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

Kwok Ping Tsang

Byunghoon Nam

University of Washington

Virginia Tech

University of Washington

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, a¢ ne Gaussian dynamic model, and the Cochrane and Piazzesi (2005) model. We …rst …nd 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 …nd that expectations play a stronger and more consistent role over the full sample period, while risk measures pick up their signi…cance post-2008. 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 2009. 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 353330, Seattle, WA 98195; [email protected]. Tsang: Department of Economics, Virginia Tech, Box 0316, Blacksburg, VA, 24061; [email protected]. Nam: Department of Economics, University of Washington, Box 353330, Seattle, WA 98195; [email protected].

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 The 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 (1998), the incorporation of the exchange rate term to an otherwise standard Taylor rule has become commonplace in recent literature, especially for modeling

1

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. The joint macro-finance strategy has proven fruitful in modeling other financial assets such as the yield curves themselves.7 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. Our 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. On the other hand, term premiums in the yield curve measure the market pricing of systematic risk of various origins over different future horizons.8 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 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 et al. (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 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. 8 Kim and Orphanides (2007) and Wright (2009), 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.

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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 (hearafter, DRA 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 2016.9 For 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. 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 five alternative methods based on different concepts of terms structure modeling that are wellknown in the literature. These include the Nelson-Siegel latent factor model (hearafter, NS model), the Nelson-Siegel latent factor model which allows interaction with macro fundamentals as discussed in DRA 2006 (hearafter, NSM model), Ang and Piazzesi (2003)’s discrete-time affine Gaussian term structure model (hearafter, Affine model) and also the Cochrane and Piazzesi (2005) approach (hearafter, CP model).10 Based on these alternative 9

We present results based on the dollar cross rates, though the qualitative conclusions extend to other pair-wise combinations of currencies. 10 As an example for the NSM model, we use an estimated VAR that allows for dynamic interactions between macro fundamentals and the yield curve factors, to construct measures of expected 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 premium between each country-pair.

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and admittedly all incomplete measures of expectation and risk, we demonstrate that either ”expectations” or ”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 explains more of exchange rate changes. We test the joint significance of each category by the Wald test and report the Hodrick’s partial R2 (Hodrick, 1992) to show how much is explained by each factors. 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. We also examine the joint significance and explanatory power of yield curve factors and macro fundamentals. 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 more recently in Lettau and Ludvigson (2005).11 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; 3) expectations generally explain the exchange rate change more than risk for the full sample period, and risk, which is not a significant factor before 2008, plays a more or less significant role after 2008, even though the results are country-dependent and model-dependent; 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 11 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, West 2007).

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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 2.1

Theoretical Framework 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, it , and the foreign country sets a corresponding i∗t . To be consistent with our empirical results below, we designate the United States as the foreign country. 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 (1998) and previous work.12 The monetary policy rules can be expressed as: it = µt + βy yet + βπ πte + δqt + ut

(1)

iUt S = µUt S + βyU S yetU S + βπU S πtU S,e + uUt S where yet is the output gap, πte is the expected inflation, and qt (= st − (pt − pUt S )) is the real exchange rate, defined as the nominal exchange rate, st , adjusted by the CPI-price level difference between home and abroad, pt − pUt S . µt absorbs the inflation and output targets and the equilibrium real interest rate, and the stochastic shock ut 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 the same policy weights, and that βy = βyU S > 0, δ > 0, βπ = βπU S > 1, and µt and µUt S are time-invariant. Under rational expectations, efficient market condition equates cross-border interest rate differentials of maturity m, iR,m , with the expected rate of home currency depreciation t 12

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 (1998), Engel, West, and Mark (2007), and Molodtsova and Papell (2009), among many others.

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and the currency risk premium over the same horizon.13 This is the risk-adjusted uncovered interest rate parity condition (UIP): m,U S iR,m = im = Et ∆st+m + ρm t t − it t , ∀m

(2)

Here ∆st+m ≡ st+m − st , and ρm 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 ρm 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): st = γftT R + κρ1t + ψEt st+1 + vt

(3)

where ftT R = [pt −pUt S , yet − yetU S , πte −πtU S,e ]0 ; vt is a function of policy error shocks ut and uUt S ; and coefficient vectors, γ, κ, and ψ, are functions of structural parameters defined above.14 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: st = λ

∞ X

ψ

j

TR Et (ft+j |It )

+ζ

j=0

∞ X

ψ j Et (ρ1t+j |It ) + εt

(4)

j=0

where εt incorporates shocks, such as that to the currency risk (ζt ), and is assumed to be 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 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 θt 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 13

By assuming rational expectations, we do not explore role of systematic expectations errors in ρ. 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. 14

6

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.15 Since nominal exchange rate is best approximated by a unit root process empirically, we focus our analyses on exchange rate change, ∆st+m , as well as excess currency returns, which we define as: m,U S XRt+m = im − ∆st+m (= ρm t − it 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: im t ≡

m−1 1 X 1  Et it+j + θtm m j=0

(6)

where θt represents the term premium perceived at t associated with holding a long bond until t + m (θtm ). 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). 2.2.1

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 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 15

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.

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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.16 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.17 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 (at least) the first present value term on the right hand side of eq.(4). Since exchange rate fundamentals are in cross-country differences, we propose to use the relative expected yields, which are the differences in the averages of expected oneperiod yields for the current and coming m − 1 periods across countries, to proxy the first discounted sum in eq.(4). 16

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. 17 Dewachter and Lyrio (2006) and Bekaert et al (2006) 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 (2006) 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.

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2.2.2

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. 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 expectation hypothesis (EH) - with the presence of time-varying risk being the leading explanation for both empirical patterns.18 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. This 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: m,U S Et ∆st+m = im − ρm t − it t m−1 m−1 i 1 X h1 1 X S − Et it+j − i1,U Et ρ1t+j = t+j m j=0 m j=0

(7) (8)

Using eq.(6), the cross-border interest rate differentials of maturity m can be expressed as: im t

−

S im,U t

m−1 i 1 X h1 1,U S = Et it+j − it+j + (θtm − θtm,U S ) m j=0

(9)

Substituting eq.(9) into eq.(7) and comparing it with eq.(8), we can say the relative term premiums of maturity m is correlated with the currency risk premiums of the same maturity: m,U S m ρm )− t = (θt − θt

m−1 1 X Et ρ1t+j m j=0

(10)

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 (2009)), there appears to be less consensus on 18

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 (2009) and Rudebusch and Swanson (2009) are recent examples of research that studies how market information about future real and nominal risks are embedded in the bond term premiums.

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their empirical or structural relationship with the macroeconomy.19 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. In the empirical section below, we extract the time-varying term premiums based on alternative frameworks of yield curves, and study their linkage with currency risk premiums.20

3 3.1

Background Empirics Data Description

The main data we examine consists of monthly observations from January 1995 to March 2016 for Australia(AU), Canada(CA), Denmark(DM), Japan(JP), New Zealand(NZ), Sweden(SD), Switzerland(SW), 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.21 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 ∆st+m = st+m − st and annualized. Tables 1A-1C report the summary statistic of the data. Considering the potential structural break due to the Great Recession, the sample period is divided by the break date, May 2008.22 Mean and standard deviation before and after the break are reported in the brackets; those before the break in the first bracket and those after the break in the 19 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. 20 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. 21 Please refer to Kushnir(2009) for details on the construction of the data. 22 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.

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second bracket. For three-month exchange rate change ∆st+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 Japan and Switzerland, as standard deviation indicates. The two commodity currencies (Australian and New Zealand dollars) were not especially volatile, though certainly have the widest swings. Turning to excess returns, XRt+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.23 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 R in the factor-loadings, we extract three factors of relative level (LR t ), relative slope (St ), and relative curvature (CtR ) as follows:24  1 − exp(−λm) − exp(−λm) + m + = − = + t λm (11) As the number of yields is larger than the number of factors, eq.(11) cannot fit all the yields perfectly, so an error term m t is appended for each maturity as a measure of the goodness 25 of fit. We see that Australia and New Zealand have a higher level factor than the US on average while Japan and Switzerland have a lower level factor than the US on average. For iR,m t

im t

S im,U t

LR t

StR



1 − exp(−λm) λm



CtR



23 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. 24 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). 25 The parameter λ, is set to 0.0609, in accordance with the literature such as Diebold and Li (2006). It controls the particular maturity the loading on the curvature is maximized.

11

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 and thus reflects long-run expectations, the positive relative level factor implies that the inflation rate of home country is expected to be higher than that of the US and vice versa. 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, implying 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.26 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.27 Figure 2A shows the m,U S , ∀m, before and after the break. As monthly average of relative yields, iR,m = im t t − it 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 the two macro variables we use: the relative unemployment gap and inflation rate between each of the eight countries to those of the US. 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, compared to that of the US. Table 1D shows the correlation between quarterly exchange rate changes and each of the relative Nelson-Siegel factors. Again, considering the potential structural break, sample period is divided by the break date, May 2008. 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 countries. The correlation of exchange rate change with the relative level becomes stronger after the break, but the opposite is true for the correlation with the relative curvature. We further presents the time-varying property of correlation by showing correlation coefficients with rolling window, as in Figures 3A, 3B and 3C. We 26

See Chen and Tsang (2013) for a more complete discussion of the relative factors. 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. 27

12

will analyze the relationship between these variables with econometric models in the later sections, but for now, we can say that a structural break is potentially detected and should not be ignored when estimating the models.

3.2

Regress the Currency Movement on Relative Yield Factors

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: R R ∆st+3 = α0 + α1 LR t + α2 St + α3 Ct + t+3 R R XRt+3 = β0 + β1 LR t + β2 St + β3 Ct + t+3

(12) (13)

To address possible parameter instabilities, we test for endogenous structural breaks in the regression. This table reports results based on Bai and Perron (2003) multiple break tests(with 15%trimming and 5% significance level), which identified 1 to 3 breaks. In order to capture the common behavior changes across countries, 1 or 2 breaks are chosen to identify the Great Recession period. The first break date is around 2007 - 2008, when the Global Financial Crisis has been triggered. The second break date is around 2011 - 2012. For economic intuition, we categorize 3 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 December 2015). The break dates are consistent with casual observations in summary statistics, as discussed earlier.28 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 R2 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 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 28

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

sign reversal. During the Crisis, higher relative level and slope factors result in depreciation of the currency and negative excess return. The ”Post-Crisis” coefficients, however, do not show consistent results across countries. 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 χ2 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 the previous sections, 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. When the 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. On the other hand, suppose the economy is in the recession and even more downturn is expected. Then, the central bank lowers its policy rate and exchange rate rises. Since the relative level represents 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.29 This line of research says that when the volatility of exchange rate is low, the currency with higher risk appreciate 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 currency of which economy is expected to have higher inflation and lower economic growth implies higher underlying risk, this currency appreciate when the volatility is low and depreciate when the volatility is high. Therefore, combining 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. 29

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. But 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

4

Decomposing the Yield Curves

In Section 2, we show 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)). The focus of this section is to decompose these two elements and explore their contribution to exchange rate and excess currency return behavior. While the general perceived risk is not observable, we isolate or extract partial measures of perceived risk from the yield curves based on the concept of bond market term premiums. Term premium is defined as the difference between the long-term yield and the expected short yields of the same horizon. We can interpret it as the extra compensation required on top on what the pure expectations hypothesis predicts. The NS model we discussed above can be used to extract premia as follows: assuming that the factors follow a VAR(1) (as in Diebold et al. (2006)), we can iterate the VAR to obtain in-sample forecasts of the factors. Using the NS formula (11), we can then obtain the predicted 1-month yield for any horizon. Subtracting the average expected 1-month yields from the actual yield of the same horizon (which is the right-hand side of (??)), we obtain the term premia for that horizon. Since we use the VAR(1) model to calculate the premia, in each period t the premia will be functions of the three factors in the same period t. As a result, when using three of the premia as calculated above to explain exchange rate change or excess return, what we are doing is equivalent to using the three factors (as in Table 2) as explanatory variables. The results in Table 2 then implies that term premia calculated using the NS model do contribute to exchange rate and excess currency return behavior. There are other ways to construct term premiums, here we first report the summary statistics based on one of the alternative methodologies we employed in this paper (summary statistics for the premia calculated based on the NS model are available upon request).

4.1

Behavior of Term Premiums

We argue that analogous to the expectation hypothesis and factor modeling for bond yields, each bond premium of maturity j perceived at time t, θtj , should be correlated with some la 1  Pj−1 tent risk factors, the weighted average of expected future short-term bond premium k=0 Et wk θt+k . However, unlike the EH for the yields, there is no arbitrage condition to determine the weights wk . In other words, under the assumption that only a limited number of latent risk factors are present, a combination of bond premiums at different horizons should span these risk. In section 3 below, we use risk premiums of three different horizons.30 30

The choice of three premiums is also consistent with the idea of three Nelson-Siegel factors. Our argument is that each of the relative NS factors have a component that is related to expectations of future

15

While in the NS model the term premium is calculated based on yields only, here we take a macro-finance approach in generating term premium. Specifically, we posit that (see references in the introduction) 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. DPR (2005) formalized this idea that yield curves and macro dynamics (specifically inflation and output gap) are jointly determined. One justification is that future short yields are determined by macroeconomic conditions via monetary policy actions such as a Taylor type rule. The perceived risk beyond this expectation would thus be the one-year yield net of this expected yield based on both future short yields and macro conditions. This “macro-yield” measure is thus a narrower concept of risk. Table 3 presents the summary statistics based on a more restrictive concept of risk. We can see that the relative risk premiums tend to be quite small. For example, the threemonth Australian premium averages to just 8 basis points, while the Swiss premium, being the largest, is around 18 basis points (lower than the US). The relative premiums for 10-year bonds can be larger, with Japan and Switzerland being a couple percentage points lower than the US. Overall, the relative term premiums are not very volatile. Although, as Figures 3 and 4 indicate, they CAN contain important information at the onset of major unexpected events such as the 2008 crisis. From Figures 3 and 4, we see clearly that pre and post, the perceived riskiness of various sovereign bonds at different horizons shifted significantly between 2008 and 2009.

4.2

Relating Risk in the Bond and FX Markets

To test the idea that the same systematic latent risk is priced in both the bond and currency markets, we test how much of the currency risk premiums relative term premiums can explain. Since we do not directly observe “risk in the relative bond markets”, we rely on certain structural concepts to identify risk. For example, of the two premiums we saw in the previous tables, one (NS) is constructed based on a VAR that has only the three NS factors, and the other (DPR) is based on a macro-finance framework that explicitly incorporates joint dynamics between macro variables and the yield curves. We consider three alternative measures in addition. Two of them are conceptually similar to the NS model and the DPR model. Rather than using the difference between macro-dynamics, and another that is latent risk. Given that we know the three relative factors explain currency dynamics, we use yield curve models to decompose them into risk vs. expectation parts.

16

successive expected future short yields (constructed using the NS factors) and the conventional fitted longer-term yield (also generated with the NS factors), we compute the term premiums using actual longer-term yields (minus expected future short yields). These two measures, which we call NS-Actual and DPR-Actual, are the above two measures plus, from a mechanical perspective, the additional Nelson-Siegel fitting errors. Conceptually, however, these fitting errors are term-specific deviations from the Nelson-Siegel fitted yields, which can reflect term-specific risk perceived at the particular point in time (relative to the N-S implied value). As such, these two risk measures based on actual yields are broader than the earlier two measures (in practice, it is certainly possibly that these fitted errors are purely noise). The last two concepts of term premium are not NS-based. First we estimate an three-factor affine model in the style of Dai and Singleton (2002). The factors are the three principal components of the yields, and the term premia are calculated as the difference between the fitted yields and the implied yields when investors are risk neutral (see Appendix C for a description of the procedure). Next we follow Cochrane and Piazzesi (2005). We extract a factor for excess bond returns of maturity of 1 year or above (see Appendix B for a description of the procedure), which is used together with the 3-month to explain excess currency return.31 We include the 3, 12, and 120-month relative premiums in order to as a proxy for the expected future short premiums in equation (X), the NPV equation in Section 2.3233 XRt+3 = β0 + β1 θtR,3 + β2 θtR,12 + β3 θtR,120 + t+3

(14)

We see that individual coefficients can be quite large and varied, mostly due to the fact that the relative premiums are quite small, as discussed earlier. The relative premiums at different maturities can be correlated both statistically and conceptually (i.e. longer term relative premiums should compensate the same shorter-term latent risk that shorter premiums do, but the weighting or loading on it would differ. This is the rational for us to include three relative premiums to allow for more flexibility in approximating the infinite sum of expected future short-term yields). The interpretation of individual coefficients is thus not very informative or meaningful. We thus focus on testing for their joint significance, as 31

Due to space limit, we do not report the summary statistics for the four alternative measures of term premium. They are available upon request. 32 Note that we use the same structural break as identified in Tables 2A/B. If the Quandt-Andrews test is conducted on this regression, a similar break date would be chosen. 33 We choose to include only three premia in the regression for two reasons. First, as explained above, in the NS model the premia will be functions of the three factors, and using three premia is equivalent to using the three factors. Since the three factors can capture the yields well and that the three factors have good explanatory power, using three premia is clearly preferred to using fewer. Second, since the premia are in general quite correlated with each other, using more than three premia can lead to the collinearity problem.

17

well as their joint explanatory power, as indicated by the adj-R2 . We report these in Tables 5 and 6. We see that the five different concepts of risk premiums deliver two remarkably consistent messages. By looking at the joint Wald test results, we first see that for five of the six currency pairs (Swiss franc being the exception again), 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 FX values. Looking at the goodness of fit criterion (adjusted R2 ), we see that term premiums can explain 10 to over 30% of the variations in excess currency returns. This is quite an impressive portion in light of the near-zero R2 typical in this literature. Comparing rows (1) and (2), the narrower concept of risk (DPR) have lower R2 than the broader concept “NS” (this complements the results will show in Table 6 where XR is regressed on expected yields, where we see the expected yields based on DPR have higher explanatory power). The comparison between measures using actual yields, rows 3 and 4, are not as clear cut, i.e. the NS-fitted errors could be mostly noise, though in a few instances, using the actual yields do improve upon previous narrower concepts, e.g. adj-R2 went up by several percents in DPR-Actual from DPR for Australia, New Zealand, and the United Kingdom.

5

The Joint Macro-Finance Approach

We regress three-month exchange rate changes on both the macro variables and the relative yield factors (controlling for structural breaks again), and test for the joint significance of each group using the Wald statistics. Table 7 shows that except for Canada, the null hypothesis that the latent yield factors do not explain exchange rate changes (No Yields) is strongly rejected. (Note that for once, Switzerland shows positive result; the null that yields have no explanatory power is rejected at the 10% level.) The null hypothesis that the (contemporaneous) macro variables have no contribution (No Macro) is rejected for Canada and New Zealand only. 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. As discussed in Section 2 (and in Chen and Tsang (2011)), the yield curves themselves contain expectations about future macro-fundamentals. We also that for all countries, except Switzerland, we can strongly reject the hypothesis that neither macro fundamentals nor yield factors can predict exchange rate movement next quarter. Note that the explanatory power of these variables can be quite high: the adjusted R2 can be up to 20% to over 35%. This level of explanatory power is rare in the context of explaining short-term currency movement such 18

as at the quarterly level here. Even in this context where dynamic interactions among these variables are ignored, we already see that both macro and term structure factors are very relevant for explaining currency movements.

5.1

A Dynamic Macro-Yield Model of Nominal Exchange Rate

Given the above results, we now extend the dynamic framework of Diebold and Li (2006) and Ang et al. (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.34 We use the atheoretical forecasting equations to capture any endogenous feedback among the variables. We estimate a six-variable VAR(1), though increasing the order of the VAR system does not change our conclusions below. We provide two measures of how well the joint model describe exchange rate movements. First, following Hodrick (1992), we calculate the partial R2 for each variable for explaining exchange change at various horizons (see Appendix D for a detailed discussion on the method). Though the variable that enters the VAR system is the one-month exchange rate change, we can use the method to calculate the explanatory power of each variable for exchange rate change of longer horizons. Table 8 shows the results for explaining exchange rate change at 1, 3, 6 and 12-month in the future. As expected, exchange rate change itself has little use for predicting its future movements (except for New Zealand where the R2 is quite large). The three NS factors, especially the slope and curvature factors, contribute substantially to explaining exchange rate change at all horizons. For example, the slope factor accounts for 15% of the variance of exchange rate change at the 12-month horizon. Once again, the factors have relatively lower R2 for Switzerland. The contribution of the two macroeconomic variables mainly appears at longer horizons. For example, inflation and unemployment each explains over 10% of the variance of Canada’s exchange rate change at the 12-month horizon. Next, we compare the in-sample fit of the joint model with a model that has only the two macroeconomic variables and exchange rate change (macro) and the ”model” that exchange rate change has a sample mean of zero (random walk, RW).35 Since the VAR system only has the 1-month exchange rate change as one of the six variables, 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 34

This non-structural VAR approach follows from Engel and West (2006), Molodtsova and Papell (2009) and so forth on the exchange rate side, and Diebold et al (2006), among others, on the finance side. 35 Using the actual sample mean instead of zero does not change the results much.

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changes. We calculate the root mean squared error (RMSE) for the joint model, macroonly model, and the random walk model (which is simple the sum of squared exchange rate change). Table 9 reports the results. The RMSE ratio is calculated as the RMSE of the joint or macro-only model divided by the RMSE of the random walk model, and a ratio less than one implies that the random walk model is inferior. For horizons up to 6 months, the joint model in general has lower RMSE ratio than the macro-only model. Consistently with our earlier results, the macro-only model improves at the longer 12-month horizon. 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. The joint model significantly fits better than a simple random walk for most cases.

6

Conclusions

This paper incorporates both macroeconomic and financial elements into exchange rate modeling. Separating out the term premiums from the yields, we 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.

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23

Appendix A. Yield Curve and the Nelson-Siegel (1987) Factors Diebold, Piazzesi and Rudebusch (2005) advocate the factor approach for yield curve modeling as it provides a succinct summary of the few sources of systematic risks that underlie the pricing of various tradable financial assets. Among the alternative model choices, this paper mainly adopts the Nelson-Siegel latent factor framework without imposing the no-arbitrage condition.36 The classic Nelson-Siegel (1987) model summarizes the shape of the yield curve using three factors: Lt (level), St (slope), and Ct (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.37 The three factors typically account for most of the information in a yield curve, with the R2 for cross-sectional fits around 0.99. While the more structural no-arbitrage 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.38 As our focus is to connect the dynamics of the yield curves with the evolution of macroeconomy and the exchange rate, our model extends the dynamic Nelson-Siegel model proposed in Diebold et al (2006) to the international setting, as presented in Section Y.Y.39

B. The Cochrane-Piazzesi (CP, 2005) Factors Following Cochrane and Piazzesi (2005) we look at annual excess returns. To be consistent with our paper all yields considered here are ”relative” yield between two countries (with US as home). Holding period return of a 12n-month bond from now to next year can be calculated as: (12n)

(12n)

rt+12 ≡ nit

(11n)

− (n − 1)it+12

36

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. 37 The level factor Lt , with its loading of unity, has equal impact on the entire yield curve, shifting it up or down. The loading on the slope factor St 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 Ct 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. 38 See, e.g. Diebold et al (2006) and Duffee (2002). 39 As discussed in Diebold et al (2006), this framework is flexible enough to match the data should they reflect the absence of arbitrage opportunities, but should transitory arbitrage opportunities actually exist, we then avoid the mis-specification problem.

24

That is, you buy the 12n-month bond now and sell it as a 11n-month bond next year. The above defines the return of such a transaction. Excess return is then defined as: ’ (12n) (12n) (12) rxt+12 ≡ rt+12 − it 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 (24) (120) rxt+12 , ..., rxt+12 , a total of nine excess returns. The CP regression involves regressing the average of the excess returns on the 12-month (24) (120) yield and the forward rates ft , ..., ft , where the definition is (12n)

ft

(12n)

≡ nit

(11n)

− (n − 1)it

The regression is then 10

1 X (12i) (12) (24) (120) rxt+12 = γ0 + γ1 it + γ2 ft ... + γ10 ft + t+12 9 i=2 The fitted value is the CP factor. We are different from the original CP setting that a) we are using relative yields and b) we extend the maturities to 10-year from 5-year.

C. The Dai-Singleton (2002) Factors (n)

We follow the discussion in Wright (2009) and let Pt denote the price at time  t of an n(n) (n) period zero-coupon bond. For a zero-couple bond, we know it = − log Pt /n. Under (n)

no-arbitrage, the price of the bond should be consistent with the pricing kernel that Pt
Et nj=1 Mt+j , where the pricing kernel Mt+1 is conditionally lognormal: Mt+1

=

  1 0 (1) 0 = exp −it − λt λt − λt t+1 2

The term λt = λ0 +λ1 Xt is a function of the state variables Xt , which in our case are the three principal components Xt of the yields. The shocks in the model t follow an iid N (0, I). (1) (1) The one-period yield it is also an affine function of the state variables, it = δ0 + δ10 Xt . The state variables follow a first-order VAR: Xt+1 = µ + ΦXt + Σt+1 Using the log-normality assumption and the VAR model for the state variables Xt , we

25

can express bond prices as a function of the state variables and other parameters: (n)

Pt

= exp (An + Bn0 Xt )

1 An+1 = δ0 + An + Bn0 (µ − Σλ0 ) + Bn0 ΣΣ0 Bn 2 Bn+1 = (Φ − Σλ1 )0 Bn − δ1 That is, bond prices (and hence bond yields) are determined recursively through An and Bn . The bond prices are calculated as if agents are risk-neutral (λ0 = λ1 = 0) but the state variables follow a different law of motion: Xt+1 = µ∗ + Φ∗ Xt + Σt+1 But that µ∗ = µ − Σλ0 and Φ∗ = Φ − Σλ1 . Following the usual practice, we first estimate for each country the parameters of the model by maximum likelihood (where each yield except the one-period yield has a normally distributed prediction error). Next, we calculate the fitted yields of the above model and the implied yields when λ0 = λ1 = 0. The difference between the two sets of yields gives us the term premia of different maturities. The maximum likelihood results are available upon request.

D. VAR Multi-Period Predictions To compute the partial R2 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 described in Section (5) can be written as: ft = Aft−1 + ηt where the constant term µ is omitted for notational convenience. Denote the information set at time t as It , which includes all current and past values of ft . A forecast of horizon m can be written as Et (ft+m |It ) = Am ft . By repeated substitution, first-order VAR can be expressed in its MA(∞) representation: ft =

∞ X

Aj ηt+j

j=0

26

The unconditional variance of ft can then be expressed as: C (0) =

∞ X

Aj QAj

0

j=0

Denoting C (j) as the jth-order covariance of ft , which is calculated as C (j) = Aj C (0), the variance of the sum, denoted as Vm , is then: Vm = mC (0) +

X

m−1 j=1 (k

  − j) C (j) + C (j)0

We are not interested in the variance of the whole vector but only that of the long-horizon exchange rate change, dst , which is the third element in the vector ft . We can define e03 = (0, 0, 1, 0, 0, 0), and express the variance of the m-period exchange rate change as e03 Vm e3 . To assess whether a variable in ft , say the level factor LR t , explains exchange rate change ∆st+m = st+m − st , we run a long-horizon regression of ∆st+m on LR The VAR t . model for ft allows us to calculate the coefficient from this regression based on only the VAR coefficient estimates. Since the level factor is the fourth element in ft , the coefficient is defined as: e0 [C (1) + ... + C (m)] e4 β4 (m) = 3 e04 C (0) e4 where vector e4 is defined as e4 = (0, 0, 0, 1, 0, 0). The numerator is the covariance between 2 R ∆st+m and LR t ,and the denominator is the variance of Lt . Finally, the R as reported in the paper is calculated as: R42 (m) = β4 (m)2

e04 C (0) e4 e03 Vm e3

The R2 for all other variables in the vector ft can be suitably obtained by replacing e4 with e1 , e2 , e3 , e5 , e6 . To calculate the total R2 for all explanatory variables, we calculate the innovation variance of the exchange rate change as e01 Wm e1 , where Wm =

m X



0 (I − A)−1 I − Aj Q I − Aj (I − A)−10

j=1

The total R2 is then: R2 (m) = 1 −

e01 Wm e1 e0m Vm em

For the calculation to be valid, we need A to be stationary.

27

E. Data Appendix Yield data: Our zero-coupon bond yield include maturities from 3 to 120 months (3 months increment) from Wright (2011). Most yields are from the central bank of each country, and each set of yields are constructed using different methods. Please refer to Wright (2011) for details on the construction of the data. The yields are from the last trading day of each month. While yields of all countries end on May 2009, some begin earlier. Yields for UK and US are available from January 1984, for Australia it is February 1987, for Canada it is January 1986, for Japan it is January 1985, for New Zealand it is January 1990, and for Switzerland it is January 1988. Macroeconomic data: We obtain headline CPI and unemployment rate from the FRED database (http://research.stlouisfed.org/fred2/). Inflation rate is defined as 12-month percentage change of the CPI. Unemployment rate is regressed on a quadratic trend, and the residual is defined as unemployment gap. Exchange rate data: End-of-period monthly exchange rates are again obtained from the FRED database. We express first-differenced (∆) logged exchange rate as ∆st = st − st−1 . (We note that we only report results based on the per-dollar rates below, but found qualitatively similar results using the non-dollar currency pairs.)

28

Table 1A. Summary Statistics for 3-Month Exchange Rate Change and Excess Currency Return

∆st+3 Mean

SD

Median Min Max AR(1) xrt+3 Mean

SD

Median Min Max AR(1)

AU

CA

DM

JP

NZ

SD

SW

UK

0.085 (-1.855) (3.457) 25.355 (19.257) (33.275) -1.779 -87.722 143.673 0.733

-0.171 (-2.433) (3.763) 16.533 (13.441) (20.340) 0.385 -59.364 67.855 0.634

0.775 (-1.397) (4.551) 20.226 (18.850) (22.020) -0.084 -49.542 81.565 0.705

0.969 (0.931) (1.037) 22.940 (23.412) (22.223) 3.079 -86.742 62.428 0.701

-0.174 (-1.255) (1.705) 25.246 (21.480) (30.762) -2.289 -94.472 95.950 0.748

0.603 (-1.554) (4.353) 22.584 (19.304) (27.080) 0.154 -67.529 100.470 0.724

-0.967 (-1.188) (-0.581) 20.226 (20.042) (20.647) -1.407 -53.085 49.901 0.664

0.565 (-1.636) (4.394) 17.058 (12.535) (22.464) -0.288 -56.075 81.255 0.729

2.158 (3.542) (-0.250) 25.567 (19.949) (33.142) 3.467 -138.916 90.208 0.738

0.458 (2.495) (-3.085) 16.586 (13.718) (20.249) -0.455 -67.157 59.776 0.636

-0.791 (1.038) (-3.972) 20.421 (19.351) (21.906) -0.008 -78.959 51.313 0.712

-3.334 (-4.616) (-1.105) 23.197 (23.754) (22.144) -4.983 -66.883 81.874 0.709

3.039 (4.092) (1.209) 25.246 (21.924) (30.213) 5.404 -90.226 97.155 0.749

-0.355 (1.524) (-3.623) 22.771 (19.983) (26.748) 0.233 -97.950 67.711 0.729

-0.437 (-1.026) (0.588) 20.540 (20.526) (20.637) -0.230 -52.243 52.594 0.674

0.469 (2.944) (-3.835) 16.986 (12.685) (22.027) 1.416 -77.908 56.624 0.728

Note: 1.∆st+3 = st+3 − st is the quarterly change of the exchange rate, where st is the logged home S,3 ) − ∆st+3 is the excess currency return defined as the return currency price per USD. 2. xrt+3 = (i3t − iU t difference between investing in the home bond over that of the US bond. 3. Sample period is from January, 1995 to March, 2016. All rates are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, 2008. 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, 2008.

29

Table 1B. Summary Statistics for Relative Level, Slope and Curvature Factors AU

CA

DM

JP

NZ

SD

SW

UK

0.969 (1.011) (0.895) 0.707 (0.819) (0.446) 0.794 -0.167 3.800 0.923

-0.044 (0.298) (-0.638) 0.773 (0.742) (0.354) -0.171 -1.145 2.404 0.940

-0.284 (0.062) (-0.886) 1.048 (1.033) (0.767) -0.415 -2.373 2.911 0.950

-2.958 (-3.145) (-2.632) 0.757 (0.703) (0.741) -2.991 -4.889 -1.057 0.902

1.143 (0.977) (1.431) 0.487 (0.370) (0.531) 1.068 0.164 2.595 0.826

-0.210 (0.243) (-0.998) 1.270 (1.350) (0.522) -0.462 -2.040 4.617 0.942

-2.064 (-1.972) (-2.222) 0.490 (0.406) (0.578) -2.098 -3.088 -0.209 0.836

-0.051 (-0.081) (0.001) 0.842 (1.026) (0.335) -0.165 -1.812 2.759 0.947

1.221 (0.636) (2.238) 1.677 (1.768) (0.807) 1.477 -1.858 4.390 0.974

0.252 (-0.305) (1.222) 1.257 (1.223) (0.496) 0.429 -3.730 2.161 0.957

0.248 (-0.421) (1.411) 1.763 (1.806) (0.849) 0.565 -3.703 5.046 0.970

0.669 (-0.397) (2.523) 2.206 (2.046) (0.799) 1.290 -3.404 4.180 0.977

1.683 (1.899) (1.307) 1.597 (1.727) (1.262) 1.760 -2.163 4.998 0.957

0.354 (-0.355) (1.589) 1.777 (1.760) (0.932) 0.599 -2.966 4.193 0.971

0.717 (-0.181) (2.280) 1.712 (1.461) (0.682) 1.197 -2.865 5.117 0.967

1.030 (1.327) (0.514) 1.381 (1.560) (0.763) 0.691 -1.824 4.164 0.965

1.140 (0.289) (2.619) 2.635 (2.463) (2.252) 0.819 -4.882 8.622 0.931

0.738 (-0.048) (2.105) 1.997 (1.762) (1.614) 0.758 -5.741 5.458 0.878

0.004 (-0.775) (1.358) 2.446 (2.624) (1.245) 0.616 -7.243 4.366 0.941

-0.426 (-2.273) (2.786) 3.357 (2.765) (1.141) -0.276 -6.665 5.777 0.959

1.532 (0.898) (2.635) 2.327 (2.375) (1.772) 1.342 -5.088 8.750 0.884

0.791 (-0.118) (2.371) 2.577 (2.468) (1.921) 0.897 -6.189 6.472 0.955

0.179 (-1.010) (2.247) 2.560 (2.253) (1.549) 0.562 -6.246 5.542 0.956

1.049 (1.377) (0.479) 1.903 (2.158) (1.158) 0.907 -4.159 5.800 0.890

LR t Mean

SD

Median Min Max AR(1) StR Mean

SD

Median Min Max AR(1) CtR Mean

SD

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 US R US R US level LR reported here. 2. Sample t = Lt − Lt , slope St = St − St , and curvature Ct = Ct − Ct period is from January, 1995 to December, 2015. 3. Sample period is divided by the breakdate, May, 2008. 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.

30

Table 1C. Summary Statistics for Macroeconomic Fundamentals

uR t Mean

SD

Median Min Max AR(1) πtR Mean

SD

Median Min Max AR(1)

AU

CA

DM

JP

NZ

SD

SW

UK

-0.010 (0.013) (-0.050) 0.322 (0.319) (0.325) -0.029 -0.838 0.790 0.793

-0.009 (0.013) (-0.049) 0.236 (0.239) (0.228) -0.021 -0.769 0.563 0.663

-0.006 (0.027) (-0.063) 0.351 (0.342) (0.360) 0.036 -1.103 0.927 0.860

0.005 (0.042) (-0.060) 0.302 (0.273) (0.337) 0.032 -0.930 0.882 0.812

-0.023 (-0.004) (-0.055) 0.374 (0.374) (0.373) -0.014 -1.027 1.025 0.815

-0.017 (-0.005) (-0.037) 0.384 (0.419) (0.313) -0.017 -0.994 1.122 0.644

-0.005 (0.038) (-0.080) 0.404 (0.388) (0.421) 0.039 -1.254 1.031 0.835

-0.005 (0.022) (-0.053) 0.302 (0.277) (0.339) -0.034 -0.975 0.719 0.866

0.394 (0.104) (0.898) 1.283 (1.321) (1.042) 0.300 -2.681 3.606 0.905

-0.390 (-0.618) (0.004) 0.854 (0.757) (0.871) -0.505 -2.630 2.233 0.910

-0.312 (-0.546) (0.095) 0.985 (0.832) (1.098) -0.440 -2.301 3.104 0.925

-2.152 (-2.666) (-1.257) 1.554 (1.139) (1.765) -2.566 -5.129 2.467 0.948

-0.111 (-0.38) (0.356) 1.188 (0.937) (1.418) -0.299 -3.142 3.773 0.900

-1.156 (-1.399) (-0.733) 1.169 (1.213) (0.955) -1.055 -4.080 1.570 0.934

-1.679 (-1.727) (-1.596) 0.789 (0.529) (1.103) -1.668 -3.927 0.925 0.904

-0.220 (-0.900) (0.962) 1.323 (0.880) (1.117) -0.319 -3.206 3.983 0.956

US is the relative unemployment rate, constructed as the difference between the Note: 1. uR t = ut − ut detrended unemployment rates in the home country and in the U.S. Time series of unemployment rate is detrended by Hodrick-Prescott filter. 2. πtR = πt −πtU S 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, 2016. 4. Sample period is divided by the breakdate, May, 2008. 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.

31

Table 1D. Correlation between Exchange Rate Change and Yield Factors

AU

CA

DM

JP

NZ

SD

SW

UK

corr(∆st+3 ,LR t )

-0.022 (0.035) (-0.113)

-0.154 (0.004) (-0.248)

0.030 (0.226) (-0.139)

0.251 (0.198) (0.381)

-0.101 (0.057) (-0.311)

-0.079 (0.036) (-0.227)

0.079 (0.114) (0.052)

-0.008 (0.031) (-0.175)

corr(∆st+3 ,StR )

-0.073 (-0.374) (0.306)

0.085 (-0.201) (0.452)

-0.086 (-0.361) (0.322)

-0.155 (-0.207) (-0.253)

0.080 (-0.215) (0.619)

-0.002 (-0.362) (0.553)

-0.164 (-0.331) (0.026)

0.077 (-0.085) (0.646)

corr(∆st+3 ,CtR )

-0.184 (-0.411) (-0.106)

0.012 (-0.141) (-0.051)

-0.156 (-0.402) (0.196)

-0.084 (-0.160) (-0.008)

-0.208 (-0.401) (-0.024)

-0.176 (-0.425) (-0.043)

-0.201 (-0.321) (-0.144)

-0.022 (-0.153) (0.335)

Note: 1. Sample period is from January, 1995 to March, 2016. 2. Sample period is divided by the breakdate, May, 2008. 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.

32

Table 2A. 3-Month Exchange Rate Change on Relative Factors R R ∆st+3 = α0,st + α1,st LR t + α2,st St + α3,st Ct + t+3    1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

where τ1 , τ2 : breakdates

AU

CA

DM

JP

NZ

SD

4.536 (3.391) -87.413** (41.211) -17.641 (13.541)

-3.395* (2.039) -16.327** (7.365)

-3.834** (1.921) -26.627** (10.917) -0.529 (4.649)

11.916 (15.811) 17.478* (10.459) 51.751*** (13.727)

8.603 (8.238) -174.043*** (47.577) -70.114*** (23.481)

-1.912 (1.886) -13.713** (6.947)

-4.216** (2.054) 25.793 (21.312) -16.778** (6.991)

-1.505 (2.257) 3.481 (5.861)

-1.469 (1.935) 5.616 (13.373) 18.885*** (2.583)

3.855 (5.194) 48.755*** (8.976) 107.637*** (22.712)

-4.232 (6.793) 46.992*** (17.708) 31.805*** (12.009)

-2.327** (1.112) 4.449 (6.522)

-2.194 (1.886) 31.260*** (10.810) 16.785** (7.513)

-2.302** (0.972) 18.259*** (5.723)

-1.538 (1.783) 8.973* (4.896) 26.978*** (5.394)

-1.142 (2.250) 35.589*** (8.566) 85.054*** (22.572)

-1.324 (1.307) 33.487*** (4.560) 22.834*** (7.116)

-1.546 (1.259) 19.191*** (4.937)

-2.535*** (0.946) -5.656 (5.393) 5.011** (2.417)

-1.217 (1.023) -0.003 (1.392)

-2.428** (1.033) 8.013 (5.263) -2.125 (2.337)

-0.337 (1.255) 4.692* (2.399) 8.597*** (2.461)

-3.573*** (1.213) 14.988*** (3.726) 2.490 (1.981)

-3.159*** (0.903) -3.368** (1.712)

0.000 0.259

0.006 0.132

0.000 0.195

0.000 0.182

0.000 0.393

0.000 0.270

May,08 Aug,11

Jan,07

May,08 Jun,11

Jul,08 Aug,12

May,08 Jun,11

May,08

SW

UK

α0 st = 1 st = 2 st = 3

4.034 (9.246) -20.748 (18.538)

0.506 (2.620) -6.986** (3.195)

α1 st = 1 st = 2 st = 3

3.577 (4.547) -17.778 (13.587)

-1.741 (2.237) 9.860 (6.007)

α2 st = 1 st = 2 st = 3

-0.774 (1.518) -12.316 (11.503)

-0.438 (1.270) 19.766*** (2.752)

α3 st = 1 st = 2 st = 3 p-value Adj. R2 τ1 τ2

-2.294*** (0.879) 4.538 (3.557) 0.101 0.096

-1.237 (0.967) 2.509 (2.171)

0.000 0.293 May,08

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 2007 2008, when the Global Financial Crisis has been triggered. The second break date is around 2011 - 2012. 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 (H0 : α1,st = α2,st = α3,st = 0, ∀st ). 4. Adjusted R2 is also reported.

33

Table 2B. 3-Month Excess Currency Return on Relative Factors R R xrt+3 = β0,st + β1,st LR t + β2,st St + β3,st Ct + t+3    1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

where τ1 , τ2 : breakdates

AU

CA

DM

JP

NZ

SD

-4.417 (3.387) 87.643** (41.217) 17.657 (13.535)

3.441* (2.039) 16.387** (7.371)

3.861** (1.923) 26.637** (10.941) 0.679 (4.668)

-11.823 (15.816) -17.422* (10.450)0 -51.712*** (13.727)

-8.580 (8.226) 174.011*** (47.505) 70.273*** (23.437)

1.968 (1.884) 13.823** (6.945)

5.188** (2.051) -24.840 (21.341) 17.873** (6.988)

2.483 (2.255) -2.362 (5.855)

2.448 (1.934) -4.586 (13.384) -17.860*** (2.582)

-2.836 (5.196) -47.882*** (8.996) -106.758*** (22.717)

5.274 (6.784) -45.948*** (17.678) -30.851** (11.985)

3.298*** (1.109) -3.316 (6.518)

3.073 (1.884) -30.359*** (10.812) -15.930** (7.512)

3.205*** (0.973) -17.354*** (5.725)

2.427 (1.783) -8.048 (4.911) -26.159*** (5.396)

2.018 (2.252) -34.828*** (8.581) -84.327*** (22.577)

2.229* (1.305) -32.528*** (4.549) -21.996*** (7.104)

2.422* (1.256) -18.246*** (4.927)

2.628*** (0.942) 5.730 (5.387) -4.903** (2.420)

1.284 (1.022) 0.111 (1.393)

2.522** (1.033) -7.902 (5.267) 2.259 (2.347)

0.437 (1.256) -4.592* (2.399) -8.473*** (2.461)

3.661*** (1.210) -14.897*** (3.722) -2.393 (1.979)

3.250*** (0.902) 3.473** (1.712)

0.000 0.272

0.001 0.137

0.000 0.209

0.000 0.199

0.000 0.393

0.000 0.282

May,08 Aug,11

Jan,07

May,08 Jun,11

Jul,08 Aug,12

May,08 Jun,11

May,08

SW

UK

β0 st = 1 st = 2 st = 3

-4.007 (9.247) 20.768 (18.553)

-0.410 (2.620) 7.007** (3.194)

β1 st = 1 st = 2 st = 3

-2.570 (4.548) 18.777 (13.596)

2.714 (2.237) -8.765 (6.000)

β2 st = 1 st = 2 st = 3

1.653 (1.517) 13.172 (11.509)

1.335 (1.27) -18.851*** (2.741)

β3 st = 1 st = 2 st = 3 p-value Adj. R2 τ1 τ2

2.390*** (0.879) -4.423 (3.558) 0.038 0.124

1.310 (0.966) -2.371 (2.165)

0.000 0.288 May,08

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 (H0 : β1,st = β2,st = β3,st = 0, ∀st ). 4. Adjusted R2 is also reported.

34

Table 3A. Summary Statistics for NS Relative Expected Yields

L(Et iR t ) Mean

SD

S(Et iR t ) Mean

SD

C(Et iR t ) Mean

SD

corr(L,S) corr(L,C) corr(S,C)

AU

CA

DM

JP

NZ

SD

SW

UK

1.939 (1.552) (2.611) 1.014 (0.880) (0.874)

-0.847 (-1.806) (0.822) 2.086 (1.925) (1.048)

-0.253 (-0.511) (0.194) 0.888 (0.861) (0.751)

-2.54 (-3.306) (-1.207) 1.301 (0.967) (0.450)

2.438 (2.442) (2.431) 0.875 (0.839) (0.940)

-0.231 (-0.283) (-0.141) 1.137 (1.225) (0.964)

-1.523 (-1.949) (-0.781) 0.951 (0.874) (0.535)

0.381 (1.012) (-0.715) 1.309 (0.966) (1.087)

0.229 (0.007) (0.615) 0.904 (0.929) (0.714)

1.069 (1.764) (-0.141) 2.000 (2.126) (0.900)

0.208 (0.134) (0.336) 0.685 (0.726) (0.587)

0.121 (-0.450) (1.114) 1.048 (0.875) (0.347)

0.376 (0.349) (0.424) 1.089 (1.080) (1.110)

0.342 (0.098) (0.768) 1.104 (1.084) (1.009)

0.135 (-0.305) (0.899) 0.869 (0.766) (0.354)

0.567 (0.216) (1.176) 1.149 (1.154) (0.849)

0.138 (-0.101) (0.554) 0.706 (0.557) (0.747)

0.350 (0.733) (-0.316) 0.897 (0.667) (0.859)

0.066 (-0.049) (0.268) 0.637 (0.603) (0.648)

0.259 (-0.129) (0.934) 0.724 (0.545) (0.451)

0.215 (0.221) (0.206) 0.600 (0.563) (0.662)

-0.022 (-0.267) (0.403) 0.844 (0.709) (0.892)

0.183 (-0.073) (0.627) 0.621 (0.537) (0.496)

0.261 (0.050) (0.628) 0.583 (0.570) (0.394)

0.509 0.887 0.353

-0.890 -0.308 0.259

0.466 0.931 0.204

0.830 0.945 0.623

0.084 0.849 -0.181

0.154 0.332 -0.033

0.682 0.924 0.504

-0.631 -0.037 0.211

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
120 0 3 6 , i , ..., i , f = (Lt , St , Ct )0 Aruoba(2006). The measurement equation is i = Λf + e , where i = i t t t t t t t t  

and Λ = 1, 1−exp(−λm) , 1−exp(−λm) − exp(−λm) . The transition equation is ft − µ = A(ft−1 − µ) + vt . 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 differenceh in the i expected yields between a country Pm−1 R,m U S,m 1 1 b E i = Et im . See pair is defined as the relative expected yield. Et im = t t+j and Et it t − Et i t t j=0 m text for details. 2. The level, slope and curvature factors of the relative expected yields are constructed R,120 R,3 R,24 as follows: L(Et iR , S(Et iR − Et iR,120 , C(Et iR − (Et iR,3 + Et iR,120 ). t t t t ) = Et i t t ) = Et it t ) = 2Et it 3. Sample period is from January, 1995 to December, 2015. All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, 2008. 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, 2008.

35

Table 3B. Summary Statistics for NSM Relative Expected Yields

L(Et iR t ) Mean

SD

S(Et iR t ) Mean

SD

C(Et iR t ) Mean

SD

corr(L,S) corr(L,C) corr(S,C)

AU

CA

DM

JP

NZ

SD

SW

UK

1.553 (1.366) (1.878) 0.937 (0.932) (0.858)

-0.738 (-0.994) (-0.294) 0.976 (0.908) (0.932)

0.046 (0.335) (-0.456) 0.961 (0.830) (0.970)

-2.552 (-3.264) (-1.313) 1.164 (0.797) (0.429)

2.573 (2.790) (2.195) 1.381 (1.469) (1.124)

0.696 (0.100) (1.732) 1.020 (0.744) (0.438)

-1.684 (-2.095) (-0.967) 0.811 (0.667) (0.471)

0.921 (1.081) (0.642) 1.007 (1.026) (0.915)

0.606 (0.193) (1.325) 1.146 (1.179) (0.610)

0.959 (0.949) (0.976) 1.019 (1.034) (1.000)

-0.109 (-0.745) (0.996) 1.328 (1.203) (0.621)

0.194 (-0.427) (1.274) 1.248 (1.150) (0.355)

0.291 (0.028) (0.750) 1.432 (1.609) (0.893)

-0.493 (-0.229) (-0.951) 1.461 (1.669) (0.827)

0.289 (-0.157) (1.065) 1.019 (0.966) (0.527)

0.072 (0.196) (-0.143) 1.146 (1.253) (0.896)

0.463 (0.191) (0.936) 0.869 (0.592) (1.056)

0.788 (0.879) (0.629) 1.326 (1.449) (1.070)

0.367 (0.253) (0.563) 1.256 (1.436) (0.829)

0.582 (0.232) (1.190) 0.803 (0.656) (0.659)

0.585 (0.306) (1.072) 0.835 (0.671) (0.872)

0.900 (0.676) (1.289) 2.047 (2.287) (1.476)

0.394 (0.229) (0.680) 0.752 (0.656) (0.822)

0.512 (0.902) (-0.166) 0.801 (0.522) (0.750)

0.290 0.497 0.365

-0.509 -0.401 0.205

-0.280 -0.076 0.442

0.738 0.832 0.549

-0.471 -0.124 0.249

-0.059 0.366 -0.182

0.642 0.734 0.189

-0.501 0.620 -0.103

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 measure
0 1−exp(−λm) ment equation is it = Λft +et , where it = i3t , i6t , ..., i120 , Λ = 0, 0, 1, 1−exp(−λm) , − exp(−λm) t λm λm and ft = (ut , πt , Lt , St , Ct )0 . The transition equation is ft − µ = A(ft−1 − µ) + vt . 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 inh the iexpected yields between a country pair is defined Pm−1 R,m U S,m 1 b1 = Et im . See text for deas the relative expected yield. Et im t − Et it t = m j=0 Et it+j and Et it tails. 2. The level, slope and curvature factors of the relative expected yields are constructed as follows: R,120 R,3 R,24 L(Et iR , S(Et iR − Et iR,120 , C(Et iR − (Et iR,3 + Et iR,120 ). 3. Sample t t t t ) = Et it t ) = Et it t ) = 2Et it period is from January, 1995 to December, 2015. All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, 2008. 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, 2008.

36

Table 3C. Summary Statistics for Affine Relative Expected Yields

L(Et iR t ) Mean

SD

S(Et iR t ) Mean

SD

C(Et iR t ) Mean

SD

corr(L,S) corr(L,C) corr(S,C)

AU

CA

DM

JP

NZ

SD

SW

UK

4.244 (3.113) (6.211) 2.273 (1.947) (1.212)

1.916 (1.127) (3.288) 1.658 (1.475) (0.884)

1.097 (0.342) (2.409) 1.864 (1.825) (1.013)

0.138 (-1.418) (2.843) 2.708 (2.110) (0.898)

3.498 (3.148) (4.108) 1.786 (1.791) (1.615)

2.242 (1.329) (3.832) 2.111 (1.968) (1.226)

0.606 (-0.503) (2.535) 2.127 (1.809) (0.916)

1.970 (2.493) (1.061) 1.432 (1.315) (1.149)

-2.023 (-1.494) (-2.943) 1.019 (0.695) (0.819)

-1.687 (-1.188) (-2.554) 1.015 (0.769) (0.781)

-1.160 (-0.761) (-1.854) 0.836 (0.639) (0.669)

-2.541 (-2.370) (-2.839) 0.681 (0.628) (0.671)

-0.633 (-0.303) (-1.206) 1.340 (0.982) (1.657)

-2.048 (-1.429) (-3.125) 1.317 (0.970) (1.138)

-1.973 (-1.746) (-2.367) 0.692 (0.581) (0.695)

-0.966 (-1.201) (-0.559) 0.770 (0.674) (0.759)

-2.013 (-1.681) (-2.592) 0.632 (0.459) (0.446)

-1.671 (-1.401) (-2.139) 0.615 (0.592) (0.286)

-1.153 (-0.823) (-1.726) 0.598 (0.465) (0.292)

-2.449 (-2.347) (-2.627) 0.245 (0.248) (0.090)

-0.671 (-0.370) (-1.195) 0.633 (0.560) (0.343)

-2.031 (-1.637) (-2.717) 0.894 (0.770) (0.648)

-1.924 (-1.705) (-2.305) 0.410 (0.339) (0.179)

-0.943 (-1.077) (-0.708) 0.263 (0.212) (0.159)

-0.733 -0.532 0.649

-0.823 -0.655 0.507

-0.708 -0.514 0.457

-0.674 -0.673 0.009

-0.605 -0.470 0.495

-0.607 -0.488 0.392

-0.723 -0.661 0.279

-0.683 -0.606 0.205

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 U S,m between a country pair is defined as the relative expected yield. Et iR,m = Et im . See text for t t − Et i t details. 2. The level, slope and curvature factors of the relative expected yields are constructed as follows: R,120 R,3 R,24 L(Et iR , S(Et iR − Et iR,120 , C(Et iR − (Et iR,3 + Et iR,120 ). 3. Sample t t t t ) = Et it t ) = Et it t ) = 2Et it period is from January, 1995 to December, 2015. All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, 2008. 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, 2008.

37

Table 3D. Summary Statistics for CP Relative Expected Yields AU

CA

DM

JP

NZ

SD

SW

UK

1.558 (1.151) (2.213) 0.982 (0.843) (0.827)

-0.323 (-0.359) (-0.266) 0.575 (0.661) (0.397)

-0.856 (-0.739) (-1.044) 0.904 (0.802) (1.023)

-2.112 (-2.952) (-0.759) 1.327 (0.931) (0.476)

2.641 (2.299) (3.191) 0.890 (0.837) (0.673)

-1.176 (-1.260) (-1.041) 0.866 (0.942) (0.713)

-1.412 (-1.753) (-0.864) 0.870 (0.865) (0.534)

0.398 (0.381) (0.426) 0.675 (0.759) (0.512)

0.440 (0.309) (0.651) 0.734 (0.799) (0.559)

0.513 (0.294) (0.865) 0.525 (0.531) (0.256)

0.712 (0.382) (1.242) 0.775 (0.794) (0.309)

-0.249 (-0.728) (0.521) 0.916 (0.835) (0.321)

-0.032 (0.126) (-0.286) 0.733 (0.749) (0.632)

1.057 (0.839) (1.407) 0.756 (0.800) (0.518)

0.071 (-0.299) (0.667) 0.697 (0.614) (0.293)

0.402 (0.697) (-0.073) 0.607 (0.535) (0.367)

0.262 (0.309) (0.186) 0.398 (0.287) (0.522)

0.277 (0.210) (0.386) 0.315 (0.260) (0.365)

0.440 (0.407) (0.491) 0.309 (0.239) (0.392)

0.021 (-0.140) (0.281) 0.410 (0.404) (0.260)

-0.014 (0.022) (-0.072) 0.380 (0.403) (0.333)

0.546 (0.485) (0.644) 0.439 (0.381) (0.506)

0.110 (0.051) (0.204) 0.316 (0.282) (0.345)

0.224 (0.395) (-0.053) 0.403 (0.303) (0.390)

0.673 0.500 0.383

0.499 0.401 0.472

0.186 0.667 0.314

0.765 0.631 0.544

0.203 0.457 0.260

0.500 0.446 0.391

0.751 0.637 0.363

0.174 0.272 0.414

L(Et iR t ) Mean

SD

S(Et iR t ) Mean

SD

C(Et iR t ) Mean

SD

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, 12 24 120 0 using V AR(1) representation. ft − µ = A(ft−1 − µ) + vt , where ft = rx12n ) , rx12n = t , it , ft , ..., ft t 12(n−1) 12n 1 12 12n 2n nit − (n − 1)it+12 2(n − 1) − it , ft = it − (n − 1)it 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 U S,m expected yields between a country pair is defined as the relative expected yield. Et iR,m = Et im . t t − Et it See text for details. 2. The level, slope and curvature factors of the relative expected yields are constructed R,120 R,24 R,48 as follows: L(Et iR , S(Et iR − Et iR,120 , C(Et iR − (Et iR,24 + Et iR,120 ). t t t t ) = Et it t ) = Et it t ) = 2Et it 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, 2015. 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, 2008. 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, 2008.

38

Table 4A. Summary Statistics for NS Relative Term Premiums

L(θtR ) Mean

SD

S(θtR ) Mean

SD

C(θtR ) Mean

SD

corr(L,S) corr(L,C) corr(S,C)

AU

CA

DM

JP

NZ

SD

SW

UK

-0.696 (-0.451) (-1.123) 0.734 (0.703) (0.575)

0.908 (2.035) (-1.054) 2.504 (2.408) (1.018)

0.016 (0.433) (-0.708) 1.021 (1.002) (0.533)

-0.368 (-0.121) (-0.798) 0.920 (0.915) (0.759)

-0.922 (-1.142) (-0.539) 0.661 (0.518) (0.710)

0.135 (0.440) (-0.395) 0.821 (0.674) (0.787)

-0.418 (-0.180) (-0.832) 0.617 (0.541) (0.515)

-0.187 (-0.763) (0.816) 1.083 (0.656) (0.938)

0.678 (0.444) (1.084) 0.688 (0.662) (0.526)

-0.903 (-2.029) (1.054) 2.414 (2.272) (0.982)

-0.014 (-0.421) (0.692) 0.978 (0.958) (0.489)

0.329 (0.071) (0.778) 0.897 (0.898) (0.699)

0.894 (1.088) (0.557) 0.608 (0.485) (0.653)

-0.104 (-0.406) (0.421) 0.786 (0.651) (0.723)

0.381 (0.146) (0.788) 0.591 (0.522) (0.473)

0.194 (0.757) (-0.785) 1.019 (0.590) (0.854)

0.333 (0.317) (0.361) 0.260 (0.295) (0.182)

-0.033 (-0.653) (1.046) 1.000 (0.664) (0.367)

-0.034 (-0.216) (0.283) 0.368 (0.329) (0.160)

-0.273 (-0.545) (0.201) 0.531 (0.472) (0.173)

0.422 (0.277) (0.675) 0.313 (0.270) (0.202)

0.367 (0.291) (0.500) 0.378 (0.358) (0.376)

-0.105 (-0.207) (0.071) 0.301 (0.308) (0.186)

0.198 (0.513) (-0.35) 0.493 (0.259) (0.276)

-1.000 -0.380 0.373

-0.998 -0.673 0.709

-1.000 -0.812 0.826

-0.999 -0.587 0.619

-0.999 0.341 -0.327

-0.998 0.054 -0.044

-0.999 -0.598 0.624

-0.999 -0.723 0.753

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 theh termi premiums between a country pair is Pm−1 R,m 1 bR,1 = θtm − θtU S,m . See text for defined as the relative term premium. θtm = bi,m t − m j=0 Et it+j and θt details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θtR ) = θtR,120 , S(θtR ) = θtR,3 − θtR,120 , C(θtR ) = 2θtR,24 − (θtR,3 + θtR,120 ). 3. Sample period is from January, 1995 to December, 2015. All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, 2008. 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, 2008.

39

Table 4B. Summary Statistics for NSM Relative Term Premiums

L(θtR ) Mean

SD

S(θtR ) Mean

SD

C(θtR ) Mean

SD

corr(L,S) corr(L,C) corr(S,C)

AU

CA

DM

JP

NZ

SD

SW

UK

-0.308 (-0.263) (-0.387) 0.780 (0.919) (0.439)

0.80 (1.223) (0.065) 0.958 (0.752) (0.825)

-0.299 (-0.429) (-0.073) 0.535 (0.448) (0.599)

-0.337 (-0.169) (-0.629) 0.708 (0.726) (0.571)

-1.054 (-1.488) (-0.300) 1.496 (1.380) (1.393)

-0.793 (0.055) (-2.267) 1.665 (1.500) (0.508)

-0.255 (-0.032) (-0.643) 0.518 (0.359) (0.525)

-0.728 (-0.829) (-0.551) 0.617 (0.480) (0.773)

0.297 (0.255) (0.371) 0.755 (0.892) (0.414)

-0.799 (-1.218) (-0.070) 0.943 (0.761) (0.771)

0.278 (0.403) (0.061) 0.474 (0.415) (0.492)

0.236 (0.051) (0.559) 0.663 (0.690) (0.465)

0.973 (1.400) (0.232) 1.474 (1.342) (1.404)

0.734 (-0.076) (2.142) 1.549 (1.354) (0.505)

0.223 (-0.005) (0.620) 0.470 (0.330) (0.412)

0.684 (0.765) (0.543) 0.519 (0.412) (0.645)

0.013 (0.032) (-0.021) 0.620 (0.646) (0.574)

-0.463 (-0.788) (0.101) 1.156 (1.244) (0.691)

-0.313 (-0.462) (-0.055) 0.750 (0.821) (0.516)

-0.609 (-0.886) (-0.127) 0.546 (0.434) (0.352)

0.053 (0.196) (-0.195) 0.447 (0.364) (0.470)

-0.546 (-0.635) (-0.391) 1.442 (1.663) (0.931)

-0.313 (-0.502) (0.016) 0.506 (0.418) (0.477)

-0.041 (-0.327) (0.456) 0.662 (0.583) (0.469)

-0.993 -0.590 0.604

-0.990 -0.485 0.572

-0.947 0.158 0.094

-0.992 -0.379 0.468

-0.998 -0.839 0.847

-0.994 0.276 -0.204

-0.982 -0.116 0.221

-0.993 0.393 -0.332

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 inhthe term premiums between a i Pm−1 ,m R,1 1 m b b country pair is defined as the relative term premium. θt = it − m j=0 Et it+j and θtR,m = θtm − θtU S,m . See text for details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θtR ) = θtR,120 , S(θtR ) = θtR,3 − θtR,120 , C(θtR ) = 2θtR,24 − (θtR,3 + θtR,120 ). 3. Sample period is from January, 1995 to December, 2015. All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, 2008. 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, 2008.

40

Table 4C. Summary Statistics for Affine Relative Term Premiums

L(θtR ) Mean

SD

S(θtR ) Mean

SD

C(θtR ) Mean

SD

corr(L,S) corr(L,C) corr(S,C)

AU

CA

DM

JP

NZ

SD

SW

UK

-2.991 (-1.972) (-4.762) 2.063 (1.824) (0.962)

-1.846 (-0.856) (-3.567) 1.786 (1.385) (0.853)

-1.347 (-0.419) (-2.962) 2.013 (1.906) (0.825)

-3.013 (-1.968) (-4.830) 2.212 (1.979) (1.182)

-1.969 (-1.789) (-2.284) 1.463 (1.453) (1.436)

-2.365 (-1.186) (-4.414) 2.221 (1.791) (1.145)

-2.518 (-1.556) (-4.192) 1.828 (1.478) (0.968)

-1.799 (-2.275) (-0.970) 1.388 (1.349) (1.020)

2.962 (1.957) (4.709) 2.012 (1.773) (0.900)

1.865 (0.906) (3.533) 1.728 (1.349) (0.795)

1.342 (0.421) (2.944) 1.964 (1.848) (0.764)

2.988 (1.958) (4.779) 2.154 (1.920) (1.116)

1.931 (1.721) (2.296) 1.423 (1.417) (1.365)

2.367 (1.194) (4.406) 2.183 (1.758) (1.062)

2.495 (1.547) (4.143) 1.784 (1.439) (0.912)

1.780 (2.244) (0.974) 1.341 (1.305) (0.975)

2.425 (1.820) (3.479) 1.100 (0.895) (0.415)

1.969 (1.452) (2.868) 0.923 (0.723) (0.385)

1.192 (0.606) (2.212) 1.114 (0.986) (0.258)

2.393 (1.708) (3.585) 1.187 (0.934) (0.319)

1.221 (0.730) (2.074) 1.004 (0.829) (0.650)

2.320 (1.618) (3.540) 1.276 (1.040) (0.477)

1.980 (1.395) (2.998) 1.033 (0.803) (0.407)

1.352 (1.587) (0.943) 0.662 (0.647) (0.458)

-1.000 -0.988 0.989

-0.999 -0.972 0.979

-0.999 -0.963 0.971

-1.000 -0.933 0.937

-0.999 -0.765 0.785

-0.999 -0.890 0.901

-1.000 -0.97 0.971

-1.000 -0.974 0.975

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 premium. θtR,m = θtm − θtU S,m . See text for details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θtR ) = θtR,120 , S(θtR ) = θtR,3 − θtR,120 , C(θtR ) = 2θtR,24 − (θtR,3 + θtR,120 ). 3. Sample period is from January, 1995 to Decembr, 2015. All relative factors are reported in annualized percentage points. 4. Sample period is divided by the breakdate, May, 2008. 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, 2008.

41

Table 4D. Summary Statistics for CP Relative Term Premiums

L(θtR ) Mean

SD

S(θtR ) Mean

SD

C(θtR ) Mean

SD

corr(L,S) corr(L,C) corr(S,C)

AU

CA

DM

JP

NZ

SD

SW

UK

-0.361 (-0.146) (-0.707) 0.544 (0.481) (0.454)

0.341 (0.509) (0.070) 0.415 (0.411) (0.246)

0.548 (0.555) (0.536) 0.496 (0.518) (0.460)

-0.720 (-0.482) (-1.104) 0.497 (0.477) (0.204)

-1.069 (-0.924) (-1.302) 0.423 (0.403) (0.346)

0.932 (1.192) (0.513) 0.603 (0.585) (0.337)

-0.488 (-0.331) (-0.741) 0.422 (0.399) (0.327)

-0.262 (-0.245) (-0.289) 0.474 (0.522) (0.387)

0.278 (0.054) (0.637) 0.434 (0.344) (0.303)

-0.289 (-0.418) (-0.083) 0.267 (0.227) (0.186)

-0.574 (-0.627) (-0.488) 0.361 (0.382) (0.309)

0.499 (0.278) (0.854) 0.415 (0.356) (0.201)

0.906 (0.699) (1.240) 0.378 (0.263) (0.283)

-0.767 (-0.991) (-0.407) 0.395 (0.310) (0.202)

0.225 (0.047) (0.513) 0.397 (0.334) (0.315)

0.205 (0.141) (0.307) 0.384 (0.439) (0.243)

-0.053 (-0.251) (0.266) 0.324 (0.211) (0.192)

-0.126 (-0.183) (-0.034) 0.186 (0.176) (0.163)

-0.499 (-0.623) (-0.300) 0.263 (0.244) (0.142)

-0.191 (-0.324) (0.022) 0.251 (0.206) (0.150)

0.329 (0.168) (0.587) 0.281 (0.198) (0.185)

-0.393 (-0.549) (-0.143) 0.305 (0.233) (0.234)

-0.136 (-0.262) (0.067) 0.248 (0.187) (0.193)

0.022 (-0.145) (0.291) 0.350 (0.296) (0.249)

-0.900 -0.473 0.708

-0.799 0.006 0.516

-0.870 -0.284 0.613

-0.875 -0.460 0.787

-0.769 -0.226 0.679

-0.858 -0.168 0.577

-0.872 -0.371 0.439

-0.833 -0.188 0.584

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 premium. θtR,m = θtm − θtU S,m . See text for details. 2. The level, slope and curvature factors of the relative term premiums are constructed as follows: L(θtR ) = θtR,120 , S(θtR ) = θtR,24 − θtR,120 , C(θtR ) = 2θtR,48 − (θtR,24 + θtR,120 ). 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, 2015. 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, 2008. 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, 2008.

42

Table 5A. Predicting 3-Month Exchange Rate Change with Relative Expected Yields R R ∆st+3 = α0,st + α1,st L(Et iR t ) + α2,st S(Et it ) + α3,st C(Et it ) + t+3

   1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

where τ1 , τ2 : breakdates

H0 : α1,st = α2,st = α3,st = 0 for all st AU

CA

DM

JP

NZ

SD

SW

UK

1) NS model p-value Adj. R2

0.000 0.334

0.000 0.242

0.000 0.134

0.000 0.126

0.000 0.389

0.000 0.310

0.000 0.166

0.000 0.358

2) NSM model p-value Adj. R2

0.000 0.318

0.000 0.224

0.000 0.271

0.024 0.076

0.000 0.391

0.000 0.338

0.000 0.191

0.000 0.352

3) Affine model p-value Adj. R2

0.000 0.397

0.000 0.202

0.000 0.244

0.000 0.188

0.000 0.402

0.000 0.325

0.001 0.159

0.000 0.339

4) CP model p-value Adj. R2

0.000 0.162

0.001 0.166

0.003 0.139

0.000 0.143

0.000 0.401

0.000 0.308

0.000 0.235

0.000 0.377

Note: 1. The level, slope and curvature factors from 4 different types of relative expected yields 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 are incorporated. The first break date is around 2007 - 2008 and the second break is around 2011 - 2012, similar to those identified in Table 2A and 2B. Exact break dates are available upon request. 3. The p-value is for the Wald test that relative expected yield factors are jointly insignificant (H0 : α1,st = α2,st = α3,st = 0, ∀st ). Newey-West standard errors are used for the Wald test. 4. Adjusted R2 is also reported.

43

Table 5B. Predicting 3-Month Excess Currency Return with Relative Expected Yields R R xrt+3 = β0,st + β1,st L(Et iR t ) + β2,st S(Et it ) + β3,st C(Et it ) + t+3

   1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

where τ1 , τ2 : breakdates

H0 : β1,st = β2,st = β3,st = 0 for all st AU

CA

DM

JP

NZ

SD

SW

UK

1) NS model p-value Adj. R2

0.000 0.345

0.000 0.247

0.000 0.149

0.000 0.144

0.000 0.390

0.000 0.322

0.000 0.191

0.000 0.354

2) NSM model p-value Adj. R2

0.000 0.330

0.000 0.229

0.000 0.285

0.006 0.094

0.000 0.393

0.000 0.349

0.000 0.216

0.000 0.348

3) Affine model p-value Adj. R2

0.000 0.407

0.000 0.207

0.000 0.257

0.000 0.207

0.000 0.403

0.000 0.337

0.000 0.185

0.000 0.335

4) CP model p-value Adj. R2

0.000 0.180

0.000 0.170

0.001 0.155

0.000 0.154

0.000 0.408

0.000 0.317

0.000 0.258

0.000 0.378

Note: 1. The level, slope and curvature factors from 4 different types of relative expected yields 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 are incorporated. The first break date is around 2008 2009 and the second break is around 2011 2012, similar to identified in Table 2A and 2B. Exact break dates are available upon request. 3. The p-value is for the Wald test that relative expected yield factors are jointly insignificant (H0 : β1,st = β2,st = β3,st = 0, ∀st ). Newey-West standard errors are used for the Wald test. 4. Adjusted R2 is also reported.

44

Table 6A. Predicting 3-Month Exchange Rate Change with Relative Term Premiums ∆st+3 = α0,st + α1,st S(θtR ) + α2,st C(θtR ) + t+3    1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

where τ1 , τ2 : breakdates

H0 : α1,st = α2,st = 0 for all st AU

CA

DM

JP

NZ

SD

SW

UK

1) NS model p-value Adj. R2

0.000 0.252

0.000 0.157

0.004 0.080

0.010 0.110

0.000 0.131

0.044 0.111

0.009 0.104

0.000 0.286

2) NSM model p-value Adj. R2

0.000 0.277

0.013 0.109

0.451 0.075

0.012 0.112

0.000 0.218

0.000 0.191

0.003 0.113

0.061 0.048

3) Affine model p-value Adj. R2

0.000 0.236

0.000 0.225

0.001 0.100

0.000 0.090

0.000 0.337

0.567 0.027

0.112 0.088

0.000 0.324

4) CP model p-value Adj. R2

0.002 0.229

0.211 0.075

0.000 0.201

0.161 0.077

0.040 0.140

0.128 0.065

0.000 0.133

0.037 0.204

Note: 1. The slope and curvature factors from 4 different types of relative term premiums 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. The level factor is not included because the correlation between the level factor and the slope factor is close to −1. 2. Structural breaks are incorporated. The first break date is around 2007 - 2008 and the second break is around 2011 - 2012, similar to those identified in Table 2A and 2B. Exact break dates are available upon request. 3. The p-value is for the Wald test that relative term premium factors are jointly insignificant (H0 : α1,st = α2,st = 0, ∀st ). Newey-West standard errors are used for the Wald test. 4. Adjusted R2 is also reported.

45

Table 6B. Predicting 3-Month Excess Currency Return with Relative Term Premiums xrt+3 = β0,st + β1,st S(θtR ) + β2,st C(θtR ) + t+3    1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

where τ1 , τ2 : breakdates

H0 : β1,st = β2,st = 0 for all st AU

CA

DM

JP

NZ

SD

SW

UK

1) NS model p-value Adj. R2

0.000 0.250

0.000 0.152

0.002 0.091

0.002 0.130

0.000 0.141

0.047 0.106

0.002 0.127

0.000 0.281

2) NSM model p-value Adj. R2

0.000 0.268

0.011 0.104

0.406 0.068

0.001 0.130

0.000 0.203

0.000 0.172

0.001 0.131

0.041 0.055

3) Affine model p-value Adj. R2

0.000 0.250

0.000 0.227

0.000 0.115

0.000 0.109

0.000 0.339

0.668 0.029

0.025 0.118

0.000 0.321

4) CP model p-value Adj. R2

0.001 0.232

0.152 0.078

0.000 0.215

0.070 0.093

0.012 0.148

0.072 0.074

0.000 0.150

0.015 0.201

Note: 1. The slope and curvature factors from 4 different types of relative term premiums 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. The level factor is not included because the correlation between the level factor and the slope factor is close to −1. 2. Structural breaks are incorporated. The first break date is around 2007 - 2008 and the second break is around 2011 - 2012, similar to those identified in Table 2A and 2B. Exact break dates are available upon request. 3. The p-value is for the Wald test that relative term premium factors are jointly insignificant (H0 : β1,st = β2,st = 0, ∀st ). Newey-West standard errors are used for the Wald test. 4. Adjusted R2 is also reported.

46

Table 7A. Explaining Exchange Rate Change Macroeconomic Fundamentals, Yield Factors, or Both? R R R R ∆st+3 = β0,st + β1,st LR t + β2,st St + β3,st Ct + β4,st ut + β5,st πt + t+3

   1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

Wald test p-values No Yields? st = 1 st = 2 st = 3 No Macro? st = 1 st = 2 st = 3 Random Walk? st = 1 st = 2 st = 3 Adj. R2 τ1 τ1

where τ1 , τ2 : breakdates

AU

CA

DM

JP

NZ

SD

SW

UK

0.000 (0.001) (0.376) (0.000) 0.182 (0.636) (0.024) (0.759) 0.000 (0.000) (0.001) (0.000)

0.000 (0.025) (0.000)

0.000 (0.000) (0.079)

0.000 (0.058) (0.000)

0.000 (0.105) (0.000)

0.577 (0.707) (0.129)

0.000 (0.019) (0.000)

0.000 (0.000) (0.000)

0.000 (0.165) (0.000)

0.000 (0.109) (0.000) (0.000) 0.000 (0.313) (0.000) (0.000) 0.000 (0.000) (0.000) (0.000)

0.007 (0.001) (0.159)

0.110 (0.840) (0.007)

0.000 (0.001) (0.000) (0.003) 0.008 (0.005) (0.227) (0.155) 0.000 (0.000) (0.000) (0.004)

0.000 (0.612) (0.000) (0.000) 0.000 (0.018) (0.000) (0.000) 0.000 (0.056) (0.000) (0.000)

0.327

0.258

0.229

0.127

0.437

0.415

0.136

0.425

May,08 Jun,11

Jan,07

May,08

Jul,08

May,08 Jun,11

May,08 Nov,11

Feb.08

May,08 Nov,12

0.000 (0.207) (0.000) 0.001 (0.003) (0.000)

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 (β1,st = β2,st = β3,st = 0, ∀st ), and the ”No Macro” row tests the null hypothesis that macroeconomic fundamentals do not matter (β4,st = β5,st = 0, ∀st ). ”Random Walk” tests the null that exchange rate follows a random walk with a possible drift (βi,st = 0, ∀st 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 st = 1” test the null hypothesis that relative yield curve factors have no explanatory power when st = 1 (β1,st =1 = β2,st =1 = β3,st =1 = 0) 3. Adjusted R2 is also reported.

47

Table 7B. Explaining Exchange Rate Change Expectation, Risk, or Both from NSM model R R R R ∆st+3 = β0,st + β1,st L(Et iR t ) + β2,st S(Et it ) + β3,st C(Et it ) + β4,st S(θt ) + β5,st C(θt ) + t+3

   1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

Wald test p-values No Expectation? st = 1 st = 2 st = 3 No Risk? st = 1 st = 2 st = 3 Random Walk? st = 1 st = 2 st = 3 Adj. R2 τ1 τ1

where τ1 , τ2 : breakdates

AU

CA

DM

JP

NZ

SD

SW

UK

0.001 (0.000) (0.613) (0.103) 0.074 (0.275) (0.017) (0.649) 0.000 (0.000) (0.000) (0.000)

0.000 (0.005) (0.000)

0.000 (0.001) (0.000) (0.000) 0.029 (0.814) (0.386) (0.003) 0.000 (0.000) (0.000) (0.000)

0.000 (0.007) (0.000)

0.000 (0.002) (0.000) (0.079) 0.000 (0.254) (0.000) (0.237) 0.000 (0.009) (0.000) (0.002)

0.000 (0.000) (0.001) (0.000) 0.000 (0.366) (0.483) (0.000) 0.000 (0.000) (0.000) (0.000)

0.000 (0.168) (0.000) (0.001) 0.000 (0.633) (0.424) (0.000) 0.001 (0.026) (0.000) (0.000)

0.000 (0.641) (0.000) (0.068) 0.013 (0.022) (0.072) (0.188) 0.000 (0.101) (0.000) (0.000)

0.342

0.228

0.276

0.245

0.409

0.353

0.220

0.388

May,08 Dec,12

Jan,07

May,08 Aug.11

Sep,08

May,08 Jun,11

May,08 Dec,12

Jun,07 Jun,11

Jun,08 Jul,11

0.748 (0.982) (0.180) 0.000 (0.000) (0.000)

0.000 (0.000) (0.000) 0.000 (0.000) (0.000)

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 (β1,st = β2,st = β3,st = 0, ∀st ), and the ”No Risk” row tests the null hypothesis that relative term premium factors do not matter (β4,st = β5,st = 0, ∀st ). ”Random Walk” tests the null that exchange rate follows a random walk with a possible drift (βi,st = 0, ∀st 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 st = 1” test the null hypothesis that relative yield curve factors have no explanatory power when st = 1 (β1,st =1 = β2,st =1 = β3,st =1 = 0) 4. Adjusted R2 is also reported.

48

Table 7C. Explaining Exchange Rate Change Expectation, Risk, or Both from Affine model R R R R ∆st+3 = β0,st + β1,st L(Et iR t ) + β2,st S(Et it ) + β3,st C(Et it ) + β4,st S(θt ) + β5,st C(θt ) + t+3

   1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

Wald test p-values No Expectation? st = 1 st = 2 st = 3 No Risk? st = 1 st = 2 st = 3 Random Walk? st = 1 st = 2 st = 3 Adj. R2 τ1 τ1

where τ1 , τ2 : breakdates

AU

CA

DM

JP

NZ

SD

SW

UK

0.000 (0.034) (0.000) (0.000) 0.000 (0.202) (0.019) (0.001) 0.000 (0.000) (0.000) (0.000)

0.001 (0.163) (0.000)

0.000 (0.319) (0.000) (0.000) 0.042 (0.414) (0.133) (0.027) 0.000 (0.000) (0.000) (0.000)

0.000 (0.031) (0.000)

0.000 (0.813) (0.000) (0.000) 0.070 (0.256) (0.742) (0.016) 0.000 (0.012) (0.000) (0.000)

0.000 (0.000) (0.000) (0.000) 0.001 (0.118) (0.023) (0.006) 0.000 (0.000) (0.000) (0.000)

0.000 (0.336) (0.000) (0.000) 0.000 (0.090) (0.000) (0.000) 0.001 (0.012) (0.000) (0.000)

0.016 (0.846) (0.002) (0.163) 0.004 (0.905) (0.952) (0.000) 0.000 (0.845) (0.000) (0.000)

0.439

0.237

0.264

0.241

0.420

0.360

0.173

0.349

May,08 Jun,11

Jul,08

May,08 Jun,11

Sep,08

May,08 Jun,11

May,08 Feb,12

Jan,09 Nov,12

May,08 Aug,11

0.000 (0.145) (0.000) 0.000 (0.120) (0.000)

0.076 (0.046) (0.079) 0.000 (0.022) (0.000)

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 (β1,st = β2,st = β3,st = 0, ∀st ), and the ”No Risk” row tests the null hypothesis that relative term premium factors do not matter (β4,st = β5,st = 0, ∀st ). ”Random Walk” tests the null that exchange rate follows a random walk with a possible drift β0,st (βi,st = 0, ∀st 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 st = 1” test the null hypothesis that relative yield curve factors have no explanatory power when st = 1 (β1,st =1 = β2,st =1 = β3,st =1 = 0) 4. Adjusted R2 is also reported.

49

Table 7D. Explaining Exchange Rate Change Expectation, Risk, or Both from CP model R R R R ∆st+3 = β0,st + β1,st L(Et iR t ) + β2,st S(Et it ) + β3,st C(Et it ) + β4,st S(θt ) + β5,st C(θt ) + t+3

   1 if 1 ≤ t < τ1 st = 2 if τ1 ≤ t < τ2   3 if τ2 ≤ t ≤ T .

Wald test p-values No Expectation? st = 1 st = 2 st = 3 No Risk? st = 1 st = 2 st = 3 Random Walk? st = 1 st = 2 st = 3 Adj. R2 τ1 τ1

where τ1 , τ2 : breakdates

AU

CA

DM

JP

NZ

SD

SW

UK

0.000 (0.000) (0.002) (0.000) 0.168 (0.776) (0.054) (0.252) 0.000 (0.000) (0.000) (0.000)

0.000 (0.207) (0.000)

0.009 (0.171) (0.071) (0.017) 0.000 (0.001) (0.096) (0.007) 0.000 (0.000) (0.003) (0.000)

0.000 (0.000) (0.000)

0.000 (0.050) (0.000) (0.000) 0.162 (0.856) (0.023) (0.583) 0.000 (0.016) (0.000) (0.000)

0.000 (0.019) (0.000)

0.000 (0.271) (0.000) (0.000) 0.000 (0.432) (0.000) (0.679) 0.001 (0.056) (0.000) (0.000)

0.000 (0.004) (0.000) (0.002) 0.042 (0.320) (0.011) (0.409) 0.000 (0.013) (0.000) (0.004)

0.352

0.154

0.263

0.170

0.405

0.242

0.252

0.386

May,08 Jan,13

Jan,07

Oct,05 Jun,11

Nov,07

Apr,08 Jun,11

May,08

Nov,07 Jun,11

May,08 Oct,11

0.939 (0.502) (0.820) 0.000 (0.228) (0.000)

0.001 (0.016) (0.001) 0.000 (0.000) (0.000)

0.838 (0.634) (0.395) 0.000 (0.000) (0.001)

Note: 1. The relative expected yield factors and the relative term premium factors are extracted from CP model. The estimation method is described in Table 3D and 4D. 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 (β1,st = β2,st = β3,st = 0, ∀st ), and the ”No Risk” row tests the null hypothesis that relative term premium factors do not matter (β4,st = β5,st = 0, ∀st ). ”Random Walk” tests the null that exchange rate follows a random walk with a possible drift (βi,st = 0, ∀st 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 st = 1” test the null hypothesis that relative yield curve factors have no explanatory power when st = 1 (β1,st =1 = β2,st =1 = β3,st =1 = 0) 4. Adjusted R2 is also reported.

50

Table 8A. Explaining Exchange Rate Changes ∆st+k with Macroeconomic Fundamentals and Yield Curve Factors Hodrick’s (1992) Partial R2 [Entire sample period] k

uR t

πtR

∆st

LR t

StR

CtR

Total R2

Australia

1 3 6 12

0.020 0.039 0.048 0.047

0.018 0.044 0.069 0.087

0.007 0.007 0.007 0.006

0.001 0.003 0.003 0.002

0.003 0.006 0.011 0.016

0.015 0.031 0.042 0.048

0.042 0.084 0.113 0.126

Canada

1 3 6 12

0.000 0.000 0.001 0.004

0.014 0.033 0.048 0.056

0.006 0.001 0.001 0.000

0.009 0.024 0.041 0.053

0.002 0.005 0.006 0.005

0.000 0.001 0.003 0.004

0.048 0.087 0.117 0.137

Denmark

1 3 6 12

0.003 0.009 0.018 0.035

0.021 0.059 0.100 0.136

0.000 0.002 0.002 0.001

0.001 0.003 0.006 0.011

0.003 0.010 0.022 0.049

0.018 0.039 0.050 0.060

0.047 0.101 0.141 0.180

Japan

1 3 6 12

0.000 0.000 0.001 0.003

0.000 0.001 0.001 0.002

0.002 0.002 0.003 0.003

0.024 0.055 0.079 0.088

0.010 0.023 0.033 0.037

0.003 0.007 0.012 0.014

0.031 0.069 0.096 0.106

New Zealand

1 3 6 12

0.011 0.026 0.036 0.039

0.038 0.094 0.139 0.160

0.000 0.003 0.005 0.006

0.008 0.020 0.027 0.029

0.001 0.002 0.001 0.000

0.010 0.023 0.030 0.031

0.050 0.117 0.165 0.180

Sweden

1 3 6 12

0.018 0.030 0.030 0.022

0.041 0.097 0.137 0.144

0.003 0.006 0.007 0.004

0.001 0.002 0.001 0.000

0.000 0.000 0.001 0.002

0.018 0.037 0.046 0.042

0.075 0.164 0.216 0.214

Switzerland

1 3 6 12

0.002 0.007 0.016 0.026

0.035 0.085 0.119 0.126

0.005 0.000 0.001 0.002

0.003 0.008 0.013 0.014

0.008 0.029 0.061 0.119

0.016 0.044 0.069 0.101

0.073 0.146 0.200 0.245

United Kingdom

1 3 6 12

0.003 0.006 0.009 0.011

0.008 0.023 0.041 0.065

0.000 0.000 0.000 0.000

0.001 0.001 0.001 0.000

0.000 0.000 0.001 0.001

0.000 0.000 0.000 0.000

0.013 0.033 0.054 0.077

51

[Bef ore the f irst break] k

uR t

πtR

∆st

LR t

StR

CtR

Total R2

Australia

1 3 6 12

0.002 0.005 0.006 0.006

0.010 0.029 0.052 0.078

0.001 0.008 0.015 0.019

0.000 0.001 0.003 0.012

0.039 0.105 0.171 0.233

0.040 0.105 0.165 0.217

0.058 0.147 0.229 0.298

Canada

1 3 6 12

0.000 0.004 0.011 0.014

0.013 0.042 0.088 0.155

0.000 0.001 0.003 0.005

0.001 0.001 0.000 0.004

0.027 0.077 0.135 0.202

0.013 0.043 0.087 0.148

0.049 0.115 0.186 0.271

Denmark

1 3 6 12

0.003 0.007 0.010 0.013

0.004 0.012 0.022 0.035

0.014 0.020 0.022 0.019

0.017 0.050 0.097 0.168

0.047 0.119 0.196 0.272

0.075 0.167 0.241 0.289

0.084 0.183 0.265 0.339

Japan

1 3 6 12

0.003 0.002 0.000 0.000

0.004 0.010 0.015 0.014

0.000 0.003 0.005 0.005

0.015 0.038 0.061 0.080

0.017 0.044 0.065 0.077

0.013 0.039 0.065 0.080

0.038 0.082 0.115 0.132

New Zealand

1 3 6 12

0.003 0.007 0.011 0.016

0.058 0.127 0.173 0.193

0.006 0.015 0.021 0.022

0.000 0.001 0.003 0.005

0.026 0.069 0.117 0.171

0.048 0.102 0.130 0.132

0.098 0.209 0.276 0.311

Sweden

1 3 6 12

0.023 0.045 0.051 0.041

0.069 0.175 0.263 0.308

0.004 0.015 0.022 0.024

0.001 0.004 0.010 0.027

0.051 0.122 0.172 0.185

0.071 0.175 0.256 0.299

0.093 0.225 0.329 0.386

Switzerland

1 3 6 12

0.000 0.000 0.001 0.004

0.030 0.049 0.046 0.029

0.007 0.015 0.026 0.037

0.003 0.008 0.015 0.025

0.074 0.182 0.286 0.388

0.059 0.159 0.270 0.383

0.116 0.254 0.368 0.474

United Kingdom

1 3 6 12

0.000 0.000 0.001 0.003

0.026 0.063 0.088 0.093

0.011 0.000 0.000 0.001

0.001 0.003 0.005 0.007

0.002 0.007 0.014 0.023

0.009 0.026 0.037 0.041

0.063 0.116 0.157 0.167

52

[Af ter the f irst break] k

uR t

πtR

∆st

LR t

StR

CtR

Total R2

Australia

1 3 6 12

0.085 0.114 0.096 0.062

0.074 0.140 0.158 0.131

0.015 0.022 0.019 0.012

0.010 0.014 0.010 0.005

0.033 0.065 0.072 0.056

0.009 0.020 0.025 0.021

0.139 0.226 0.235 0.183

Canada

1 3 6 12

0.003 0.002 0.000 0.000

0.022 0.073 0.131 0.195

0.017 0.001 0.002 0.000

0.028 0.059 0.065 0.040

0.101 0.232 0.250 0.154

0.003 0.013 0.044 0.102

0.207 0.334 0.391 0.368

Denmark

1 3 6 12

0.006 0.017 0.034 0.062

0.098 0.280 0.377 0.341

0.009 0.005 0.006 0.001

0.001 0.014 0.039 0.081

0.024 0.045 0.023 0.000

0.002 0.001 0.011 0.014

0.217 0.350 0.401 0.370

Japan

1 3 6 12

0.004 0.025 0.057 0.060

0.023 0.025 0.006 0.007

0.021 0.012 0.009 0.006

0.057 0.100 0.103 0.080

0.041 0.073 0.081 0.070

0.001 0.007 0.019 0.033

0.167 0.280 0.303 0.264

New Zealand

1 3 6 12

0.026 0.059 0.070 0.071

0.040 0.127 0.195 0.226

0.001 0.025 0.039 0.031

0.046 0.121 0.154 0.137

0.141 0.278 0.265 0.156

0.000 0.001 0.003 0.005

0.234 0.382 0.403 0.326

Sweden

1 3 6 12

0.010 0.034 0.047 0.043

0.036 0.101 0.165 0.198

0.001 0.021 0.021 0.008

0.010 0.027 0.030 0.016

0.104 0.210 0.212 0.119

0.010 0.007 0.000 0.002

0.234 0.403 0.435 0.348

Switzerland

1 3 6 12

0.024 0.069 0.096 0.096

0.047 0.161 0.251 0.297

0.057 0.001 0.000 0.000

0.006 0.010 0.009 0.001

0.003 0.000 0.008 0.027

0.014 0.027 0.009 0.004

0.236 0.303 0.344 0.337

United Kingdom

1 3 6 12

0.014 0.016 0.008 0.000

0.069 0.165 0.239 0.242

0.011 0.018 0.010 0.001

0.000 0.014 0.053 0.096

0.107 0.227 0.254 0.162

0.067 0.075 0.037 0.005

0.237 0.369 0.379 0.317

Note: 1. The partial R2 reports the contribution of each variable in explaining ∆st+k for k = 1, 3,
6, 12. R R R R It is constructed by first estimating ft − µ = A(ft−1 − µ) + vt , where ft = uR t , πt , ∆st , Lt , St , Ct , and b then using A and the estimated covariance matrix of the V AR(1), as in Hodrick (1992). See text for details. 2. We report the partial R2 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, 2016. 3. Note that individual R2 ’s do not add up to the total R2 as the variables are correlated.

53

Table 9. Predicting Exchange Rate Change In-Sample: Model Comparisons RMSE Ratios and Diebold-Mariano Statistics [Entire sample period] k

AU

CA

DM

JP

NZ

SD

SW

UK

0.983 (1.188) 0.988 (1.375) 0.979 (1.464)

0.990 (0.800) 0.989 (1.373) 0.977 (1.559)

0.990 (1.240) 0.985 (1.602) 0.975** (2.058)

0.999 (0.348) 0.987 (1.289) 0.985 (1.500)

0.980 (1.579) 0.990 (1.315) 0.974* (1.850)

0.978* (1.743) 0.978** (2.207) 0.960** (2.394)

0.977* (1.668) 0.988 (1.050) 0.963** (1.988)

0.995 (0.690) 0.999 (0.319) 0.994 (0.759)

0.960* (1.712) 0.977* (1.700) 0.951** (2.143)

0.979 (0.971) 0.980 (1.363) 0.953* (1.661)

0.980 (0.990) 0.983 (0.955) 0.965 (1.487)

0.998 (0.625) 0.963* (1.852) 0.96** (2.078)

0.941** (1.965) 0.972* (1.768) 0.924** (2.226)

0.944* (1.851) 0.956** (2.084) 0.905*** (2.787)

0.971 (1.384) 0.979 (0.935) 0.947* (1.827)

0.987 (0.912) 0.997 (0.369) 0.984 (0.912)

0.938** (2.356) 0.976 (1.296) 0.929*** (2.685)

0.965 (1.313) 0.968 (1.574) 0.927* (1.933)

0.969 (1.040) 0.977 (1.024) 0.958 (1.147)

0.998 (0.328) 0.942** (2.461) 0.938*** (2.748)

0.910*** (2.659) 0.970* (1.739) 0.895*** (2.745)

0.919** (2.227) 0.958** (2.063) 0.882*** (3.048)

0.961 (1.445) 0.959 (1.159) 0.928 (1.585)

0.978 (1.128) 0.996 (0.321) 0.977 (1.051)

0.933*** (3.319) 0.980 (0.769) 0.918*** (3.097)

0.973 (1.391) 0.975 (1.224) 0.943* (1.794)

0.975 (0.784) 0.974 (0.932) 0.963 (0.748)

1.000 (-0.062) 0.930*** (3.075) 0.931*** (3.219)

0.914*** (3.601) 0.991 (0.447) 0.904*** (3.272)

0.913** (2.541) 0.980 (1.310) 0.921*** (3.225)

0.975 (1.013) 0.932 (1.416) 0.930 (1.170)

0.983 (0.658) 1.001 (-0.060) 0.986 (0.552)

k=1 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k=3 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k=6 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k = 12 RMSE(Macro/RW) RMSE(Yield/RW) RMSE(Joint/RW)

54

[Bef ore the f irst break] k

AU

CA

DM

JP

NZ

SD

SW

UK

0.994 (0.645) 0.965* (1.888) 0.965* (1.868)

0.995 (0.507) 0.978 (1.316) 0.974 (1.412)

0.991 (0.993) 0.959** (2.172) 0.957** (2.165)

0.995 (0.531) 0.991 (0.782) 0.983 (1.338)

0.971* (1.845) 0.965* (1.707) 0.949** (2.273)

0.962** (1.964) 0.955** (2.269) 0.951** (2.370)

0.978 (1.344) 0.970* (1.690) 0.950** (2.173)

0.980 (1.559) 0.986 (1.240) 0.968* (1.789)

0.980 (1.020) 0.897** (2.010) 0.895** (2.050)

0.981 (0.704) 0.949 (1.184) 0.951 (1.155)

0.992 (0.500) 0.906** (2.389) 0.899** (2.465)

1.000 (-0.025) 0.975 (1.175) 0.973 (1.170)

0.932** (2.101) 0.904** (2.412) 0.865*** (2.865)

0.898** (1.991) 0.877*** (2.646) 0.867** (2.488)

0.989 (0.475) 0.931 (1.612) 0.918 (1.635)

0.975 (0.937) 0.983 (0.640) 0.955 (1.127)

0.957* (1.715) 0.826** (2.217) 0.811** (2.377)

0.969 (0.917) 0.924 (1.250) 0.923 (1.140)

0.985 (0.653) 0.817*** (3.103) 0.808*** (3.049)

0.999 (0.041) 0.943** (2.222) 0.940* (1.938)

0.892*** (3.011) 0.861*** (3.349) 0.803*** (3.491)

0.829** (2.337) 0.803*** (3.100) 0.782*** (2.711)

0.993 (0.271) 0.863** (2.007) 0.856* (1.913)

0.969 (0.899) 0.986 (0.486) 0.951 (1.067)

0.949*** (3.022) 0.808*** (2.802) 0.756*** (3.270)

0.963 (1.549) 0.840** (2.277) 0.845* (1.845)

0.978 (0.855) 0.790*** (3.441) 0.763*** (3.209)

0.972 (1.242) 0.903*** (3.448) 0.888*** (3.614)

0.898*** (4.039) 0.865*** (4.233) 0.775*** (4.174)

0.799*** (3.280) 0.782*** (4.193) 0.745*** (3.696)

1.007 (-0.230) 0.770** (2.573) 0.769** (2.522)

0.970 (0.951) 1.009 (-0.409) 0.969 (0.844)

k=1 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k=3 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k=6 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k = 12 RMSE(Macro/RW) RMSE(Yield/RW) RMSE(Joint/RW)

55

[Af ter the f irst break] k

AU

CA

DM

JP

NZ

SD

SW

UK

0.944 (1.318) 0.958 (1.041) 0.936 (1.334)

0.975 (1.005) 0.925** (2.209) 0.894*** (2.619)

0.935** (2.054) 0.978 (1.098) 0.898** (2.185)

0.982 (0.751) 0.955 (1.193) 0.939 (1.536)

0.970 (1.290) 0.903** (2.184) 0.882** (2.442)

0.980 (1.001) 0.905 (1.626) 0.877** (1.977)

0.947 (1.303) 0.957 (1.161) 0.882** (1.973)

0.959 (1.148) 0.948 (0.713) 0.906 (1.197)

0.871* (1.757) 0.914* (1.659) 0.860* (1.831)

0.957 (1.089) 0.851** (2.511) 0.790*** (2.767)

0.847** (2.327) 0.956 (1.373) 0.818** (2.162)

0.963 (1.227) 0.857 (1.593) 0.818** (1.960)

0.924 (1.444) 0.773* (1.854) 0.724** (2.121)

0.947 (1.365) 0.806** (2.072) 0.736** (2.410)

0.919* (1.739) 0.987 (0.328) 0.854** (2.476)

0.882* (1.756) 0.768 (1.521) 0.717* (1.925)

0.863** (2.095) 0.913** (2.207) 0.850** (2.243)

0.938 (1.365) 0.825** (2.521) 0.767*** (2.647)

0.818** (2.093) 0.941 (1.364) 0.861 (1.386)

0.952 (1.095) 0.880* (1.895) 0.913 (1.282)

0.892* (1.842) 0.782 (1.533) 0.749** (2.073)

0.928** (1.997) 0.841* (1.959) 0.763** (2.336)

0.890** (2.180) 0.988 (0.248) 0.924 (1.279)

0.835** (1.969) 0.796 (1.432) 0.782** (1.978)

0.985 (0.379) 1.004 (-0.080) 0.979 (0.480)

0.946 (1.364) 0.921 (1.376) 0.946 (0.682)

0.965 (0.347) 0.949 (1.044) 1.036 (-0.359)

0.942 (1.157) 0.915* (1.843) 1.027 (-0.405)

0.954 (0.623) 1.007 (-0.045) 0.968 (0.315)

0.973 (0.409) 0.990 (0.163) 1.015 (-0.157)

0.927 (1.194) 1.031 (-0.982) 1.024 (-0.308)

0.922 (0.811) 1.026 (-0.334) 1.099 (-0.968)

k=1 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k=3 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k=6 RMSE(Macro/RW) RMSE (Yield/RW) RMSE(Joint/RW) k = 12 RMSE(Macro/RW) RMSE(Yield/RW) RMSE(Joint/RW)

Note: 1. Predicted exchange rate changes Et (∆st+k ) for k = 1, 3, 6, 12 are generated by estimating a V AR(1): ft − µ = A(ft−1 − µ) + vt 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 R R March, 2016. 2. For the macro-only model (labelled ”Macro”), f = u , π , ∆s . For the yield-only t t t t
R R model(labelled ”Yield:),
ft = ∆st , LR . For the macro-finance model (labelled ”Joint”), ft = t , St , Ct R R R R uR . 3. RMSE ratio reports the model root mean squared prediction errors over t , πt , ∆st , Lt , St , Ct 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.

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Figure 1A: 3-Month Exchange Rate Change (Annualized %; Home Currency/USD)

Note: 1. Figure 1A shows the quarterly change of the exchange rate, ∆st+3 = st+3 − st , where st is the logged home currency price per USD. 2. Sample period is from January, 1995 to March, 2016. All rates are in annualized percentage points.

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Figure 1B: 3-Month Excess Currency Return (Annualized %; Home Currency/USD)

S,3 Note: 1. Figure 1B shows the excess currency return, xrt+3 = (i3t − iU ) − ∆st+3 . 2. Sample period is t from January, 1995 to March, 2016. All rates are in annualized percentage points.

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Figure 2A: Relative Yield Curves Before and After the Break (Annualized %)

U S,m Note: 1. Figure 2A shows the monthly averages of relative yields, iR,m = im , over January, 1995 t t − it - April, 2008 (Blue solid line) and over May, 2008 - 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, 2008.

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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 US level factor, LR is in blue. Relative slope factor, StR = St − StU S is in red. Relative curvature t = Lt − Lt R US factor, Ct = Ct − Ct 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.

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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, 1995 December, 1995 and the last window is for January, 2015 - December, 2015.

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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, 1995 December, 1995 and the last window is for January, 2015 - December, 2015.

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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, 1995 - December, 1995 and the last window is for January, 2015 - December, 2015.

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Figure 4A: Decomposed Yield Curve by NS model (Annualized %)

Note: 1. Figure 4A shows the monthly averages over January, 1995 - December, 2015 of the relative yields (Blue solid line), the relative expected yields (Red dashed line) and the relative term premiums (Green solid line). The relative expected yields and the relative term premiums are estimated by Nelson-Siegel model, as described in Table 3A and 4A. 2. Sum of relative expected yield and relative term premium at each maturity is equal to the relative yield.

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Figure 4B: Decomposed Yield Curve by NSM model (Annualized %)

Note: Figure 4B shows the monthly averages over January, 1995 - December, 2015 of the relative yields (Blue solid line), the relative expected yields (Red dashed line) and the relative term premiums (Green solid line). The relative expected yields and the relative term premiums are estimated by Nelson-Siegel with Macro variable model, as described in Table 3B and 4B. 2. Sum of relative expected yield and relative term premium at each maturity is equal to the relative yield.

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Figure 4C: Decomposed Yield Curve by Affine model (Annualized %)

Note: Figure 4C shows the monthly averages over January, 1995 - December, 2015 of the relative yields (Blue solid line), the relative expected yields (Red dashed line) and the relative term premiums (Green solid line). The relative expected yields and the relative term premiums are estimated by Affine model, as described in Table 3C and 4C. 2. Sum of relative expected yield and relative term premium at each maturity is equal to the relative yield.

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Figure 4D: Decomposed Yield Curve by CP model (Annualized %)

Note: Figure 4C shows the monthly averages over January, 1995 - December, 2015 of the relative yields (Blue solid line), the relative expected yields (Red dashed line) and the relative term premiums (Green solid line). The relative expected yields and the relative term premiums are estimated by Cochrane-Piazessi model, as described in Table 3D and 4D. The relative expected yields and the relative term premiums from CP model exist for 24− to 120−month maturities. 2. Sum of relative expected yield and relative term premium at each maturity is equal to the relative yield.

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Figure 5A: Comparison of the Relative Expected Yields across models (Annualized %)

Note: Figure 5A shows the monthly averages over January, 1995 - December, 2015 of the relative expected yields from NS (Blue), NSM (Red), Affine (Black) and CP (Green) model. The relative expected yields from CP model exist for 24− to 120−month maturities.

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Figure 5B: Comparison of the Relative Term Premiums across models (Annualized %)

Note: Figure 5B shows the monthly averages over January, 1995 - December, 2015 of the relative term premiums from NS (Blue), NSM (Red), Affine (Black) and CP (Green) model. The relative term premiums from CP model exist for 24− to 120−month maturities.

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Figure 6A: NS Relative Expected Yield Curves Before and After the Break (Annualized %)

U S,m Note: Figure 6A shows the monthly averages of relative expected yields, Et iR,m = Et i m , over t t − Et it January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). All yields are annualized. The relative expected yields are estimated by Nelson-Siegel model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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Figure 6B: NSM Relative Expected Yield Curves Before and After the Break (Annualized %)

U S,m Note: Figure 6B shows the monthly averages of relative expected yields, Et iR,m = Et i m , over t t − Et it January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). All yields are annualized. The relative expected yields are estimated by Nelson-Siegel with Macro variables model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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Figure 6C: Affine Relative Expected Yield Curves Before and After the Break (Annualized %)

U S,m Note: Figure 6C shows the monthly averages of relative expected yields, Et iR,m = Et i m , over t t − Et it January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). All yields are annualized. The relative expected yields are estimated by Affine model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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Figure 6D: CP Relative Expected Yield Curves Before and After the Break (Annualized %)

U S,m Note: Figure 6D shows the monthly averages of relative expected yields, Et iR,m = Et i m , over t t − Et it January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). All yields are annualized. The relative expected yields are estimated by Cochrane-Piazzesi model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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Figure 7A: NS Relative Term Premium Curves Before and After the Break (Annualized %)

Note: Figure 7A shows the monthly averages of relative term premiums, θtR,m = θtm − θtU S,m , over January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). The relative term premiums are estimated by Nelson-Siegel model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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Figure 7B: NSM Relative Term Premium Curves Before and After the Break (Annualized %)

Note: Figure 7B shows the monthly averages of relative term premiums, θtR,m = θtm − θtU S,m , over January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). The relative term premiums are estimated by Nelson-Siegel with Macro variables model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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Figure 7C: Affine Relative Term Premium Curves Before and After the Break (Annualized %)

Note: Figure 7C shows shows the monthly averages of relative term premiums, θtR,m = θtm − θtU S,m , over January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). The relative term premiums are estimated by Affine model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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Figure 7D: CP Relative Term Premium Curves Before and After the Break (Annualized %)

Note: Figure 7D shows shows the monthly averages of relative term premiums, θtR,m = θtm − θtU S,m , over January, 1995 - April, 2008 (Blue solid line) and over May, 2008 - Dec, 2015 (Red dashed line). The relative term premiums are estimated by Cochrane-Piazzesi model. 2. The break date is chosen, considering that the most common breakdate by the structural break tests in the related regressions is May, 2008.

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