffer from the omitted variable problem and thus the interpretation of coefficients may be misleading. 18

20 both the bond and currency markets. Since we do not directly observe risk either in the relative bond markets or in the currency market, we rely on certain structural concepts to identify risk which we estimate by NS, NSM, Affine and CP model. To verify these ideas, we run the following regressions: 39 s t+3 = β 0 + β 1 S(θt R ) + β 2 C(θt R ) + ɛ t+3 (18) XR t+3 = α 0 + α 1 S(θt R ) + α 2 C(θt R ) + ɛ t+3 (19) The joint Wald test results and the goodness of fit measures are reported in Tables 6A and 6B. We see that the four different concepts of risk premiums deliver two important messages. By looking at the joint Wald test results, we first see that for most of currency pairs, the relative premiums are strong and robust determinants of currency excess returns, supporting the view that differential risks in the relative bond markets are priced into the corresponding currency values. Looking at the goodness of fit criterion (adjusted R 2 ), we see that relative term premiums can explain up to 34% of the variations in currency returns even though adjusted R 2 s are low for some countries depending on models used. The p- values in sub-periods tell us when risk measures are insignificant. The joint hypothesis that the relative term premium factors have no explanatory power is rejected mostly during the Crisis, but cannot be rejected for many countries before or after the Crisis. This is because investors are more aware of risk when recipient country s economy condition is unfavorable and financial market is volatile. Moreover, comparing the explanatory power of relative term premium factors to relative expected yield factors, the latter explains more (except for Australia, Denmark in CP model). 4.3 Comparing the Role of Expectations and Risk We showed in the previous sub-section that explanatory power of each of expectations and risk is considerably high. Then, the next question would be which of expectations and risk explain more of variation in currency movement. We regress three-month exchange rate changes on relative expected yield factors and relative term premium factors, and test for the joint significance of each group in sub-periods identified by the structural breaks, using the Wald statistics. 40 We report the results from NSM and Affine model only since NS, NSM and CP model share the similar decomposed results of yield curves. 39 As explained in the previous sub-section, level factor is excluded from regressors in order to avoid the multi-collinearity problem. 40 Concerned about multi-collinearity problem due to use of the same underlying factors, we perform the the Belsley collinearity test and find no severe collinearity. The 19

21 regression equation is as follows: s t+3 = β 0 + β 1 L(E t i R t ) + β 2 S(E t i R t ) + β 3 C(E t i R t ) + β 4 S(θ R t ) + β 5 C(θ R t ) + ɛ t+3 (20) Tables 7A and 7B show that for the full sample period, the null hypothesis that the expectations do not explain exchange rate changes( No expectations? ) is rejected for all the currencies and the null that the risks have no explanatory power ( No risk? ) is rejected except for Canada in NSM model. The null hypothesis that neither expected yield factors nor term premium factors predict exchange rate movement( RW? ) is strongly rejected for all the countries. The explanatory power of this joint model improves over the Nelson-Siegel factor model discussed in Section 3. The adjusted R 2 s increase by 2%p to 18%p. We then compare the statistical significance of expectations and risk in sub-sample periods. null hypothesis No expectations? cannot be rejected for some countries before the Crisis, but mostly rejected during the Crisis. The null hypothesis No risk? cannot be rejected for most of countries before the Crisis, but for a few countries during the Crisis. The This results tell us that before the Crisis, currency risks have little additional explanatory power beyond what expectations explain, but during the Crisis when the underlying risk is high, they do have a role in explaining the currency movement in addition to expectations. As a next step, we try to show quantatively the portion explained by each components: expectation and risk. We first construct a six-variable VAR(1), which consists of one-month exchange rate change, three factors from relative expected yields and two factors from relative term premiums. Following Hodrick (1992), we calculate the partial R 2 for each variable for explaining exchange change at various horizons. 41 Though the variable that enters the VAR system is the one-month exchange rate change, we can iterate forward the VAR to calculate the explanatory power of each variable for exchange rate change of longer horizons. Tables 8A and 8B show the results for explaining exchange rate change at 1, 3, 6 and 12-month in the future. We see the consistent result with the Wald test that expectations explain more than risks in the full sample period (with the exception of Japan). Looking at the partial R 2 for each components over horizons, we find that risks pick up the share in longer horizons. Another aspect of this analysis is to compare the explanatory power of each variable for currency movements before and after the structural break. We divide the sample period into two sub-periods by the first break date around 2008 and calculate the Hodrick s partial R 2 using the sub-sample data. 42 Unfortunately, the results are model-dependent. In NSM model, relative portion explained by risks increases after the first break (except for Japan and the UK). On the other hand, according to the 41 See Appendix for a detailed discussion on the method. 42 We do not divide the sample period into three sub-periods identified by two breaks because with three sub-periods, the number of observation is not enough to produce partial R 2 over longer horizons. 20

22 Affine model, expectations explains more after the break even though risks still explain considerable amount. The bottom line, as seen from the Wald test and the partial R 2 analysis, is that the expectations play a significant and strong role consistently over the full sample period, while risks pick up their significance after The Joint Macro-Finance Approach 5.1 The Joint Macro-Finance Model We have shown that both expectations and risk are important determinants in explaining the exchangre rate dynamics, lending support on our idea that the macro and the finance approaches should be combined. Now, we propose the joint macro-finance approach. Since yield curve contains information about both expectation and risk and it can interact with macro variables, we regress the exchange rate change directly on relative Nelson-Siegel factors and macro variables, instead of extracting the expectation and risk components from the yield curves and regressing on them. This is a natural extention of Ang and Piazzesi (2003) and DRA (2006) to international setting. 43 Specifically, we run the following regressions for each of the eight country pairs and report the results in Tables 9: s t+3 = β 0 + β 1 L R t + β 2 S R t + β 3 C R t + β 4 u R t + β 5 π R t + ɛ t+3 (21) For the full sample period, the null hypothesis that the latent yield factors do not explain exchange rate changes ( No Yields? ) is strongly rejected. The null hypothesis that the (contemporaneous) macro variables have no contribution ( No Macro? ) cannot be rejected for Australia, Canada and Japan. Note that this result does not imply macro fundamentals overall do not affect exchange rate movements, but that contemporaneous macro fundamentals have no additional explanatory power once the yield curve factors are included. discussed in Section 2 (and in Chen and Tsang, 2013), the yield curves themselves contain expectations about future macro-fundamentals. As We can strongly reject the hypothesis that neither macro fundamentals nor yield factors can predict exchange rate movement next quarter for all the countries. quite high: the adjusted R 2 can be up to 44%. Note that the explanatory power of these variables can be This level of explanatory power is rare in the context of explaining short-term currency movement such as at the quarterly level here. Moreover, the explanatory power of the joint model is better than that of the yield-only 43 For example, since NSM model uses a VAR(1) model with three Nelson-Siegel factors and macro variables, expected yields and term premiums in each period t are functions of these variables in the same period t. As a result, when using relative expected yield factors and relative term premium factors to explain exchange rate changes, what we are doing is conceptually equivalent to using the three factors and macro variables as explanatory variables. 21

23 model discussed in Section 3 and similar to that of NSM model in Section 4. The statistical significance depends on the sub-sample periods. Yield factors are consistently significant in explaining the exchange rate changes as the null No Yields? is rejected except one country before the Crisis and two countries during the Crisis. On the other hand, the null No Macro? cannot be rejected for five countries before the Crisis and for two countries during the Crisis. Macro variables have little additional explanatory power before the Crisis, but do gain their significance during the Crisis. We conjecture that investors become more sensitive to development of macro variables during the Crisis, affecting the currency movements. This results are in line with the findings in Section 4 that risk factors become more significant during the Crisis. Since economic agents perceive risk embedded in the economy through macro variables especially during the recession, macro variables and risks play a significant role in determining the exchange rate. and Ang et al. Given the above results, we extend the dynamic framework of Diebold and Li (2006) (2006) to the international setting, and estimate a VAR system of the relative latent yield factors, Taylor rule macro fundamentals, and the monthly exchange rate change. Following previous work in both the international macro and finance literature, we do not structurally estimate a Taylor rule, nor impose any structural restrictions in our VAR estimations. 44 feedback among the variables. We use the atheoretical forecasting equations to capture any endogenous We estimate a six-variable VAR(1), though increasing the order of the VAR system does not change our conclusions below. Following Hodrick (1992), we calculate the partial R 2 horizons. for each variable for explaining exchange change at various Table 10 shows the results for explaining exchange rate change at 1, 3, 6 and 12-month in the future. For the full sample period, macro variables explain more than three Nelson-Siegel factors for five countries. This result is somewhat counter-intuitive because we argue that the yields contain information about current and future expected macro variables and risks, and thus would be natural to have more explanatory power than contemporaneous macro variables. Total R 2 increases at longer horizons, but not as much as found in previous sections. To resolve these conflicts, we do the same analysis with sub-samples divided by the first break date around the findings in the Wald test. the UK. Now, we have more sensible results, consistent with Before the first break, yield factors explains more except for But, after the break, macro variables explains more for Australia, Denmark and Switzerland and gain more portion than before the break for other countries, especially in the long horizons. 44 This non-structural VAR approach follows from Engel and West (2006), Molodtsova and Papell (2009) and so forth on the exchange rate side, and DRA (2006), among others, on the finance side. 45 We do not divide the sample period into three sub-periods identified by two breaks because with three sub-periods, the number of observation is not enough to produce partial R 2 over longer horizons. 22

24 5.2 Predictability We compare the in-sample fit of our models to a benchmark model that exchange rate change follow a random walk with a drift (RW). Models we consider are: 1) model that has only two macroeconomic variables (Macro-only); 2) model that has only three Nelson-Siegel latent factors (Yield-only); 3) model that has both macroeconomic variables and yield factors (Joint). Since the VAR system only has the one-month exchange rate change, we iterate the estimated VAR forward to obtain predicted 1-month exchange rate changes for different horizons. We then sum up the predicted values to obtain the predicted 3, 6, and 12-month exchange rate changes. We calculate the root mean squared error (RMSE) for the joint model, macro-only model, yield-only model and the random walk model. Table 11 reports the results. The RMSE ratio is calculated as the RMSE of the joint or macro-only or yieldonly model divided by the RMSE of the random walk model, and a ratio less than one implies that the random walk model is inferior. We also calculate the Diebold-Mariano statistic for each case by regressing the difference in squared errors on a constant, and a constant that is significantly larger than zero implies that the corresponding model significantly predicts better than the random walk model in sample. For the full sample period, results show that the joint model has better in-sample predictability over other models. RMSE ratios for the joint model are all below one and lower than those for the macro-only and the yield-only model in all the horizons and for all the countries. The macro-only model performs poorly in the horizon up to 3-months, but well in 6- and 12-month horizons. DM statistics for the joint model are significantly larger than zero for 3-month or longer horizons. Once we divide the sample period into two sub-periods considering a structural break, predictability of all models improves as shown by decrease in RMSE ratio and more rejection of the null from DM test. Three models predict the exchange rate changes well before the break at all horizons, but not after the break at longer horizons. 46 Again, the joint model consistently has lower RMSE ratio than other models before and after the break. Comparing the macro-only model and the yield-only model, the yields-only model performs better than the macro-only model at all horizons before the break (except for the UK). But, the macro-only model outperforms the yield-only model for Australia, Denmark and Switzerland after the break. 6 Conclusions This paper incorporates both macroeconomic and financial elements into exchange rate modeling. Separating out the expected yields and the term premiums from the yields, we 46 This might be partly because sample size after the break is too small. 23

25 show that investors expectation about the future path of monetary policy and their perceived risk both drive exchange rate dynamics. We then propose a joint model where macroeconomic fundamentals targeted in Taylor-rule monetary policy to interact with latent risk factors embedded in cross-country yield curves to jointly determine exchange rate dynamics. As the term structure factors capture expectations and perceived risks about the future economic conditions, they fit naturally into the present-value framework of nominal exchange rate models. Our joint macro-finance model fits the data well, especially at shorter horizons, and provides strong evidence that both macro fundamentals and latent financial factors matter for exchange rate dynamics. 24

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29 Appendix A. Decomposing the Yield Curve by the Nelson-Siegel Framework The Nelson-Siegel latent factor framework (Nelson and Siegel, 1987) provides a succinct summary of the few sources of systematic risks that underlie the pricing of various tradable financial assets. 47 The classic Nelson-Siegel (1987) model summarizes the shape of the yield curve using three factors: L t (level), S t (slope), and C t (curvature). Compared to the no-arbitrage affine or quadratic factor models, these factors are easy to estimate, can capture the various shapes of the empirically observed yield curves, and have simple intuitive interpretations. 48 The three factors typically account for most of the information in a yield curve, with the R 2 for cross-sectional fits around While the more structural noarbitrage factor models also fit cross-sectional data well, they do not provide as good a description of the dynamics of the yield curve over time. 49 We extract relative expected yields and relative term premiums from the crosscountry yield curves using the Nelson-Siegel framework, based on Diebold, Rudebusch and Aruoba (DRA, 2006). First, assuming that the factors follow a VAR(1), we simultaneously fit the yield curve for each country at each point in time and estimate the underlying dynamics of Nelson-Siegel factors by employing the state-space and Kalman filter approach. As discussed in DRA (2006), this one-step approach improves upon the two-step estimation procedure of Diebold and Li (2006). 50 In this paper, we explore two different dynamics of yield factors: one is a dynamics of yield factors only (NS model) and the other is a joint dynamics of yield factors and macro fundamentals such as unemployment rate and inflation rate (NSM model). Specifically, even though two models share the same measurement equation, which relates a set of N yields to state vector, the transition equation follows different 47 Since the Nelson-Siegel framework is by now well-known, we refer interested readers to Chen and Tsang (2013) and references therein for a more detailed presentation of it. 48 The level factor L t, with its loading of unity, has equal impact on the entire yield curve, shifting it up or down. The loading on the slope factor S t equals 1 when m = 0 and decreases down to zero as maturity m increases. The slope factor thus mainly affects yields on the short end of the curve; an increase in the slope factor means the yield curve becomes flatter, holding the long end of the yield curve fixed. The curvature factor C t is a medium term factor, as its loading is zero at the short end, increases in the middle maturity range, and finally decays back to zero. It captures the curvature of the yield curve is at medium maturities. See Chen and Tsang (2013) and references therein. 49 See, e.g. Diebold, Rudebusch and Aruoba (2006) and Duffee (2002). 50 In Diebold and Li (2006), with λ held fixed at , the level, slope, and curvature parameters for each monthly yield curve are estimated. This process is repeated for all observed yield curves, and provides a time series of estimates of the unobserved level, slope, and curvature factors. Then, it fits a first-order autoregressive model to the time series of factors derived in the first step. 28

30 dynamics. As such, the state-space model representation is as follows: (MeasurementEquation) i t = Λf t + e t (T ransitionequation) f t µ = A(f t 1 µ) + v ( ) (( ) t ( e t 0 i.i.d.n, 0 v t H 0 0 Q )) where i t = (i m 1 t, i m 2 t,..., i m N t ), f t = (L t, S t, C t ) in the NS model, f t = (u t, π t, L t, S t, C t ) in the NSM model, 1 exp( λm 1 1 ) 1 exp( λm 1 ) λm 1 λm 1 exp( λm 1 ) 1 exp( λm 1 2 ) 1 exp( λm 2 ) Λ = λm 2 λm 2 exp( λm 2 ) in the NS model, exp( λm N ) 1 exp( λm N ) λm N λm N exp( λm N ) 1 exp( λm ) 1 exp( λm 1 ) λm 1 λm 1 exp( λm 1 ) 1 exp( λm ) 1 exp( λm 2 ) Λ = λm 2 λm 2 exp( λm 2 ) in the NSM model exp( λm N ) 1 exp( λm N ) λm N λm N exp( λm N ) By applying the Kalman filter, we obtain the maximum likelihood estimates for parameters including VAR coefficients and optimal filtered and smoothed estimates of yield factors. 51 Next, iterating the estimated VAR, we can calculate in-sample forecasts of the factors: ˆ f t+j ˆµ = Âj ( ˆf t ˆµ), for j = 1, 2,...,, for all t Using the Nelson-Siegel formula with m = 1, we obtain the predicted 1-month yield over future horizons: E t i 1 t+j = ˆL t+j + Ŝt+j ( ) 1 exp( λ) λ + Ĉt+j ( 1 exp( λ) λ ) exp( λ) The expected yield of maturity m is defined as the average of the expected 1-month yields over m 1 maturities and the term premiums of the same maturity is calculated by substracting 51 For details of Kalman filtering and related issues, see DRA (2006). 29

31 the expected yield from the fitted yield: E t i m t = 1 m m 1 j=0 θ m t = î m t E t i m t E t [ i 1 t+j ] Finally, relative expected yields and relative term premiums are calculated by the differences in expected yields and term premiums between each country-pair: E t i R,m t = E t i m t E t i m,us t θ R,m t = θt m θ m,us t B. Decomposing the Yield Curve by the Affine model We follow the discrete-time affine Gaussian term structure model, based on Ang and Piazzesi(2003). Let Pt m denote the price at time t of an m-period zero-coupon bond. For a zero-couple bond, we know i m t = log(pt m )/m. Under no-arbitrage, the price of the bond should be consistent with the pricing kernel that Pt m = E t ( m j=1 M t+j), where the pricing kernel M t+1 is conditionally lognormal: M t+1 = exp ( i 1t 12 λ tλ t λ tɛ ) t+1, ɛ t i.i.d.n(0, I) The term λ t = λ 0 +λ 1 X t is a time-varying market price of risk, where X t is the state variables, which in our case are the three principal components of the yields. The one-period yield i i t is also an affine function of the state variables, i 1 t = δ 0 + δ 1X t. The state variables follow a first-order Gaussian VAR. Under objective probability measure P : X t+1 = µ + ΦX t + Σɛ t+1 Under risk-neutral probability measure Q: X t+1 = µ Q + Φ Q X t + Σɛ Q t+1 where µ Q = µ Σλ 0, Φ Q = Φ Σλ 1 Using the log-normality assumption and the VAR model for the state variables X t, we can express bond prices and yields as a function of the state variables and other parameters. 30

32 The model-implied bond prices and yields are: P m t = exp (A m + B mx t ), i m t = log(pt m )/m where A m+1 = A m + B mµ Q B mσσ B m δ 0 B m+1 = Φ Q B m δ 1 The risk-neutral bond prices and yields are: P t m = exp (A m + B mx t ), ĩ m t = log( P t m )/m where Ãm+1 = Ãm + B mµ B mσσ Bm δ 0 B m+1 = Φ B m δ 1 That is, bond prices and yields are determined recursively through A m and B m. And the model-implied bond prices and yields are calculated as if agents are risk-neutral (λ 0 = λ 1 = 0) but the state variables follow a different law of motion. When estimating the model, considering small sample bias due to high persistence of interest rate, we follow the bias correction method proposed by Bauer, Rudebusch and Wu (2012). The idea is that after estimating µ and Φ under P measure by ordinary least squares (OLS), it corrects the possible mean bias by bootstrap bias correction and indirect inference. Then, given bias-corrected µ and Φ, the remaining parameters (µ Q, Φ Q, Σ, δ 0, δ 1 ) are estimated by maximum likelihood estimation (MLE). 52 The estimated risk-neutral yields(ĩ m t ) are used as expected yields and the differences between model-impled yields and risk-neutral yields(i m t ĩ m t ) are defined as term premiums. Again, for our cross-country analysis, relative expected yields and relative term premiums are obtained by the cross-country differences. C. Decomposing the Yield Curve by the Cochrane-Piazzesi model Following Cochrane and Piazzesi (2005) we look at annual excess returns. period return of a 12n-month bond from now to next year can be calculated as: Holding rt+12 12n ni 12n t (n 1)i 12(n 1) t+12, where n = 2, 3,..., For details of bias correction estimation for the Affine model, see Bauer, Rudebusch and Wu (2012). 31

33 That is, you buy the 12n-month bond now and sell it as a 12(n 1)-month bond next year. The above defines the return of such a transaction. rx 12n t+12 rt+12 12n i 12 t Excess return is then defined as: The term tells you the extra return you get from the transaction over a riskless 12n-month bond. In the data, we have 12, 24,..., 120-month bonds. The ten yields allow us to define rx 24 t+12,..., rx 120 t+12, a total of nine excess returns. The forward rate at time t for loans between time t + n 1 and t + n is also defined as f 12n t ni 12n t (n 1)i 12(n 1) t The CP regression involves regressing the bond excess returns on the 12-month yield and all the forward rates: 53 rx 12n t+12 = γ 0 + γ 1 i 12 t + γ 2 f 24 t γ 10 f 120 t + ɛ t+12, for n = 2, 3..., 10 We borrow the concept of the CP regression, but modify it to a VAR(1) representation in order to obtain the predicted excess returns in the future periods. Specifically, we estimate the following VAR(1) system: CP t+1 µ = A(CP t µ) + e t where CP t = (rx 12n t+12, i 12 t, f 24 t,..., f 120 t ), for n = 2, 3,..., 10 After estimating the parameters, we iterate the VAR to obtain in-sample forecasts of the excess returns at any horizons: ĈP t+12h ˆµ = Â12h (ĈP t ˆµ), for h = 1, 2,...,, for all t The expected excess returns with 12n month maturity bond at t + 12h is the first column of ĈP t+12h. Next, by using the relationship between expected excess returns and term premiums, we calculate the term premiums: θ 12n t = 1 n n 2 ( ) E t rx 12(n h) t+12(h+1) h=0 53 In Cochrane-Piazzesi (2005), it runs a regression of the average excess return on the 12-month yield and all the forward rates, in the sense that expected excess returns of all maturities share the same single factor, and calls this single-factor model as a restricted model. Here, since we want to derive the term premiums at different maturities from the excess returns, we rely on an unrestricted model in which the excess returns at different maturities are assumed to have different factors. 32

34 We can easily prove this relationship by the definitions of excess returns and term premiums: < proof > RHS = 1 [ ] E t (rx 12n n t+12) + E t (rx 12(n 1) t+24 ) E t (rx 24 t+12(n 1)) = 1 [( )] ni 12n t (n 1)E t (i 12(n 1) t+12 ) i 12 t n + 1 [( )] (n 1)E t (i 12(n 1) t+12 ) (n 2)E t (i 12(n 2) t+24 ) E t (i 12 n t+12) [( 2Et (i 24 n t+12(n 2)) E t (i 12 t+12(n 1)) E t (i 12 t+12(n 2)) )] = 1 [ ni 12n t i 12 t E t (i 12 n t+12)... E t (i 12 t+12(n 2)) E t (i 12 t+12(n 1)) ] =i 12n t 1 n n 1 E t (i 12 t+12h) = LHS h=0 The expected yields then are defined as the difference between the term premiums and the actual yields at the same maturity. Then, relative expected yields and relative term premiums are calculated by the cross-county differences. D. VAR Multi-Period Predictions To compute the partial R 2 for each variable and their total contribution in the VAR, we follow the procedure as described in Hodrick (1992). The method is also adopted in Campbell and Shiller (1988), Kandel and Stambaugh (1988) and Campbell (1991), among others. The VAR models in Section 5 can be written as: f t = Af t 1 + e t where the constant term µ is omitted for notational convenience. Denote the information set at time t as I t, which includes all current and past values of f t. A forecast of horizon m can be written as E t (f t+m I t ) = A m f t. By repeated substitution, first-order VAR can be expressed in its MA( ) representation: f t = A j e t j j=0 where the covariance matrix of e t is Q. Then, the unconditional variance of f t can then be expressed as: C(0) = A j QA j j=0 33

35 Denoting C(j) as the jth-order covariance of f t, which is calculated as C(j) = A j C(0), the variance of the sum of m consecutive f t s, denoted as V m, is then: V m = mc(0) + m 1 j=1 (m j) [C(j) + C(j) ] We are not interested in the variance of the whole vector but only that of the long-horizon exchange rate change, s t, which is the third element in the vector f t. e 3 We can define = (0, 0, 1, 0, 0, 0), and express the variance of the m-period exchange rate change as e 3V m e 3. To assess whether a variable in f t, say the relative level factor L R t, explains exchange rate change s t+m = s t+m s t, we run a long-horizon regression of s t+m on L R t. VAR model for f t allows us to calculate the coefficient from this regression based on only the VAR coefficient estimates. Since the relative level factor is the fourth element in f t, the coefficient is defined as: β 4 (m) = e 3 [C(1) C(m)] e 4 e 4C(0)e 4 where vector e 4 is defined as e 4 = (0, 0, 0, 1, 0, 0). The numerator is the covariance between s t+m and L R t,and the denominator is the variance of L R t. the paper is calculated as: R 2 4(m) = β 4 (m) 2 e 4C(0)e 4 e 3V m e 3 The Finally, the R 2 as reported in The R 2 for all other variables in the vector f t can be suitably obtained by replacing e 4 with e 1, e 2, e 3, e 5, e 6. To calculate the total R 2 for all explanatory variables, we calculate the innovation variance of the exchange rate change as e 3W m e 3, where W m = m (I A) 1 (I A j )Q(I A j ) (I A) 1 j=1 The total R 2 is then: R 2 (m) = 1 e 3W m e 3 e mv m e m For the calculation to be valid, we need A to be stationary. 34

36 Table 1A. Summary Statistics for 3-Month Exchange Rate Change and Excess Currency Return AU CA DK JP NZ SE CH UK s t+3 Mean (-1.855) (-2.433) (-1.397) (0.931) (-1.255) (-1.554) (-1.188) (-1.636) (3.457) (3.763) (4.551) (1.037) (1.705) (4.353) (-0.581) (4.394) SD (19.257) (13.441) (18.850) (23.412) (21.480) (19.304) (20.042) (12.535) (33.275) (20.340) (22.020) (22.223) (30.762) (27.080) (20.647) (22.464) Median Min Max AR(1) xr t+3 Mean (3.542) (2.495) (1.038) (-4.616) (4.092) (1.524) (-1.026) (2.944) (-0.250) (-3.085) (-3.972) (-1.105) (1.209) (-3.623) (0.588) (-3.835) SD (19.949) (13.718) (19.351) (23.754) (21.924) (19.983) (20.526) (12.685) (33.142) (20.249) (21.906) (22.144) (30.213) (26.748) (20.637) (22.027) Median Min Max AR(1) Note: 1. s t+3 = s t+3 s t is the quarterly change of the exchange rate, where s t is the logged home currency price per USD. 2. xr t+3 = (i 3 t i US,3 t ) s t+3 is the excess currency return defined as the return difference between investing in the home bond over that of the US bond. 3. Sample period is from January, 1995 to March, All rates are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

37 Table 1B. Summary Statistics for Relative Level, Slope and Curvature Factors AU CA DK JP NZ SE CH UK L R t Mean (1.011) (0.298) (0.062) (-3.145) (0.977) (0.243) (-1.972) (-0.081) (0.895) (-0.638) (-0.886) (-2.632) (1.431) (-0.998) (-2.222) (0.001) SD (0.819) (0.742) (1.033) (0.703) (0.370) (1.350) (0.406) (1.026) (0.446) (0.354) (0.767) (0.741) (0.531) (0.522) (0.578) (0.335) Median Min Max AR(1) St R Mean (0.636) (-0.305) (-0.421) (-0.397) (1.899) (-0.355) (-0.181) (1.327) (2.238) (1.222) (1.411) (2.523) (1.307) (1.589) (2.280) (0.514) SD (1.768) (1.223) (1.806) (2.046) (1.727) (1.760) (1.461) (1.560) (0.807) (0.496) (0.849) (0.799) (1.262) (0.932) (0.682) (0.763) Median Min Max AR(1) Ct R Mean (0.289) (-0.048) (-0.775) (-2.273) (0.898) (-0.118) (-1.010) (1.377) (2.619) (2.105) (1.358) (2.786) (2.635) (2.371) (2.247) (0.479) SD (2.463) (1.762) (2.624) (2.765) (2.375) (2.468) (2.253) (2.158) (2.252) (1.614) (1.245) (1.141) (1.772) (1.921) (1.549) (1.158) Median Min Max AR(1) Note: 1. We estimate the Nelson-Siegel yield curve model to obtain the level, slope and curvature factors for each country. The US factors are then subtracted from those of the other countries to get the relative level L R t = L t L US t, slope St R = S t St US, and curvature Ct R = C t Ct US reported here. 2. Sample period is from January, 1995 to December, Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. 4. Note that positive relative level factor implies that the long-term yield of home country is relatively higher than that of the U.S. Positive relative slope factor implies that the yield curve slope of home country is relatively flatter than that of the U.S. Positive relative curvature factor implies that the yield curve of home country is relatively hump-shaped, compared to that of the U.S. 36

38 Table 1C. Summary Statistics for Macroeconomic Fundamentals AU CA DK JP NZ SE CH UK u R t Mean (0.013) (0.013) (0.027) (0.042) (-0.004) (-0.005) (0.038) (0.022) (-0.050) (-0.049) (-0.063) (-0.060) (-0.055) (-0.037) (-0.080) (-0.053) SD (0.319) (0.239) (0.342) (0.273) (0.374) (0.419) (0.388) (0.277) (0.325) (0.228) (0.360) (0.337) (0.373) (0.313) (0.421) (0.339) Median Min Max AR(1) πt R Mean (0.104) (-0.618) (-0.546) (-2.666) (-0.38) (-1.399) (-1.727) (-0.900) (0.898) (0.004) (0.095) (-1.257) (0.356) (-0.733) (-1.596) (0.962) SD (1.321) (0.757) (0.832) (1.139) (0.937) (1.213) (0.529) (0.880) (1.042) (0.871) (1.098) (1.765) (1.418) (0.955) (1.103) (1.117) Median Min Max AR(1) Note: 1. u R t = u t u US t is the relative unemployment rate, constructed as the difference between the detrended unemployment rates in the home country and in the U.S. Time series of unemployment rate is detrended by Hodrick-Prescott filter. 2. πt R = π t πt US is the relative inflation rate, defined as the 12-month change of the CPI in each country relative to that in the US. 3. Sample period is from January, 1995 to December, Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. 37

39 Table 1D. Correlation between Exchange Rate Change and Yield Factors AU CA DK JP NZ SE CH UK corr( s t+3,l R t ) (0.035) (0.004) (0.226) (0.198) (0.057) (0.036) (0.114) (0.031) (-0.113) (-0.248) (-0.139) (0.381) (-0.311) (-0.227) (0.052) (-0.175) corr( s t+3,s R t ) (-0.374) (-0.201) (-0.361) (-0.207) (-0.215) (-0.362) (-0.331) (-0.085) (0.306) (0.452) (0.322) (-0.253) (0.619) (0.553) (0.026) (0.646) corr( s t+3,c R t ) (-0.411) (-0.141) (-0.402) (-0.160) (-0.401) (-0.425) (-0.321) (-0.153) (-0.106) (-0.051) (0.196) (-0.008) (-0.024) (-0.043) (-0.144) (0.335) Note: 1. Sample period is from January, 1995 to March, Sample period is divided by the breakdate, May, Correlation coefficients before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. 38

40 Table 2A. 3-Month Exchange Rate Change on Relative Factors s t+3 = β 0,st + β 1,st L R t + β 2,st S R t + β 3,st C R t + ɛ t+3 1 if 1 t < τ 1 s t = 2 if τ 1 t < τ 2 3 if τ 2 t T. where τ 1, τ 2 : breakdates AU CA DK JP NZ SE CH UK β 0 s t = * ** (3.391) (2.039) (1.921) (15.811) (8.238) (1.886) (2.620) s t = ** ** ** * *** ** ** (41.211) (7.365) (10.917) (10.459) (47.577) (6.947) (9.246) (3.195) s t = *** *** (13.541) (4.649) (13.727) (23.481) (18.538) β 1 s t = ** ** (2.054) (2.257) (1.935) (5.194) (6.793) (1.112) (2.237) s t = *** *** (21.312) (5.861) (13.373) (8.976) (17.708) (6.522) (4.547) (6.007) s t = ** *** *** *** (6.991) (2.583) (22.712) (12.009) (13.587) β 2 s t = ** (1.886) (0.972) (1.783) (2.250) (1.307) (1.259) (1.270) s t = *** *** 8.973* *** *** *** *** (10.810) (5.723) (4.896) (8.566) (4.560) (4.937) (1.518) (2.752) s t = ** *** *** *** (7.513) (5.394) (22.572) (7.116) (11.503) β 3 s t = *** ** *** *** (0.946) (1.023) (1.033) (1.255) (1.213) (0.903) (0.967) s t = * *** ** *** (5.393) (1.392) (5.263) (2.399) (3.726) (1.712) (0.879) (2.171) s t = ** *** (2.417) (2.337) (2.461) (1.981) (3.557) p-value Adj. R τ 1 May,08 Jan,07 May,08 Jul,08 May,08 May,08 May,08 τ 2 Aug,11 Jun,11 Aug,12 Jun,11 Jun,11 Note: 1. We first regress 3-month exchange rate changes on the relative NS factors and then apply the Bai-Perron(2003) test(with 15%trimming and 5% significance level) to detect the multiple structural breaks in the regression. For some countries, structural breaks are detected in the late 90 s or early 00 s, but in order to capture the common structural break behavior across countries, 1 or 2 breaks are chosen to identify the Great Recession period, as reported in the last rows. The first break date is around , when the Global Financial Crisis has been triggered. The second break date is around Then, structural break dummy variables which identify each sub-period are incorporated into the regression. 2. Coefficient estimates are reported with the Newey-West standard errors in the parentheses. Asterisks indicate significance levels at 1% (***), 5% (**), and 10% (*) respectively. 3. P -value is for the Wald test that factors jointly have no explanatory power (H 0 : β 1,st = β 2,st = β 3,st = 0, s t ). 4. Adjusted R 2 is also reported. 39

41 Table 2B. 3-Month Excess Currency Return on Relative Factors xr t+3 = α 0,st + α 1,st L R t + α 2,st S R t + α 3,st C R t + ɛ t+3 1 if 1 t < τ 1 s t = 2 if τ 1 t < τ 2 3 if τ 2 t T. where τ 1, τ 2 : breakdates AU CA DK JP NZ SE CH UK α 0 s t = * 3.861** (3.387) (2.039) (1.923) (15.816) (8.226) (1.884) (2.620) s t = ** ** ** * *** ** ** (41.217) (7.371) (10.941) (10.450)0 (47.505) (6.945) (9.247) (3.194) s t = *** *** (13.535) (4.668) (13.727) (23.437) (18.553) α 1 s t = ** *** (2.051) (2.255) (1.934) (5.196) (6.784) (1.109) (2.237) s t = *** *** (21.341) (5.855) (13.384) (8.996) (17.678) (6.518) (4.548) (6.000) s t = ** *** *** ** (6.988) (2.582) (22.717) (11.985) (13.596) α 2 s t = *** * 2.422* (1.884) (0.973) (1.783) (2.252) (1.305) (1.256) (1.27) s t = *** *** *** *** *** *** (10.812) (5.725) (4.911) (8.581) (4.549) (4.927) (1.517) (2.741) s t = ** *** *** *** (7.512) (5.396) (22.577) (7.104) (11.509) α 3 s t = *** ** *** 3.250*** (0.942) (1.022) (1.033) (1.256) (1.210) (0.902) (0.966) s t = * *** 3.473** 2.390*** (5.387) (1.393) (5.267) (2.399) (3.722) (1.712) (0.879) (2.165) s t = ** *** (2.420) (2.347) (2.461) (1.979) (3.558) p-value Adj. R τ 1 May,08 Jan,07 May,08 Jul,08 May,08 May,08 May,08 τ 2 Aug,11 Jun,11 Aug,12 Jun,11 Jun,11 Note: 1. The break dates are chosen by the Bai-Perron(2003) test and incorporated into the regressions as described in Table 2A. 2. Coefficient estimates are reported with the Newey-West standard errors in the parentheses. Asterisks indicate significance levels at 1% (***), 5% (**), and 10% (*) respectively. 3. P -value is for the Wald test that factors jointly have no explanatory power (H 0 : α 1,st = α 2,st = α 3,st = 0, s t ). 4. Adjusted R 2 is also reported. 40

42 Table 3A. Summary Statistics for NS Relative Expected Yields L(E t i R t ) AU CA DK JP NZ SE CH UK Mean (1.552) (-1.806) (-0.511) (-3.306) (2.442) (-0.283) (-1.949) (1.012) (2.611) (0.822) (0.194) (-1.207) (2.431) (-0.141) (-0.781) (-0.715) SD S(E t i R t ) (0.880) (1.925) (0.861) (0.967) (0.839) (1.225) (0.874) (0.966) (0.874) (1.048) (0.751) (0.450) (0.940) (0.964) (0.535) (1.087) Mean (0.007) (1.764) (0.134) (-0.450) (0.349) (0.098) (-0.305) (0.216) (0.615) (-0.141) (0.336) (1.114) (0.424) (0.768) (0.899) (1.176) SD C(E t i R t ) (0.929) (2.126) (0.726) (0.875) (1.080) (1.084) (0.766) (1.154) (0.714) (0.900) (0.587) (0.347) (1.110) (1.009) (0.354) (0.849) Mean (-0.101) (0.733) (-0.049) (-0.129) (0.221) (-0.267) (-0.073) (0.050) (0.554) (-0.316) (0.268) (0.934) (0.206) (0.403) (0.627) (0.628) SD (0.557) (0.667) (0.603) (0.545) (0.563) (0.709) (0.537) (0.570) (0.747) (0.859) (0.648) (0.451) (0.662) (0.892) (0.496) (0.394) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Nelson-Siegel relative expected yield is computed as follows: First, the Nelson-Siegel latent factors are estimated by the state-space model and Kalman Filter, following Diebold, Rudebusch and Aruoba(2006). The measurement equation is i t = Λf t + e t, where i t = ( ), ( ) i 3 t, i 6 t,..., i 120 t ft = (L t, S t, C t ) and Λ = exp( λm). The transition equation is f t µ = A(f t 1 µ) + v t. 1, 1 exp( λm) λm, 1 exp( λm) λm Second, by iterating the V AR(1) representation of the transition equation, we obtain in-sample forecasts of NS factors. Third, by using the measurement equation, which is the Nelson-Siegel fitted yield, we obtain the predicted 1-month yield over future horizon. Lastly, the expected yield is constructed as the average expected relative 1 month yields over m consecutive months. The difference in the] expected yields between a country [î1 t+j pair is defined as the relative expected yield. E t i m t = 1 m 1 m j=0 E t and E t i R,m t = E t i m t E t i US,m t. See text for details. 2. The level, slope and curvature factors of the relative expected yields are constructed as follows: L(E t i R t ) = E t i R,120 t, S(E t i R t ) = E t i R,3 t E t i R,120 t, C(E t i R t ) = 2E t i R,24 t (E t i R,3 t + E t i R,120 t ). 3. Sample period is from January, 1995 to December, All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

43 Table 3B. Summary Statistics for NSM Relative Expected Yields L(E t i R t ) AU CA DK JP NZ SE CH UK Mean (1.366) (-0.994) (0.335) (-3.264) (2.790) (0.100) (-2.095) (1.081) (1.878) (-0.294) (-0.456) (-1.313) (2.195) (1.732) (-0.967) (0.642) SD S(E t i R t ) (0.932) (0.908) (0.830) (0.797) (1.469) (0.744) (0.667) (1.026) (0.858) (0.932) (0.970) (0.429) (1.124) (0.438) (0.471) (0.915) Mean (0.193) (0.949) (-0.745) (-0.427) (0.028) (-0.229) (-0.157) (0.196) (1.325) (0.976) (0.996) (1.274) (0.750) (-0.951) (1.065) (-0.143) SD C(E t i R t ) (1.179) (1.034) (1.203) (1.150) (1.609) (1.669) (0.966) (1.253) (0.610) (1.000) (0.621) (0.355) (0.893) (0.827) (0.527) (0.896) Mean (0.191) (0.879) (0.253) (0.232) (0.306) (0.676) (0.229) (0.902) (0.936) (0.629) (0.563) (1.190) (1.072) (1.289) (0.680) (-0.166) SD (0.592) (1.449) (1.436) (0.656) (0.671) (2.287) (0.656) (0.522) (1.056) (1.070) (0.829) (0.659) (0.872) (1.476) (0.822) (0.750) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Nelson-Siegel with Macro variables relative expected yield is computed as follows: First, the Nelson-Siegel latent factors are estimated by the state-space model and Kalman Filter, allowing the interaction between yield factors and macro variables as in Diebold, Rudebusch and Aruoba(2006). The measurement equation is i t = Λf t +e t, where i t = ( ) ), i 3 t, i 6 t,..., i 120 t Λ = (0, 0, 1, 1 exp( λm) λm, 1 exp( λm) λm exp( λm) and f t = (u t, π t, L t, S t, C t ). The transition equation is f t µ = A(f t 1 µ) + v t. Second, by iterating the V AR(1) representation of the transition equation, we obtain in-sample forecasts of NS factors. Third, by using the measurement equation, which is the Nelson-Siegel fitted yield, we obtain the predicted 1-month yield over future horizon. Lastly, the expected yield is constructed as the average expected relative 1 month yields over m consecutive months. The difference in the expected yields between a country pair is defined as the relative expected yield. E t i m t = 1 ] m 1 m j=0 E t [î1 t+j and E t i R,m t = E t i m t E t i US,m t. See text for details. 2. The level, slope and curvature factors of the relative expected yields are constructed as follows: L(E t i R t ) = E t i R,120 t, S(E t i R t ) = E t i R,3 t E t i R,120 t, C(E t i R t ) = 2E t i R,24 t (E t i R,3 t + E t i R,120 t ). 3. Sample period is from January, 1995 to December, All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

44 Table 3C. Summary Statistics for Affine Relative Expected Yields L(E t i R t ) AU CA DK JP NZ SE CH UK Mean (3.113) (1.127) (0.342) (-1.418) (3.148) (1.329) (-0.503) (2.493) (6.211) (3.288) (2.409) (2.843) (4.108) (3.832) (2.535) (1.061) SD S(E t i R t ) (1.947) (1.475) (1.825) (2.110) (1.791) (1.968) (1.809) (1.315) (1.212) (0.884) (1.013) (0.898) (1.615) (1.226) (0.916) (1.149) Mean (-1.494) (-1.188) (-0.761) (-2.370) (-0.303) (-1.429) (-1.746) (-1.201) (-2.943) (-2.554) (-1.854) (-2.839) (-1.206) (-3.125) (-2.367) (-0.559) SD C(E t i R t ) (0.695) (0.769) (0.639) (0.628) (0.982) (0.970) (0.581) (0.674) (0.819) (0.781) (0.669) (0.671) (1.657) (1.138) (0.695) (0.759) Mean (-1.681) (-1.401) (-0.823) (-2.347) (-0.370) (-1.637) (-1.705) (-1.077) (-2.592) (-2.139) (-1.726) (-2.627) (-1.195) (-2.717) (-2.305) (-0.708) SD (0.459) (0.592) (0.465) (0.248) (0.560) (0.770) (0.339) (0.212) (0.446) (0.286) (0.292) (0.090) (0.343) (0.648) (0.179) (0.159) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Affine relative expected yield is computed as follows: First, following the discrete-time affine Gaussian term structural model proposed by Ang and Piazzesi(2003) and mean-bias-correction model proposed by Bauer, Rudebusch and Wu(2012), the model-implied yields and the risk-neutral yields are estimated. Second, the expected yield is the risk-neutral yield and the difference in the expected yields between a country pair is defined as the relative expected yield. E t i R,m t = E t i m t E t i US,m t. See text for details. 2. The level, slope and curvature factors of the relative expected yields are constructed as follows: L(E t i R t ) = E t i R,120 t, S(E t i R t ) = E t i R,3 t E t i R,120 t, C(E t i R t ) = 2E t i R,24 t (E t i R,3 t + E t i R,120 t ). 3. Sample period is from January, 1995 to December, All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

45 Table 3D. Summary Statistics for CP Relative Expected Yields L(E t i R t ) AU CA DK JP NZ SE CH UK Mean (1.151) (-0.359) (-0.739) (-2.952) (2.299) (-1.260) (-1.753) (0.381) (2.213) (-0.266) (-1.044) (-0.759) (3.191) (-1.041) (-0.864) (0.426) SD S(E t i R t ) (0.843) (0.661) (0.802) (0.931) (0.837) (0.942) (0.865) (0.759) (0.827) (0.397) (1.023) (0.476) (0.673) (0.713) (0.534) (0.512) Mean (0.309) (0.294) (0.382) (-0.728) (0.126) (0.839) (-0.299) (0.697) (0.651) (0.865) (1.242) (0.521) (-0.286) (1.407) (0.667) (-0.073) SD C(E t i R t ) (0.799) (0.531) (0.794) (0.835) (0.749) (0.800) (0.614) (0.535) (0.559) (0.256) (0.309) (0.321) (0.632) (0.518) (0.293) (0.367) Mean (0.309) (0.210) (0.407) (-0.140) (0.022) (0.485) (0.051) (0.395) (0.186) (0.386) (0.491) (0.281) (-0.072) (0.644) (0.204) (-0.053) SD (0.287) (0.260) (0.239) (0.404) (0.403) (0.381) (0.282) (0.303) (0.522) (0.365) (0.392) (0.260) (0.333) (0.506) (0.345) (0.390) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Cochrane-Piazessi relative expected yield is computed as follows: First, following the unrestricted Cochrane-Piazessi regression(cochrane and Piazessi, 2003), the excess return of multi year bond over 1 year bond is regressed on 1 year yields and forward rates at 2 to 10 year forward rates, using V AR(1) representation. f t µ = A(f t 1 µ) + v t, where f t = ( rx 12n t, i 12 t, ft 24,..., ft 120 ), rx 12n t = ni 12n t (n 1)i 1 t+122(n 1) i 12 t, ft 12n = i 2n t (n 1)i 12(n 1) t for n = 2, 3,..., 10. Second, by iterating the V AR(1) process, we obtain in-sample forecasts of excess returns. Third, by using the relationship between the excess return and the term premium, we obtain the term premium at each maturity. Lastly, the expected yield is difference between the actual yields and term premiums. And the difference in the expected yields between a country pair is defined as the relative expected yield. E t i R,m t = E t i m t E t i US,m t. See text for details. 2. The level, slope and curvature factors of the relative expected yields are constructed as follows: L(E t i R t ) = E t i R,120 t, S(E t i R t ) = E t i R,24 t E t i R,120 t, C(E t i R t ) = 2E t i R,48 t (E t i R,24 t + E t i R,120 t ). Since the shortest maturity of the relative expected yield from the CP approach is 24 month, the factors of CP model is calculated using 24, 48 and120 month maturities rather than 3, 24 and120 month maturities as in NS, NSM and Affine model. 3. Sample period is from January, 1996 to December, All relative factors are reported in annualized percentage points. The length of sample period is 1 year shorter than other models because the estimates are based on the 1 year-holding excess return. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

46 Table 4A. Summary Statistics for NS Relative Term Premiums L(θ R t ) AU CA DK JP NZ SE CH UK Mean (-0.451) (2.035) (0.433) (-0.121) (-1.142) (0.440) (-0.180) (-0.763) (-1.123) (-1.054) (-0.708) (-0.798) (-0.539) (-0.395) (-0.832) (0.816) SD S(θ R t ) (0.703) (2.408) (1.002) (0.915) (0.518) (0.674) (0.541) (0.656) (0.575) (1.018) (0.533) (0.759) (0.710) (0.787) (0.515) (0.938) Mean (0.444) (-2.029) (-0.421) (0.071) (1.088) (-0.406) (0.146) (0.757) (1.084) (1.054) (0.692) (0.778) (0.557) (0.421) (0.788) (-0.785) SD C(θ R t ) (0.662) (2.272) (0.958) (0.898) (0.485) (0.651) (0.522) (0.590) (0.526) (0.982) (0.489) (0.699) (0.653) (0.723) (0.473) (0.854) Mean (0.317) (-0.653) (-0.216) (-0.545) (0.277) (0.291) (-0.207) (0.513) (0.361) (1.046) (0.283) (0.201) (0.675) (0.500) (0.071) (-0.35) SD (0.295) (0.664) (0.329) (0.472) (0.270) (0.358) (0.308) (0.259) (0.182) (0.367) (0.160) (0.173) (0.202) (0.376) (0.186) (0.276) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Nelson-Siegel relative term premium is computed as follows: First, using the state-space model, Kalman filter and iterated V AR(1), the expected in-sample forecasts of NS factors are estimated, as described in Table 3A. Second, using the Nelson-Siegel formula, expected relative 1-month yields and the fitted m month yields are constructed. Third, the term premium is defined as the difference between the fitted m month yield and the average expected relative 1 month yields over m consecutive months, which is the expected m month yield. The difference in the term premiums between a country pair is defined as the relative term premiums. θt m = î,m t 1 [îr,1 ] m 1 m j=0 E t t+j and θ R,m t = θt m θ US,m t. See text for details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θt R ) = θ R,120 t, S(θt R ) = θ R,3 t θ R,120 t, C(θt R ) = 2θ R,24 t (θ R,3 t + θ R,120 t ). 3. Sample period is from January, 1995 to December, All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

47 Table 4B. Summary Statistics for NSM Relative Term Premiums L(θ R t ) AU CA DK JP NZ SE CH UK Mean (-0.263) (1.223) (-0.429) (-0.169) (-1.488) (0.055) (-0.032) (-0.829) (-0.387) (0.065) (-0.073) (-0.629) (-0.300) (-2.267) (-0.643) (-0.551) SD S(θ R t ) (0.919) (0.752) (0.448) (0.726) (1.380) (1.500) (0.359) (0.480) (0.439) (0.825) (0.599) (0.571) (1.393) (0.508) (0.525) (0.773) Mean (0.255) (-1.218) (0.403) (0.051) (1.400) (-0.076) (-0.005) (0.765) (0.371) (-0.070) (0.061) (0.559) (0.232) (2.142) (0.620) (0.543) SD C(θ R t ) (0.892) (0.761) (0.415) (0.690) (1.342) (1.354) (0.330) (0.412) (0.414) (0.771) (0.492) (0.465) (1.404) (0.505) (0.412) (0.645) Mean (0.032) (-0.788) (-0.462) (-0.886) (0.196) (-0.635) (-0.502) (-0.327) (-0.021) (0.101) (-0.055) (-0.127) (-0.195) (-0.391) (0.016) (0.456) SD (0.646) (1.244) (0.821) (0.434) (0.364) (1.663) (0.418) (0.583) (0.574) (0.691) (0.516) (0.352) (0.470) (0.931) (0.477) (0.469) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Nelson-Siegel with Macro variables relative term premium is computed as follows: First, using the state-space model, Kalman filter and iterated V AR(1), the expected in-sample forecasts of NS factors are estimated, as described in Table 3B. Second, using the Nelson-Siegel formula, expected relative 1-month yields and the fitted m month yields are constructed. Third, the term premium is defined as the difference between the fitted m month yield and the average expected relative 1 month yields over m consecutive months, which is the expected m month yield. The difference in the term premiums between a country pair is defined as the relative term premiums. θt m = î,m t 1 [îr,1 ] m 1 m j=0 E t t+j and θ R,m t = θt m θ US,m t. See text for details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θt R ) = θ R,120 t, S(θt R ) = θ R,3 t θ R,120 t, C(θt R ) = 2θ R,24 t (θ R,3 t + θ R,120 t ). 3. Sample period is from January, 1995 to December, All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

48 Table 4C. Summary Statistics for Affine Relative Term Premiums L(θ R t ) AU CA DK JP NZ SE CH UK Mean (-1.972) (-0.856) (-0.419) (-1.968) (-1.789) (-1.186) (-1.556) (-2.275) (-4.762) (-3.567) (-2.962) (-4.830) (-2.284) (-4.414) (-4.192) (-0.970) SD S(θ R t ) (1.824) (1.385) (1.906) (1.979) (1.453) (1.791) (1.478) (1.349) (0.962) (0.853) (0.825) (1.182) (1.436) (1.145) (0.968) (1.020) Mean (1.957) (0.906) (0.421) (1.958) (1.721) (1.194) (1.547) (2.244) (4.709) (3.533) (2.944) (4.779) (2.296) (4.406) (4.143) (0.974) SD C(θ R t ) (1.773) (1.349) (1.848) (1.920) (1.417) (1.758) (1.439) (1.305) (0.900) (0.795) (0.764) (1.116) (1.365) (1.062) (0.912) (0.975) Mean (1.820) (1.452) (0.606) (1.708) (0.730) (1.618) (1.395) (1.587) (3.479) (2.868) (2.212) (3.585) (2.074) (3.540) (2.998) (0.943) SD (0.895) (0.723) (0.986) (0.934) (0.829) (1.040) (0.803) (0.647) (0.415) (0.385) (0.258) (0.319) (0.650) (0.477) (0.407) (0.458) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Affine relative term premium is computed as follows: First, following the discretetime affine Gaussian term structural model proposed by Ang and Piazzesi(2003) and mean-bias-correction model proposed by Bauer, Rudebusch and Wu(2012), the model-implied yields and the risk-neutral yields are estimated. Second, the term premium is defined as the difference between the model-implied yields and the risk-neutral yields. The difference in the term premiums between a country pair is defined as the relative term premiums. θ R,m t = θt m θ US,m t. See text for details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θt R ) = θ R,120 t, S(θt R ) = θ R,3 t θ R,120 t, C(θt R ) = 2θ R,24 t (θ R,3 t + θ R,120 t ). 3. Sample period is from January, 1995 to Decembr, All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

49 Table 4D. Summary Statistics for CP Relative Term Premiums L(θ R t ) AU CA DK JP NZ SE CH UK Mean (-0.146) (0.509) (0.555) (-0.482) (-0.924) (1.192) (-0.331) (-0.245) (-0.707) (0.070) (0.536) (-1.104) (-1.302) (0.513) (-0.741) (-0.289) SD S(θ R t ) (0.481) (0.411) (0.518) (0.477) (0.403) (0.585) (0.399) (0.522) (0.454) (0.246) (0.460) (0.204) (0.346) (0.337) (0.327) (0.387) Mean (0.054) (-0.418) (-0.627) (0.278) (0.699) (-0.991) (0.047) (0.141) (0.637) (-0.083) (-0.488) (0.854) (1.240) (-0.407) (0.513) (0.307) SD C(θ R t ) (0.344) (0.227) (0.382) (0.356) (0.263) (0.310) (0.334) (0.439) (0.303) (0.186) (0.309) (0.201) (0.283) (0.202) (0.315) (0.243) Mean (-0.251) (-0.183) (-0.623) (-0.324) (0.168) (-0.549) (-0.262) (-0.145) (0.266) (-0.034) (-0.300) (0.022) (0.587) (-0.143) (0.067) (0.291) SD (0.211) (0.176) (0.244) (0.206) (0.198) (0.233) (0.187) (0.296) (0.192) (0.163) (0.142) (0.150) (0.185) (0.234) (0.193) (0.249) corr(l,s) corr(l,c) corr(s,c) Note: 1. The Cochrane-Piazessi relative expected yield is computed as follows: First, following the unrestricted Cochrane-Piazessi regression with V AR(1) representation, and iterated V AR(1), we obtain insample forecasts of excess returns. Second, by using the relationship between the excess return and the term premium, we obtain the term premium at each maturity. The difference in the term premiums between a country pair is defined as the relative term premiums. θ R,m t = θt m θ US,m t. See text for details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θt R ) = θ R,120 t, S(θt R ) = θ R,24 t θ R,120 t, C(θt R ) = 2θ R,48 t (θ R,24 t + θ R,120 t ). Since the shortest maturity of the relative term premium from the CP approach is 24 month, the factors of CP model is calculated using 24, 48 and120 month maturities rather than 3, 24 and120 month maturities. 3. Sample period is from January, 1996 to December, All relative factors are reported in annualized percentage points. The length of sample period is 1 year shorter than other models because the estimates are based on the 1 year-holding excess return. 4. Sample period is divided by the breakdate, May, Mean and standard deviation before and after the breakdate are reported in brackets; those before the breakdate in the first bracket and those after the breakdate in the second bracket. The breakdate is chosen, considering that the most common breakdate by the structural break tests in the later sections is May,

50 Table 5A. Predicting 3-Month Exchange Rate Change with Relative Expected Yields 1) NS model s t+3 = β 0,st + β 1,st L(E t i R t ) + β 2,st S(E t i R t ) + β 3,st C(E t i R t ) + ɛ t+3 s t = 1 (if 1 t < τ 1 ), 2 (if τ 1 t < τ 2 ), 3 (if τ 2 t T ). AU CA DK JP NZ SE CH UK p-value s t = 1 (0.000) (0.001) (0.000) (0.018) (0.000) (0.001) (0.150) s t = 2 (0.000) (0.001) (0.197) (0.002) (0.000) (0.022) (0.000) (0.000) s t = 3 (0.215) (0.033) (0.000) (0.001) (0.000) (0.839) (0.304) Adj. R τ 1 May,08 Jan,07 May,08 May,08 May,08 Feb,08 May,08 τ 2 Jun,11 Jun,10 Aug,12 Jun,11 Jan,12 Jun,11 Jun,11 2) NSM model p-value s t = 1 (0.000) (0.000) (0.000) (0.006) (0.000) (0.002) (0.537) s t = 2 (0.000) (0.000) (0.000) (0.014) (0.000) (0.000) (0.000) (0.000) s t = 3 (0.000) (0.000) (0.013) (0.001) (0.000) (0.628) (0.009) Adj. R τ 1 May,08 Jan,07 May,08 May,08 May,08 Jun,07 Jun,08 τ 2 Dec,12 May,12 Aug,12 Jun,11 Feb,12 Jun,11 Jul,11 3) Affine model p-value s t = 1 (0.000) (0.000) (0.000) (0.007) (0.002) (0.000) (0.001) (0.379) s t = 2 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.002) (0.000) s t = 3 (0.004) (0.000) (0.002) (0.001) (0.885) (0.188) Adj. R τ 1 May,08 Jan,07 May,08 Sep,08 May,08 May,08 Feb,08 May,08 τ 2 Dec,12 Jun,11 Jun,11 Feb,12 Jun,11 Aug,11 4) CP model p-value s t = 1 (0.219) (0.013) (0.000) (0.000) (0.000) (0.006) (0.007) s t = 2 (0.000) (0.000) (0.025) (0.002) (0.000) (0.189) (0.000) (0.000) s t = 3 (0.000) (0.000) (0.000) (0.000) (0.000) (0.455) Adj. R τ 1 Jan,09 Jan,07 May,08 Apr,08 Oct,05 Oct,07 May,08 τ 2 Jan,13 Sep,12 Jun,11 Apr,10 Jun,11 May,11 Note: 1. The relative expected yield factors from 4 models are used in the above regression. 1) NS model, 2) NSM model, 3) Affine model, 4) CP model are described in Table 3A, 3B, 3C and 3D, respectively. 2. Structural breaks(τ 1, τ 2 ) are incorporated. 3. The p-value is for the Wald test that factors are jointly insignificant (H 0 : β 1,st = β 2,st = β 3,st = 0, s t ). The p-values for each sub-period divided by the break dates are also reported in brackets. Newey-West standard errors are used for the Wald test. 4. Adjusted R 2 is also reported. 49

51 Table 5B. Predicting 3-Month Excess Currency Return with Relative Expected Yields 1) NS model xr t+3 = α 0,st + α 1,st L(E t i R t ) + α 2,st S(E t i R t ) + α 3,st C(E t i R t ) + ɛ t+3 s t = 1 (if 1 t < τ 1 ), 2 (if τ 1 t < τ 2 ), 3 (if τ 2 t T ). AU CA DK JP NZ SE CH UK p-value s t = 1 (0.002) (0.016) (0.000) (0.046) (0.000) (0.004) (0.243) s t = 2 (0.000) (0.000) (0.130) (0.024) (0.000) (0.016) (0.000) (0.000) s t = 3 (0.207) (0.031) (0.000) (0.001) (0.000) (0.818) (0.298) Adj. R τ 1 May,08 Jan,07 May,08 May,08 May,08 Feb,08 May,08 τ 2 Jun,11 Jun,10 Aug,12 Jun,11 Jan,12 Jun,11 Jun,11 2) NSM model p-value s t = 1 (0.000) (0.001) (0.000) (0.015) (0.000) (0.012) (0.797) s t = 2 (0.000) (0.000) (0.000) (0.152) (0.000) (0.000) (0.000) (0.000) s t = 3 (0.000) (0.000) (0.013) (0.001) (0.000) (0.564) (0.009) Adj. R τ 1 May,08 Jan,07 May,08 May,08 May,08 Jun,07 Jun,08 τ 2 Dec,12 May,12 Aug,12 Jun,11 Feb,12 Jun,11 Jul,11 3) Affine model p-value s t = 1 (0.000) (0.002) (0.000) (0.035) (0.005) (0.000) (0.005) (0.598) s t = 2 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) s t = 3 (0.003) (0.000) (0.001) (0.001) (0.871) (0.179) Adj. R τ 1 May,08 Jan,07 May,08 Sep,08 May,08 May,08 Feb,08 May,08 τ 2 Dec,12 Jun,11 Jun,11 Feb,12 Jun,11 Aug,11 4) CP model p-value s t = 1 (0.477) (0.078) (0.002) (0.003) (0.000) (0.027) (0.027) s t = 2 (0.000) (0.000) (0.014) (0.010) (0.000) (0.134) (0.000) (0.000) s t = 3 (0.000) (0.000) (0.000) (0.000) (0.000) (0.456) Adj. R τ 1 Jan,09 Jan,07 May,08 Apr,08 Oct,05 Oct,07 May,08 τ 2 Jan,13 Sep,12 Jun,11 Apr,10 Jun,11 May,11 Note: 1. The relative expected yield factors from 4 models are used in the above regression. 1) NS model, 2) NSM model, 3) Affine model, 4) CP model are described in Table 3A, 3B, 3C and 3D, respectively. 2. Structural breaks(τ 1, τ 2 ) are incorporated. 3. The p-value is for the Wald test that relative expected yield factors are jointly insignificant (H 0 : α 1,st = α 2,st = α 3,st = 0, s t ). Newey-West standard errors are used for the Wald test. The p-values for each sub-period divided by the break dates are also reported in brackets. 4. Adjusted R 2 is also reported. 50

52 Table 6A. Predicting 3-Month Exchange Rate Change with Relative Term Premiums 1) NS model s t+3 = β 0,st + β 1,st S(θ R t ) + β 2,st C(θ R t ) + ɛ t+3 s t = 1 (if 1 t < τ 1 ), 2 (if τ 1 t < τ 2 ), 3 (if τ 2 t T ). AU CA DK JP NZ SE CH UK p-value s t = 1 (0.064) (0.085) (0.000) (0.009) (0.041) (0.079) s t = 2 (0.000) (0.001) (0.633) (0.001) (0.000) (0.016) (0.000) (0.000) s t = 3 (0.018) (0.177) (0.097) (0.061) Adj. R τ 1 May,08 Oct,07 May,08 Jan,09 May,08 May,08 τ 2 Dec,12 Jun,11 Aug,12 Jun,11 2) NSM model p-value s t = 1 (0.133) (0.225) (0.267) (0.460) (0.674) (0.041) s t = 2 (0.000) (0.001) (0.054) (0.000) (0.000) (0.000) (0.000) (0.005) s t = 3 (0.040) (0.420) (0.000) (0.014) (0.016) Adj. R τ 1 May,08 Oct,07 May,08 Mar,08 May,08 Oct,08 τ 2 Dec,12 Aug,12 May,12 My,12 Jun,11 3) Affine model p-value s t = 1 (0.000) (0.066) (0.000) (0.000) (0.061) (0.310) s t = 2 (0.014) (0.000) (0.509) (0.005) (0.000) (0.736) (0.000) (0.000) s t = 3 (0.744) (0.103) (0.000) (0.128) (0.684) (0.023) Adj. R τ 1 May,08 May,08 Mar,08 May,08 Jul,09 May,08 τ 2 Jun,11 Jun,11 Apr,10 Jun,11 Jun,11 Aug,11 4) CP model p-value s t = 1 (0.079) (0.024) (0.000) (0.162) (0.020) (0.002) (0.036) (0.606) s t = 2 (0.002) (0.102) (0.011) (0.006) (0.005) (0.246) (0.008) (0.002) s t = 3 (0.267) (0.056) (0.362) (0.628) Adj. R τ 1 May,08 Oct,07 Sep,05 May,07 Feb,08 Mar,08 Jun,07 Sep,07 τ 2 Jun,11 Feb,12 Jun,11 Sep,10 Note: 1. The relative term premium factors from 4 models are used in the above regression. 1) NS model, 2) NSM model, 3) Affine model, 4) CP model are described in Table 4A, 4B, 4C and 4D, respectively. 2. Structural breaks(τ 1, τ 2 ) are incorporated. 3. The p-value is for the Wald test that factors are jointly insignificant (H 0 : β 1,st = β 2,st = 0, s t ). The p-values for each sub-period divided by the break dates are also reported in brackets. Newey-West standard errors are used for the Wald test. 4. Adjusted R 2 is also reported. 51

53 Table 6B. Predicting 3-Month Excess Currency Return with Relative Term Premiums 1) NS model xr t+3 = α 0,st + α 1,st S(θ R t ) + α 2,st C(θ R t ) + ɛ t+3 s t = 1 (if 1 t < τ 1 ), 2 (if τ 1 t < τ 2 ), 3 (if τ 2 t T ). AU CA DK JP NZ SE CH UK p-value s t = 1 (0.095) (0.105) (0.000) (0.019) (0.068) (0.126) s t = 2 (0.000) (0.002) (0.672) (0.007) (0.000) (0.009) (0.001) (0.000) s t = 3 (0.018) (0.155) (0.097) (0.053) Adj. R τ 1 May,08 Oct,07 May,08 Jan,09 May,08 May,08 τ 2 Dec,12 Jun,11 Aug,12 Jun,11 2) NSM model p-value s t = 1 (0.140) (0.403) (0.259) (0.579) (0.482) (0.048) s t = 2 (0.000) (0.001) (0.070) (0.001) (0.000) (0.000) (0.000) (0.006) s t = 3 (0.041) (0.421) (0.000) (0.019) (0.016) Adj. R τ 1 May,08 Oct,07 May,08 Mar,08 May,08 Oct,08 τ 2 Dec,12 Aug,12 May,12 My,12 Jun,11 3) Affine model p-value s t = 1 (0.000) (0.159) (0.000) (0.001) (0.053) (0.551) s t = 2 (0.012) (0.000) (0.479) (0.048) (0.000) (0.596) (0.003) (0.000) s t = 3 (0.689) (0.109) (0.000) (0.107) (0.656) (0.022) Adj. R τ 1 May,08 May,08 Mar,08 May,08 Jul,09 May,08 τ 2 Jun,11 Jun,11 Apr,10 Jun,11 Jun,11 Aug,11 4) CP model p-value s t = 1 (0.146) (0.059) (0.000) (0.429) (0.040) (0.007) (0.072) (0.692) s t = 2 (0.002) (0.113) (0.004) (0.004) (0.005) (0.291) (0.006) (0.002) s t = 3 (0.336) (0.067) (0.362) (0.640) Adj. R τ 1 May,08 Oct,07 Sep,05 May,07 Feb,08 Mar,08 Jun,07 Sep,07 τ 2 Jun,11 Feb,12 Jun,11 Sep,10 Note: 1. The relative term premium factors from 4 models are used in the above regression. 1) NS model, 2) NSM model, 3) Affine model, 4) CP model are described in Table 3A, 3B, 3C and 3D, respectively. 2. Structural breaks(τ 1, τ 2 ) are incorporated. 3. The p-value is for the Wald test that factors are jointly insignificant (H 0 : α 1,st = α 2,st = 0, s t ). The p-values for each sub-period divided by the break dates are also reported in brackets. Newey-West standard errors are used for the Wald test. 4. Adjusted R 2 is also reported. 52

54 Table 7A. Explaining Exchange Rate Change Expectation, Risk, or Both from NSM model s t+3 = β 0,st + β 1,st L(E t i R t ) + β 2,st S(E t i R t ) + β 3,st C(E t i R t ) + β 4,st S(θ R t ) + β 5,st C(θ R t ) + ɛ t+3 1 if 1 t < τ 1 s t = 2 if τ 1 t < τ 2 3 if τ 2 t T. where τ 1, τ 2 : breakdates Wald test p-values AU CA DK JP NZ SE CH UK No Expectation? s t = 1 (0.000) (0.005) (0.001) (0.007) (0.002) (0.000) (0.168) (0.641) s t = 2 (0.613) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000) s t = 3 (0.103) (0.000) (0.079) (0.000) (0.001) (0.068) No Risk? s t = 1 (0.275) (0.982) (0.814) (0.000) (0.254) (0.366) (0.633) (0.022) s t = 2 (0.017) (0.180) (0.386) (0.000) (0.000) (0.483) (0.424) (0.072) s t = 3 (0.649) (0.003) (0.237) (0.000) (0.000) (0.188) Random Walk? s t = 1 (0.000) (0.000) (0.000) (0.000) (0.009) (0.000) (0.026) (0.101) s t = 2 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) s t = 3 (0.000) (0.000) (0.002) (0.000) (0.000) (0.000) Adj. R τ 1 May,08 Jan,07 May,08 Sep,08 May,08 May,08 Jun,07 Jun,08 τ 2 Dec,12 Aug.11 Jun,11 Dec,12 Jun,11 Jul,11 Note: 1. The relative expected yield factors and the relative term premium factors are extracted from NSM model. The estimation method is described in Table 3B and 4B. We perform the Belsley collinearity test(belsley, 1991) to detect any multicollinearity among regressors and find no severe collinearity. 2. The row labeled No Expectation reports the p-values of the Wald tests for the null hypothesis that relative expected yield factors have no explanatory power (β 1,st = β 2,st = β 3,st = 0, s t ), and the No Risk row tests the null hypothesis that relative term premium factors do not matter (β 4,st = β 5,st = 0, s t ). Random Walk tests the null that exchange rate follows a random walk with a possible drift (β i,st = 0, s t and i). Newey-West standard errors are used for the regressions. 3. The Wald tests are performed for each subperiod divided by the break dates. For example, No Yields when s t = 1 test the null hypothesis that relative yield curve factors have no explanatory power when s t = 1 (β 1,st=1 = β 2,st=1 = β 3,st=1 = 0) 4. Adjusted R 2 is also reported. 53

55 Table 7B. Explaining Exchange Rate Change Expectation, Risk, or Both from Affine model s t+3 = β 0,st + β 1,st L(E t i R t ) + β 2,st S(E t i R t ) + β 3,st C(E t i R t ) + β 4,st S(θ R t ) + β 5,st C(θ R t ) + ɛ t+3 1 if 1 t < τ 1 s t = 2 if τ 1 t < τ 2 3 if τ 2 t T. where τ 1, τ 2 : breakdates Wald test p-values AU CA DK JP NZ SE CH UK No Expectation? s t = 1 (0.034) (0.163) (0.319) (0.031) (0.813) (0.000) (0.336) (0.846) s t = 2 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.002) s t = 3 (0.000) (0.000) (0.000) (0.000) (0.000) (0.163) No Risk? s t = 1 (0.202) (0.145) (0.414) (0.046) (0.256) (0.118) (0.090) (0.905) s t = 2 (0.019) (0.000) (0.133) (0.079) (0.742) (0.023) (0.000) (0.952) s t = 3 (0.001) (0.027) (0.016) (0.006) (0.000) (0.000) Random Walk? s t = 1 (0.000) (0.120) (0.000) (0.022) (0.012) (0.000) (0.012) (0.845) s t = 2 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) s t = 3 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Adj. R τ 1 May,08 Jul,08 May,08 Sep,08 May,08 May,08 Jan,09 May,08 τ 1 Jun,11 Jun,11 Jun,11 Feb,12 Nov,12 Aug,11 Note: 1. The relative expected yield factors and the relative term premium factors are extracted from Affine model. The estimation method is described in Table 3C and 4C. We perform the Belsley collinearity test(belsley, 1991) to detect any multicollinearity among regressors and find no severe collinearity. 2. The row labeled No Expectation reports the p-values of the Wald tests for the null hypothesis that relative expected yield factors have no explanatory power (β 1,st = β 2,st = β 3,st = 0, s t ), and the No Risk row tests the null hypothesis that relative term premium factors do not matter (β 4,st = β 5,st = 0, s t ). Random Walk tests the null that exchange rate follows a random walk with a possible drift β 0,st (β i,st = 0, s t and i). Newey-West standard errors are used for the regressions. 3. The Wald tests are performed for each subperiod divided by the break dates. For example, No Yields when s t = 1 test the null hypothesis that relative yield curve factors have no explanatory power when s t = 1 (β 1,st=1 = β 2,st=1 = β 3,st=1 = 0) 4. Adjusted R 2 is also reported. 54

56 Table 8A. Explaining Exchange Rate Changes s t+k with Relative Expected Yield Factors and Relative Term Premiium Factors [Entire sample period] from NSM model Hodrick s (1992) Partial R 2 k s t L(E t i R t ) S(E t i R t ) C(E t i R t ) S(θt R ) C(θt R ) Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom

57 [Before the first break] k s t L(E t i R t ) S(E t i R t ) C(E t i R t ) S(θt R ) C(θt R ) Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom

58 [After the first break] k s t L(E t i R t ) S(E t i R t ) C(E t i R t ) S(θt R ) C(θt R ) Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom Note: 1. The partial R 2 reports the contribution of each variable in explaining s t+k for k = 1, 3, 6, 12. It is constructed by first estimating f t µ = A(f t 1 µ)+v t, where f t = ( s t, L(E t i R t ), S(E t i R t ), C(E t i R t ), S(θt R ), C(θt R ) ), and then using  and the estimated covariance matrix of the V AR(1), as in Hodrick (1992). See text for details. 2. We report the partial R 2 for 3 different sample periods; 1) an entire sample period, from January, 1995 to March, 2016, 2) from January, 1995 to the first break, which is identified in Table 7A, 3) from the first break to March, Note that individual R 2 s do not add up to the total R 2 as the variables are correlated. 57

59 Table 8B. Explaining Exchange Rate Changes s t+k with Relative Expected Yield Factors and Relative Term Premiium Factors [Entire sample period] from Affine model Hodrick s (1992) Partial R 2 k s t L(E t i R t ) S(E t i R t ) C(E t i R t ) S(θt R ) C(θt R ) Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom

60 [Before the first break] k s t L(E t i R t ) S(E t i R t ) C(E t i R t ) S(θt R ) C(θt R ) Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom

61 [After the first break] k s t L(E t i R t ) S(E t i R t ) C(E t i R t ) S(θt R ) C(θt R ) Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom Note: 1. The partial R 2 reports the contribution of each variable in explaining s t+k for k = 1, 3, 6, 12. It is constructed by first estimating f t µ = A(f t 1 µ)+v t, where f t = ( s t, L(E t i R t ), S(E t i R t ), C(E t i R t ), S(θt R ), C(θt R ) ), and then using  and the estimated covariance matrix of the V AR(1), as in Hodrick (1992). See text for details. 2. We report the partial R 2 for 3 different sample periods; 1) an entire sample period, from January, 1995 to March, 2016, 2) from January, 1995 to the first break, which is identified in Table 7B, 3) from the first break to March, Note that individual R 2 s do not add up to the total R 2 as the variables are correlated. 60

62 Table 9. Explaining Exchange Rate Change Macroeconomic Fundamentals, Yield Factors, or Both? s t+3 = β 0,st + β 1,st L R t + β 2,st S R t + β 3,st C R t + β 4,st u R t + β 5,st π R t + ɛ t+3 1 if 1 t < τ 1 s t = 2 if τ 1 t < τ 2 3 if τ 2 t T. where τ 1, τ 2 : breakdates AU CA DK JP NZ SE CH UK Wald test p-values No Yields? s t = 1 (0.001) (0.025) (0.000) (0.058) (0.001) (0.109) (0.001) (0.612) s t = 2 (0.376) (0.000) (0.079) (0.000) (0.000) (0.000) (0.159) (0.000) s t = 3 (0.000) (0.003) (0.000) (0.000) No Macro? s t = 1 (0.636) (0.840) (0.105) (0.707) (0.005) (0.313) (0.207) (0.018) s t = 2 (0.024) (0.007) (0.000) (0.129) (0.227) (0.000) (0.000) (0.000) s t = 3 (0.759) (0.155) (0.000) (0.000) Random Walk? s t = 1 (0.000) (0.019) (0.000) (0.165) (0.000) (0.000) (0.003) (0.056) s t = 2 (0.001) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) s t = 3 (0.000) (0.004) (0.000) (0.000) Adj. R τ 1 May,08 Jan,07 May,08 Jul,08 May,08 May,08 Feb.08 May,08 τ 1 Jun,11 Jun,11 Nov,11 Nov,12 Note: 1. The row labeled No Yields reports the p-values of the Wald tests for the null hypothesis that relative yield curve factors have no explanatory power (β 1,st = β 2,st = β 3,st = 0, s t ), and the No Macro row tests the null hypothesis that macroeconomic fundamentals do not matter (β 4,st = β 5,st = 0, s t ). Random Walk tests the null that exchange rate follows a random walk with a possible drift (β i,st = 0, s t and i). Newey-West standard errors are used for the regressions. 2. The Wald tests are performed for each sub-period divided by the break dates. For example, No Yields when s t = 1 test the null hypothesis that relative yield curve factors have no explanatory power when s t = 1 (β 1,st=1 = β 2,st=1 = β 3,st=1 = 0) 3. Adjusted R 2 is also reported. 61

63 Table 10. Explaining Exchange Rate Changes s t+k with Macroeconomic Fundamentals and Yield Curve Factors [Entire sample period] Hodrick s (1992) Partial R 2 k u R t πt R s t L R t St R Ct R Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom

64 [Before the first break] k u R t πt R s t L R t St R Ct R Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom

65 [After the first break] k u R t πt R s t L R t St R Ct R Total R 2 Australia Canada Denmark Japan New Zealand Sweden Switzerland United Kingdom Note: 1. The partial R 2 reports the contribution of each variable in explaining s t+k for k = 1, 3, 6, 12. It is constructed by first estimating f t µ = A(f t 1 µ) + v t, where f t = ( ) u R t, πt R, s t, L R t, St R, Ct R, and then using  and the estimated covariance matrix of the V AR(1), as in Hodrick (1992). See text for details. 2. We report the partial R 2 for 3 different sample periods; 1) an entire sample period, from January, 1995 to March, 2016, 2) from January, 1995 to the first break, which is identified in Table 9, 3) from the first break to March, Note that individual R 2 s do not add up to the total R 2 as the variables are correlated. 64

66 Table 11. Predicting Exchange Rate Change In-Sample: Model Comparisons [Entire sample period] RMSE Ratios and Diebold-Mariano Statistics k AU CA DK JP NZ SE CH UK k = 1 RMSE(Macro/RW) * 0.977* (1.188) (0.800) (1.240) (0.348) (1.579) (1.743) (1.668) (0.690) RMSE (Yield/RW) ** (1.375) (1.373) (1.602) (1.289) (1.315) (2.207) (1.050) (0.319) RMSE(Joint/RW) ** * 0.960** 0.963** (1.464) (1.559) (2.058) (1.500) (1.850) (2.394) (1.988) (0.759) k = 3 RMSE(Macro/RW) 0.960* ** 0.944* (1.712) (0.971) (0.990) (0.625) (1.965) (1.851) (1.384) (0.912) RMSE (Yield/RW) 0.977* * 0.972* 0.956** (1.700) (1.363) (0.955) (1.852) (1.768) (2.084) (0.935) (0.369) RMSE(Joint/RW) 0.951** 0.953* ** 0.924** 0.905*** 0.947* (2.143) (1.661) (1.487) (2.078) (2.226) (2.787) (1.827) (0.912) k = 6 RMSE(Macro/RW) 0.938** *** 0.919** (2.356) (1.313) (1.040) (0.328) (2.659) (2.227) (1.445) (1.128) RMSE (Yield/RW) ** 0.970* 0.958** (1.296) (1.574) (1.024) (2.461) (1.739) (2.063) (1.159) (0.321) RMSE(Joint/RW) 0.929*** 0.927* *** 0.895*** 0.882*** (2.685) (1.933) (1.147) (2.748) (2.745) (3.048) (1.585) (1.051) k = 12 RMSE(Macro/RW) 0.933*** *** 0.913** (3.319) (1.391) (0.784) (-0.062) (3.601) (2.541) (1.013) (0.658) RMSE(Yield/RW) *** (0.769) (1.224) (0.932) (3.075) (0.447) (1.310) (1.416) (-0.060) RMSE(Joint/RW) 0.918*** 0.943* *** 0.904*** 0.921*** (3.097) (1.794) (0.748) (3.219) (3.272) (3.225) (1.170) (0.552) 65

67 [Before the first break] k AU CA DK JP NZ SE CH UK k = 1 RMSE(Macro/RW) * 0.962** (0.645) (0.507) (0.993) (0.531) (1.845) (1.964) (1.344) (1.559) RMSE (Yield/RW) 0.965* ** * 0.955** 0.970* (1.888) (1.316) (2.172) (0.782) (1.707) (2.269) (1.690) (1.240) RMSE(Joint/RW) 0.965* ** ** 0.951** 0.950** 0.968* (1.868) (1.412) (2.165) (1.338) (2.273) (2.370) (2.173) (1.789) k = 3 RMSE(Macro/RW) ** 0.898** (1.020) (0.704) (0.500) (-0.025) (2.101) (1.991) (0.475) (0.937) RMSE (Yield/RW) 0.897** ** ** 0.877*** (2.010) (1.184) (2.389) (1.175) (2.412) (2.646) (1.612) (0.640) RMSE(Joint/RW) 0.895** ** *** 0.867** (2.050) (1.155) (2.465) (1.170) (2.865) (2.488) (1.635) (1.127) k = 6 RMSE(Macro/RW) 0.957* *** 0.829** (1.715) (0.917) (0.653) (0.041) (3.011) (2.337) (0.271) (0.899) RMSE (Yield/RW) 0.826** *** 0.943** 0.861*** 0.803*** 0.863** (2.217) (1.250) (3.103) (2.222) (3.349) (3.100) (2.007) (0.486) RMSE(Joint/RW) 0.811** *** 0.940* 0.803*** 0.782*** 0.856* (2.377) (1.140) (3.049) (1.938) (3.491) (2.711) (1.913) (1.067) k = 12 RMSE(Macro/RW) 0.949*** *** 0.799*** (3.022) (1.549) (0.855) (1.242) (4.039) (3.280) (-0.230) (0.951) RMSE(Yield/RW) 0.808*** 0.840** 0.790*** 0.903*** 0.865*** 0.782*** 0.770** (2.802) (2.277) (3.441) (3.448) (4.233) (4.193) (2.573) (-0.409) RMSE(Joint/RW) 0.756*** 0.845* 0.763*** 0.888*** 0.775*** 0.745*** 0.769** (3.270) (1.845) (3.209) (3.614) (4.174) (3.696) (2.522) (0.844) 66

68 [After the first break] k AU CA DK JP NZ SE CH UK k = 1 RMSE(Macro/RW) ** (1.318) (1.005) (2.054) (0.751) (1.290) (1.001) (1.303) (1.148) RMSE (Yield/RW) ** ** (1.041) (2.209) (1.098) (1.193) (2.184) (1.626) (1.161) (0.713) RMSE(Joint/RW) *** 0.898** ** 0.877** 0.882** (1.334) (2.619) (2.185) (1.536) (2.442) (1.977) (1.973) (1.197) k = 3 RMSE(Macro/RW) 0.871* ** * 0.882* (1.757) (1.089) (2.327) (1.227) (1.444) (1.365) (1.739) (1.756) RMSE (Yield/RW) 0.914* 0.851** * 0.806** (1.659) (2.511) (1.373) (1.593) (1.854) (2.072) (0.328) (1.521) RMSE(Joint/RW) 0.860* 0.790*** 0.818** 0.818** 0.724** 0.736** 0.854** 0.717* (1.831) (2.767) (2.162) (1.960) (2.121) (2.410) (2.476) (1.925) k = 6 RMSE(Macro/RW) 0.863** ** * 0.928** 0.890** 0.835** (2.095) (1.365) (2.093) (1.095) (1.842) (1.997) (2.180) (1.969) RMSE (Yield/RW) 0.913** 0.825** * * (2.207) (2.521) (1.364) (1.895) (1.533) (1.959) (0.248) (1.432) RMSE(Joint/RW) 0.850** 0.767*** ** 0.763** ** (2.243) (2.647) (1.386) (1.282) (2.073) (2.336) (1.279) (1.978) k = 12 RMSE(Macro/RW) (0.379) (1.364) (0.347) (1.157) (0.623) (0.409) (1.194) (0.811) RMSE(Yield/RW) * (-0.080) (1.376) (1.044) (1.843) (-0.045) (0.163) (-0.982) (-0.334) RMSE(Joint/RW) (0.480) (0.682) (-0.359) (-0.405) (0.315) (-0.157) (-0.308) (-0.968) Note: 1. Predicted exchange rate changes E t ( s t+k ) for k = 1, 3, 6, 12 are generated by estimating a V AR(1): f t µ = A(f t 1 µ) + v t and then iterating it forward k-periods. Estimation and prediction is performed for 3 different sample periods: 1) an entire sample period, from January, 1995 to March, 2016, 2) from January, 1995 to the first break, which is identified in Table 7A, 3) from the first break to March, For the macro-only model (labelled Macro ), f t = ( ) u R t, πt R, s t. For the yield-only model(labelled Yield:), f t = ( ) ( ) s t, L R t, St R, Ct R. For the macro-finance model (labelled Joint ), ft = u R t, πt R, s t, L R t, St R, Ct R. 3. RMSE ratio reports the model root mean squared prediction errors over the ones from a random walk with a drift prediction. A ratio below 1 means the model has explanatory power. 4. The number in the parentheses below each ratio is the t-statistics from the Diebold-Mariano test of equal predictability, where a rejection indicates superior prediction from the model over the random walk. Asterisks indicate significance levels at 1% (***), 5% (**), and 10% (*) respectively. 67

69 Figure 1A: 3-Month Exchange Rate Change (Annualized %; Home Currency/USD) Note: 1. Figure 1A shows the quarterly change of the exchange rate, s t+3 = s t+3 s t, where s t is the logged home currency price per USD. 2. Sample period is from January, 1995 to March, All rates are in annualized percentage points. 68

70 Figure 1B: 3-Month Excess Currency Return (Annualized %; Home Currency/USD) Note: 1. Figure 1B shows the excess currency return, xr t+3 = (i 3 t i US,3 t ) s t Sample period is from January, 1995 to March, All rates are in annualized percentage points. 69

71 Figure 2A: Relative Yield Curves Before and After the Break (Annualized %) Note: 1. Figure 2A shows the monthly averages of relative yields, i R,m t = i m t i US,m t, over January, April, 2008 (Blue solid line) and over May, Dec, 2015 (Red dashed line). All yields are annualized. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May,

72 Figure 2B: Relative Yield Curve Factors over time Note: 1. Figure 2B shows the relative yield curve factors, estimated by the Nelson-Siegel model. Relative level factor, L R t = L t L US t is in blue. Relative slope factor, St R = S t St US is in red. Relative curvature factor, Ct R = C t Ct US is in green. 2. Note that these are the relative yield curve factors. Positive relative level factor implies that the long-term yield of home country is relatively higher than that of the U.S. Positive relative slope factor implies that the yield curve slope of home country is relatively flatter than that of the U.S.. Positive relative curvature factor implies that the yield curve of home country is relatively hump-shaped, compared to that of the U.S. 71

73 Figure 3A: Time-varying correlation between Exchange Rate Change and Relative Level Factor Note: Figure 3A shows the correlation between 3-month exchange rate change and relative level factor. Correlation coefficient is computed over 12-month moving windows. The first window is for January, December, 1995 and the last window is for January, December,

74 Figure 3B: Time-varying correlation between Exchange Rate Change and Relative Slope Factor Note: Figure 3B shows the correlation between 3-month exchange rate change and relative slope factor. Correlation coefficient is computed over 12-month moving windows. The first window is for January, December, 1995 and the last window is for January, December,

75 Figure 3C: Time-varying correlation between Exchange Rate Change and Relative Curvature Factor Note: Figure 3C shows the correlation between 3-month exchange rate change and relative curvature factor. Correlation coefficient is computed over 12-month moving windows. The first window is for January, December, 1995 and the last window is for January, December,