Long term government bond yield correlations

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Long term government bond yield correlations

Jasper Schmidt

Student number: s1900447 Msc Finance, Faculty of Economics and Business, University of Groningen. Supervisor: R. Klijnstra

Abstract:

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1. Introduction

Since the economic crisis and the following Euro crisis there has been increased attention for default risks of nations. The differences in bond yields between troublesome southern European countries and their better performing northern counterparts have been increasing significantly. Germany, who’s 10Y government bond yield was hovering around 4 percent only a couple years ago is now in a situation where it can borrow money for a rate lower than inflation. If one were to isolate Germany from the rest of the world and see it as a standalone entity no one would think that country risk has decreased for Germany since before the economic crisis in 2008. The hypothesis is that the international market character of the bond market causes that investors make a trade-off between which bonds to buy. While objectively the risks in a particular country might have gone up, it’s risk premium on government bonds could go down. Simply because there are other countries that are performing worse. The second question this raises is which countries are connected and till what extent. Four countries, the United States, United Kingdom, Japan and Germany will be researched in this paper. For this each country will be ‘stripped’ from their internal risks as much as possible, and what is left will be regressed on the stripped yields from other countries. Within the euro zone these effects should be expected because they share a common market and currency. The choice between a US bond and a Japanese bond is perhaps less apparent. Money flees to less risky assets when the risk profile in a certain part of the world increases but it is uncertain if it can flee anywhere it wants.

1.1 Literature

Maltritz (2012) researched the determinants of sovereign yield spreads in the Eurozone. His focus was on country internal economic and budgetary drivers that influence the spread on yields within the Eurozone. Several of his determinants came out as significant which would imply that investors follow these determinants and make a choice in which bonds to invest within the Eurozone. In this paper the bond yield will be corrected for these determinants to check whether investors still weigh bonds against each other based on something else than rational economic circumstances. Ludger, Hagen and von Wolswijk (2010) researched the impact of the financial crisis on the risk perception of investors on government bonds. They found that since the financial crisis yields change more heavily in reaction to bad economic and budgetary circumstances. They also found differences between countries in the severity of the reaction to the economic and budgetary performance of governments. Germany and US act as ‘safe havens’. If their budget deficit increases and their economic outlook worsens the yield spread reacts less than that of other countries. This would imply that the spread is not

necessarily an objective measure of the default risk but that emotional decisions are made as to in which bonds money should be invested. Favero and Missale (2012) mention that there are no differences in liquidity due to different market sizes. Germany and the US both act as a safe haven but even though the US is a bigger market there is no larger liquidity. Thus different size countries are comparable purely on their internal drivers for default risk, which is the main driver of bond yield spreads. There are however several other papers that find that liquidity does matter. Such as Longstaff (2002), who argues that in risky times investors flee to more liquid bonds. In addition, Maltritz (2012) and, Bernoth, von Hagen and Schuknecht (2006) use a measure of bond liquidity for their estimation of yield structures.

Balli (2009) argues that not even the European bond market is fully integrated because countries react differently to global shocks. Even though there is an integrated market and the countries use the same currency the internal drivers do not predict the bond yield spread. Because country’s react differently to shocks and their economies are structured differently it is expected that the yield spread of each country is affected by different variables. In this paper the yield estimation s are done separately for each country and it is not a problem that they use different variables when comparing the residuals. Manganelli and Wolswijk (2009) researched

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the European market because this is perceived as an integrated market with a common currency. There are mixed results as to how integrated to bond market is, mainly because countries react differently to international shocks. The main conclusion from the literature is that there is no set framework of variables that can be used to estimate the bond yield. Almost every paper uses a different set of powers that have influence, and often different

variables are used to measure the same powers. In this paper a set of variables will be used based on the overview of literature, the choices that have been made are explained in in 2.3 Variables and dependable. As Ludger, Hagen and von Wolswijk (2010) argued that bond yields are not entirely formed by rational

expectations but also by emotional decision making there is part of the bond yield estimation that is not captured by the variables. Any differences between estimation and actual (the residuals) is either caused by a missing variable or by this emotional decision making. There are two reasons why there can be correlation in the residuals of different countries. One is the so called ‘flight to quality’ in which investors flee from unsafe assets (such as stocks) to safe government bonds in times of distress. The seconds is a relative value argument in which investors weigh certain bonds against each other, of bond yields in country A go down than investors will be motivated to buy bonds from country B which increases demand for bonds of that country and will thus drop the yield.

2. Model and hypotheses 2.1 Hypotheses

The main hypothesis:

H0: There is a positive relationship between bond yields in country A and country B, after correcting for internal economic variables.

H1: There is no positive relationship between bond yields in country A and country B, , after correcting for internal economic variables.

Supporting hypotheses:

H0: Variable A has a significant impact on the yield spread and has the expected sign.

H1: Variable A does not have a significant impact on the yield spread or does not have the expected sign.

The expectations are mentioned in 2.2 variables and dependable. There are eleven variables for each country, so a total of 44 of these hypotheses.

2.2 Basic model

The model exists of two parts, the first in which the bond yield for a particular country is estimated using internal variables. And the second in which the residuals of the estimations in the first part are used to estimate the residuals of another country.

𝑦𝑎= ∁ + 𝛽𝑎+ 𝜖

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the dependable. As an example take the debt level which increases the likelihood of default which increases the yield spread but it also increases liquidity which has a dampening effect on the spread. For this reason a broad significance level of 10% is used .

𝑌𝑖𝑒𝑙𝑑 𝐶𝑜𝑢𝑛𝑡𝑟𝑦𝑎− 𝑃𝑜𝑙𝑖𝑐𝑦 𝑅𝑎𝑡𝑒 = ∁ + 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐴 + 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐵 + ⋯ . + 𝜖

The internal variables used for the estimation can be different from country to country. Because each will use the variables that give the most closely related estimation to the actual path. This is done individually for the United States, United Kingdom, Japan and Germany. The residuals of these regressions are the part of the yield spread that is above or below of what is to be expected given the average level of risk attributed to the bond on the basis of the variables. This excess or shortage of yield is then regressed on the excess and shortage of the spreads of other countries. Because there is a reasonable expectation for heteroskedasticity in the residuals, the GARCH (Generalized Autoregressive Conditional Heteroskedastic) model made by Bollerslev (1986) is used for some estimations. This is used when there are periods of high variance and periods of low variance in the estimation, a basic Least Squares model assumes the variance is constant. Because the research concerns government bond yields and the timeframe includes the largest economic crisis since the 1930s it is expected that the variance will have large differences over time and that these bundle up in short periods.

𝜎𝑡2= 𝛼0+ 𝛼1𝑢𝑡−12 + 𝛽 𝜎𝑡−12

Above is the basic GARCH(1,1) model, which should be sufficient to capture the changes in variances. This is used for the estimations of the United States, United Kingdom and Germany for the large period. Japan shows no changes in variance and thus uses the least squares model. The different smaller periods all use the least squares model because over these timeframes the variance can be considered constant. The residuals will be saved and regressed against each other using the same GARCH or Least squares model depending on whether the variance showed change over time.

𝑅𝑎= ∁ + 𝑅1+ 𝑅2+ ⋯ + 𝜖

The results of this show whether there is a correlation in the bond spread of different countries that cannot be attributed due to correlation in the economic variables.

2.3 Variables and dependable

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Bond yield

The ten year government bond yield data comes from the OECD main economic indicators program. Economic growth

Used by Rowland and Torres (2004) and Maltritz (2012), they both use an index of the actual economic growth. But Since the dependable (yield spread) is a ten year obligation the buyer will care about the health of the economy in the longer term and not necessarily the growth of just this year . Edward (1986) uses the investments to GNP ratio as a proxy for the prospects on future growth. In this paper Purchasers Managers Indexes (PMI) are used as a proxy for the expected future growth of the country’s economy. The PMI’s are provided by Markit and are based on surveys of several hundred purchasing managers of companies within the country. It summarizes the direction the economy of the country is thought to be heading. Although such forecasts are more often than not incorrect their results should still be in line with the thoughts of the average buyer of government bonds . And thus correctly represent the information they use to form a price for the bonds in the market place. This variable is expected to have a positive sign, it indicates a large future growth of equity and the government must offer higher yields to be able to attract capital even though the risk for an investor is lower. For the Japanese estimations a similar variable is used that is provided by the Cabinet Office of Japan because Markit does not have the Japanese for the desired timeframe. This economic outlook is formed by a survey that covers 15,000 companies that have their headquarters or principal offices in Japan and have a capital stock of over ten million yen.

Interest expenditures

The total interest expenditures by the government on its current debt expressed as a percentage of GDP. It serves as an indication of how much new debt the economy will be able to carry and how risky that will be. If the percentage is low the yield of new bonds is expected to be low because the government is more capable of carrying the debt and vice versa. The data is from AMECO, which is the annual macro-economic database of the European Commission's Directorate General for Economic and Financial Affairs (DG ECFIN). I could not find any literature that uses this variable in estimating bond yields but I think it is an important measure of how much weight the government debt is currently having on the economy of that country. Debt to GDP partially does the same and is also in the estimation , but also including this emphasizes the actual costs that the debt brings.

Policy Rate

The rate at which central banks charge loans to commercial banks. It is set by the European Central Bank, Federal Reserve, Bank of England and the Bank of Japan for respectively Germany, USA, UK, and Japan. It could be seen as a short term lending rate, which will be used as a risk free rate of the country. Therefor it is deducted from the 10 year bond yield to achieve a yield spread. One of the big advantages of this approach is that it removes the clear downward trend from the bond yield. This is needed because a random variable that also happens to have a trend or that is registered on an index basis would most likely correlate with the bond yield, purely on the basis of the continuous downward or upward motion. All the data is provided by the central banks mentioned earlier.

Money Supply (M1 and M3)

Several definitions of the money supply exists, depending on how many sources you want to include. The European Central Bank (ECB) differentiates between the narrow (M1), intermediate (M2) and broad (M3) money supply. The website of the ECB gives a nice overview of the components of each of these definitions.

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Intermediate money (M2) comprises narrow money (M1) and, in addition, deposits with a maturity of up to two years and deposits redeemable at a period of notice of up to three months. Depending on their degree of moneyness, such deposits can be converted into components of narrow money, but in some cases there may be restrictions involved, such as the need for advance notification, delays, penalties or fees. The definition of M2 reflects the particular interest in analysing and monitoring a monetary aggregate that, in addition to currency, consists of deposits which are liquid.

Broad money (M3) comprises M2 and marketable instruments issued by the MFI sector. Certain money market instruments, in particular money market fund (MMF) shares/units and repurchase agreements are included in this aggregate. A high degree of liquidity and price certainty make these instruments close substitutes for deposits. As a result of their inclusion, M3 is less affected by substitution between various liquid asset categories than narrower definitions of money, and is therefore more stable.

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1

₎

Both the narrow and broad money supply definitions will be included in the estimations. M1 will be included because it consists of funds that can immediately be invested and it should thus have a negative effect on the yield spread. When there are large liquid funds in bank accounts the banks will try to invest this in liquid assets so they can comply to their obligations to deposit holders when needed. Government bonds are generally very liquid assets because the total value of them is relatively large and it is a very standardized financial product that is easily traded. M3 is included because it includes all forms of what according to the ECB can be considered to be money, and thus includes everything that can be invested in government bonds. It also comprises the large interventions in monetary policy that followed after the economic crisis in 2008. Quantative easing, which envelopes the purchase of large quantities of financial assets (usually short term government bonds), this extra demand increases the prices of these assets and thus subsequently lowers their yield. Data is provided by OECD main Economic Indicators, and is on an index basis with 2010 being 100. For Germany the data for the entire Euro Zone is used because it is considered to be one money market.

Reserves

Reserves in this paper are defined as foreign exchange and gold held by the government The data is from Oxford Economics. This variable is used in multiple other papers in varying forms. Min (1998), Rowland and Torres (2004) and Dailami, Masson and Padou (2005) all used the same form as used in this paper, reserves as a percentage of the GDP. Others like Kamin and von Kleist (1999), and Arora and Cerisola (2001) used the reserves as a percentage of imports. I think the relation to GDP is preferred because it gives a better notion of its size relative to country, the ratio against imports has the downside that more open economies get a higher ratio while just imports are irrelevant for inflation or default risks. There are two ways in which the reserves can influence the yield spread. The first is as a possible protection measure against inflation for the government. If the government wants to bring inflation down it can use its reserves to buy large sums of its own currency, this will increase the currency’s value and decrease the prices of imported goods. Besides this, increasing reserves indicates a money inflow which happens in economically good times, which correlates with high yield. Depending on which of the effects dominates the sign can be either negative or positive.

Inflation

This paper researches 10 year government bond so the inflation relevant in is that of the future 10 years. There were no inflation expectation numbers available for such a long timeframe, most focused on 6 months to a year ahead. The IFO institute however conducts a survey among representatives of multinational enterprises and economic experts which is focused on the trend they expect, which can be interpreted as a inflation expectation for the longer term. This variable is expected to have a positive correlation with the yield spread because investors want compensation for the inflation in the timeframe of the bond. Used by Lemmen and Goodhart (1999) and Maltritz (2012) for estimating the sovereign bond yield spread.

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Primary surplus

The government’s budget balance before interest expenditures as a percentage of GDP. Serves as an indication of how good the government will be able to carry new debt without cutting in regular expenses. Bernoth, von Hagen and Schuknecht (2006), and Schuknecht, von Hagen and Wolswijk (2010) add the fiscal balance which includes the interest expenditures, those however are estimated separately in this paper. Expected to have a negative relation with the yield spread. The data is from the OECD economic outlook program.

Debt to GDP

The amount of debt held by the central government as a percentage of the GDP as registered by Oxford Economics. A larger current debt is harder to carry for an economy and thus increases risks for investors. Used in almost every other paper involving government bond yields, including: Min (1998), Lemmen and Goodhart (1999), Kamin and von Kleist (1999), and Maltritz (2012). Baldacci, Emanuele, and Manmothan S. Kumar (2010) specifically research the influence of the debt to GDP ratio on the yield of government bonds, they found that a rise of five percent in the ratio could increase the yield by as much as one percent. Expected to have a positive correlation with the yield spread.

Net national savings

Net national Savings is the sum of private and government savings minus the consumption of fixed capital. An increase in these savings means that there will be more money to invest. Part of this will be invested in government bonds, and thus larger national savings will decrease the yield spread. This variable is not used in any earlier research that I could find for estimating the bond yield. The data is from AMECO.

Trade Balance

Next to internal risks a country is also exposed to external risks through international trade. Exports cause a country to have additional funds to pay off their debt which should reduce default risk. But when you have a trade deficit a country with which you have a deficit will have large amounts of your currency. The United States has a large trade deficit with China, the Chinese have for a large part invested their dollars in US government bonds effectively increasing the demand for US bonds. It is however doubtful that Germany’s large trade surplus causes them to pay more on their debt. Thus the trade balance can have a positive or negative sign depending on which of the effects dominates. These effects are captured by the visible trade balance, which is the sum of exports and imports. This variable is expressed as a percentage of the GDP of that country, when there is a negative trade balance it is a negative percentage and when positive its positive. It is used by Maltritz (2012) for estimating the bond yield spread. The data is from Oxford Economics.

Bond liquidity

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3 Results

The sample comprises four countries, the United States, Japan, United Kingdom and Germany. These are chosen because they are big and developed economies and all offer an abundance of available economic data. The starting date is 1992 which is 2 years after the German unification and the year in which a lot of the economic data for a single Germany begins. Most of the data is on a quarterly basis, some annual data is reformed to a quarterly frequency using Cubic Spline. The policy rate is interpreted as the risk free rate for the country in question, and thus subtracted from the 10 year bond yield. If a variable is not significant at the 10% level it is left out of the estimation.

The ups and downs of the actual line from the estimated lines are temporary extremes, they might be impossible to catch in a model using economic variables because they are likely to be caused by investor overreaction. The psychological foundation of this sentiment has been researched by Barberis, Schleifner and Vishny (1998). They divide it in two different effects, overreaction and under reaction both with exactly opposite effects. The study involved US stocks, but a similar effect is probable in the bond market. Strings of good or bad news can over or undervalue a bond which disconnects its value from its fundamentals. In case of bonds these fundamentals are the economic variables used in the model. The peaks and valleys that are not explained by these variables could thus be explained by the over- and under reaction of investors. Overall most of the estimations seem to catch the general trend and even a lot of the short term ups and downs. The bumps could be removed by adding the residuals of the estimations of other countries in the regression, this catches the sentiment of investors and the trade-off they make between bonds of different countries because of that.

3.1. Entire period estimation

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Table 1 – Yield estimation

Sample (adjusted): 1992Q1 – 2013Q4 Method: GARCH (LS for japan)

Dependent Variable: 10Y Bond yield – policy rate Observations per country: 88

United States United Kingdom Japan Germany

Variables Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Constant 7.364485*** (1.214186) [0.0000] 3.943733*** (0.541003) [0.0000] 7.633970*** (0.672823) [0.0000] -3.338665** (1.445098) [0.0209] Economic Growth 0.052884*** (0.009260) [0.0000] 0.011259** (0.005069) [0.0263] 0.015630*** (0.002305) [0.0000] 0.054562*** (0.008961) [0.0000] Inflation 0.074981** (0.035741) [0.0359] -0.307213 (0.074594) [0.0001] -0.287943*** (0.040174) [0.0000] Interest Expenditures -1.001276*** (2.784405) [0.0001] -1.854497*** (0.361414) [0.0000] -1.548256*** (0.501724) [0.0020] M1 0.082273*** (0.014275) [0.0000] -0.068091*** (0.012590) [0.0000] -0.051344*** (0.018109) [0.0058] -0.138164*** (0.018726) [0.0000] M3 -0.031781*** (0.009567) [0.0009] 0.152736*** (0.012206) [0.0000] 0.184174*** (0.044123) [0.0001] 0.120894*** (0.016347) [0.0000] Reserves 53.89880*** (11.15976) [0.0000] 6.889063** (3.142446) [0.0314] 22.82393*** (7.543641) [0.0025] Primary Surplus -0.406300*** (0.063918) [0.0000] -0.125026*** (0.009355) [0.0000] -0.176756*** (0.022345) [0.0000] Debt to GDP -0.141173*** (0.018280) [0.0000] -0.074841*** (0.013644) [0.0000] 0.075610*** (0.016930) [0.0000] National Savings -0.002696*** (0.000610) [0.0000] -0.008963*** (0.003219) [0.0054] -4.71E-05*** (8.54E-06) [0.0000] -0.002899*** (0.000979) [0.0031] Net trade 1.050585*** (0.063758) [0.0000] 0.463994*** (0.079876) [0.0000] -0.337218*** (0.058103) [0.0000] -0.251111*** (0.038578) [0.0000] Liquidity 20.90489*** (2.784405) [0.0000] -239.4513*** (16.51273) [0.0000] 3.610794* (2.012801) [0.0768] 25.93188** (12.18796) [0.0334] Adjusted R-squared 0.738376 0.793319 0.685313 0.720442 -*,**,*** represent significance at a 10%, 5%, or 1% -Estimated using EViews.

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Table 2 – Variable signs

Variable Expectation US UK Japan Germany

Economic Growth _Positive _Positive _Positive _Positive _Positive

Inflation _Positive _{Insignificant} _Positive _Negative _Negative

Interest Expenditures _Positive _Negative _{Insignificant} _Negative _negative M1 _Negative _Positive _Negative _Negative _Negative M3 _Negative _negative _Positive _Positive _Positive

Reserves _Inconclusive _{Insignificant} _Positive _Positive _Positive

Primary Surplus Negative Negative Negative Insignificant Negative

Debt to GDP _Positive _Negative _{Insignificant} _Negative _Positive

National Savings _Negative _Negative _Negative _Negative _Negative

Net Trade _Inconclusive _Positive _Positive _Negative _Negative

Liquidity _Negative _Positive _Negative _Positive _Positive

Table 3 – Cross-Residual regression

Sample (adjusted): 1992Q1 – 2013Q4 Observation per country: 88 Method: GARCH (LS for Japan) Dependent Variable: Residual series

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3.1.1 Cross-Residual regression

Table 3 contains the correlation of the residuals of the bond yield estimation for each country using the EGARCH method. The United States shows a significant relation with the United Kingdom and Japan. The United Kingdom shows a relationship with the United States and Germany. Japan shows a relation with the United Kingdom. And Germany shows a significant relation with the United Kingdom.

3.1.2 Cross yield regression

The 10 year bond yields are regressed on each other to look for correlations before compensating for any of the internal variables. All the bond yields correlate with each other except for Germany and Japan. It is to be expected that all the bond yields correlate with each other, this is caused mainly by correlation in economic circumstances. Due to international trade economic growth is highly correlated and in extension of that the government finances.

Table 5 – Cross Bond yield regression Sample (adjusted): 1992Q1 – 2013Q4 Observation per country: 88

Method: least squares

Dependent Variable: 10Y Bond yield

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In the same way we will now look at potential differences in these relationships during different periods. For this three time-periods, crisis, pre-crisis and the 90s. which will run from respectively 2006Q4 until 2013Q4, 1999Q4 until 2006Q4 and 1992Q4 until 1999Q4.

3.2 Crisis period

Because the residuals of all countries show no evidence of a changing variance over this time period, the least squares method is used for the estimations. A total of 20 variables, out of 44, have a significant correlation with one of the countries, against 39 during the whole time period (1992-2013). Half of those 20 variables have the same sign as expected. The adjusted R-squared is higher for the crisis period than for the whole timeframe, with an average of 93% against an average of 72%.

Table 7 shows the results of the estimation and table 6 gives an overview of the signs of the significant (at 10% level) variables. Economic growth is only significant for Germany but it is negative what is not expected. Inflation is significantly positive for the United States and Germany. The only variable that is significant for all the countries is Interest expenditures. It is negative, where a positive sign was expected, probably because of its correlation with economic output as explained earlier. Both M1 and M3 are significant for the United States and the United Kingdom, where the first is negative for both countries and the second positive. M3 is negative for Japan and M1 is positive for Germany. The primary surplus and debt to GDP are negative for the United States, where only the first was expected to be so. Debt to GDP is also significant for Japan and Germany, both with a positive sign. National savings is the only variable that is insignificant for every country during the crisis period. Net trade is significantly positive for the US and UK. Germany ran a positive trade balance for the entire period, and Japans’ balance only turned negative at the very end. The US and UK both have negative trade balances during the entire crisis period. Liquidity has a positive significant effect for the United States and Germany, while it is negative for Japan.

Table 6 – Variable signs crisis period

Economic Growth _Positive _{Insignificant} _{Insignificant} _{Insignificant} _Negative

Inflation _Positive _Positive _{Insignificant} _{Insignificant} _Positive

Interest Expenditures _Positive _Negative _Negative _Negative _Negative

M1 _Negative _Negative _Negative _{Insignificant} _Positive M3 _Negative _Positive _Positive _negative _{Insignificant} Reserves _Inconclusive _Positive _{Insignificant} _{Insignificant} _{Insignificant} Primary Surplus Negative negative Insignificant Insignificant Insignificant

Debt to GDP _Positive _Negative _{Insignificant} _Positive _Positive

National Savings _Negative _{Insignificant} _{Insignificant} _{Insignificant} _{Insignificant} Net Trade _Inconclusive _Positive _Positive _{Insignificant} _{Insignificant}

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Table 7 – Yield estimation crisis period

Sample (adjusted): 2006Q4 – 2013Q4 Method: Least Squares

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Sample (adjusted): 2006Q4 – 2013Q4 Observation per country: 29 Method: Least Squares

Dependent Variable: Residual series

Variables Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Constant -8.61E-16 (0.017586) [1.0000] -4.12E-15 (0.069543) [1.0000] 2.31E-15 (0.014029) [1.0000] 2.83E-15 (0.027933) [1.0000] United States 1.094980 (0.759966) [0.1620] 0.078900 (0.158769) [0.6236] 0.844629*** (0.269035) (0.0043] United Kingdom 0.070022 (0.048598) [0.1620] 0.048180 (0.039180) [0.2303] 0.025689 (0.080168) [0.7513] Japan 0.123976 (0.249474) [0.6236] 1.183848 (0.962705) [0.2303] 0.092207 (0.397780) [0.8186] Germany 0.334785*** (0.106637) [0.0043] 0.159229 (0.496909) [0.7513] 0.023260 (0.100342) [0.8186] Adjusted R-squared 0.352641 0.135559 0.019673 0.282116 -*,**,*** represent significance at a 10%, 5%, or 1% -Estimated using EViews.

In table 8 the results from the cross residual regression from the crisis time period are presented. Only Germany and the United States show a significant correlation. Which might be an indication of them being so called safe havens. During the distressed times of the crisis, Germany and the United States both might be considered safe not purely on the basis of their economic variables. This irrational effect, which causes them to have a yield spread lower than what they should have, makes their residuals correlate.

3.3. Pre-Crisis period

Because the residuals of all the countries show no evidence of a changing variance over this time period the least squares method is used for the estimations. The average adjusted R-squared is about 85%, which is eight percent lower than during the crisis period. 18 out of 44 variables show a significant correlation with one of the

countries. Of those 18 variables only 7 have the same sign as expected.

Table 10 shows the data from the crisis-period estimations. There is no variable that shows a significant

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net trade, all of them are positive. It also has the lowest adjusted r-squared at about 65%. The reserves are insignificant for all countries, for most countries this variables stayed about equal for the entire period, except for Japan which increased its reserves from about 6,5% late 1999 to 20% in 2006.

Table 10 – estimation pre-crisis period

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Table 9 – Variable signs pre-crisis period

Economic Growth _Positive _Positive _{Insignificant Insignificant} _Positive Inflation _Positive _{Insignificant} _Negative _{Insignificant Insignificant} Interest Expenditures _Positive _Negative _{Insignificant Insignificant} _Negative M1 _Negative _{Insignificant} _Negative _{Insignificant} _Negative M3 _Negative _{Insignificant} _Positive _{Insignificant Insignificant} Reserves _{Inconclusive Insignificant Insignificant Insignificant Insignificant} Primary Surplus Negative Negative Negative Positive Insignificant Debt to GDP _Positive _{Insignificant Insignificant Insignificant} _Negative National Savings _Negative _{Insignificant} _Positive _Positive _Negative Net Trade _Inconclusive _Positive _{Insignificant} _Positive _{Insignificant} Liquidity Negative Insignificant Insignificant Insignificant Positive

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Just as during the crisis period Germany and the United States show a correlation in the residuals. But now there is also a correlation between Germany and the United Kingdom. Both correlations are positive as is expected.

3.4. 90s period

Out of the 44 variable-country combinations, 26 are significant. 15 of those 26 have the same sign as expected. The average adjusted r-squared is 91% , with japan having the lowest at 86% and Germany the highest at 98%. Economic growth and national savings are both significant with the expected sign for the US, Japan and Germany. The money supply variables are significant for the US, UK and Germany, in which M1 is always negative and M3 positive. The primary surplus and debt to GDP are significant for the UK and Germany, both positive for the UK and negative for Germany. The interest expenditures is negative for the UK, Japan and Germany, they are all negative just like in all the other estimations. Both the inflation and reserves are significant for japan and Germany, inflation is positive for Japan and negative for japan, the reserves have the sign the other way around. Liquidity is positive for Germany and negative for the UK. Net trade is only significant for

Germany and it is negative as expected. Out of all the separate periods the 90s had the most significant variables, mostly due to Germany having them all as significant.

Table 12 – Variable signs 90s period

Economic Growth _Positive _Positive _{Insignificant} _Positive _Positive

Inflation _Positive _{Insignificant} _{Insignificant} _Positive _Negative

Interest Expenditures _Positive _{Insignificant} _Negative _Negative _Negative M1 _Negative _Negative _Negative _{Insignificant} _Negative M3 _Negative _Positive _Positive _{Insignificant} _Positive Reserves _Inconclusive _{Insignificant} _{Insignificant} _Negative _Positive Primary Surplus _Negative _{Insignificant} _Positive _{Insignificant} _Negative

Debt to GDP _Positive _{Insignificant} _Positive _{Insignificant} _Negative

National Savings _Negative _negative _{Insignificant} _Negative _Negative

Net Trade _Inconclusive _{Insignificant} _{Insignificant} _{Insignificant} _Negative

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Table 13 – Yield estimation 90s period

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Table 14 – Cross-Residual regression 90s period

Variables Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Constant 2.78E-15 (0.043854) [1.0000] -1.85E-14 (0.079387) [1.0000] -4.07E-15 (0.033990) [1.0000] 1.10E-14 (0.024492) [1.0000] United States 0.619909* (0.340159) [0.0804] 0.244670 (0.147087) [0.1087] -0.052399 (0.111203) [0.6416] United Kingdom 0.189170* (0.103802) [0.0804] -0.014627 (0.085581) [0.8657] 0.118042** (0.057007) [0.0489] Japan 0.407289 (0.244848) [0.1087] -0.079790 (0.466847) [0.8657] 0.184346 (0.139315) [0.1977] Germany -0.168000 (0.356536) [0.6416] 1.240215** (0.598947) [0.0489] 0.355059 (0.268326) [0.1977] Adjusted R-squared 0.132345 0.181415 0.084410 0.127540 -*,**,*** represent significance at a 10%, 5%, or 1% -Estimated using EViews.

3.5. Periods comparison

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Table 15 – Significant variables

United States United

Kingdom Japan Germany

Economic Growth 2 0 1 3 Inflation 1 1 1 2 Interest Expenditures 3 2 1 3 M1 2 3 0 3 M3 2 3 1 1 Reserves 1 0 1 1 Primary Surplus 2 2 1 1 Debt to GDP 1 1 1 3 National Savings 1 1 2 2 Net trade 2 1 1 1 Liquidity 1 1 2 3

The cross-residual regressions, which can be seen in table 3, 8 and 14 have different correlations in most periods. But there is a line visible in what is significant and when. During the 90s the United Kingdom correlates with the United States and Germany. Then in the new millennium the correlation between the US and UK disappears and Germany now correlates with the US and UK. During the crisis the UK’s correlation with Germany disappears and only Germany and the US correlate. Japan never correlates with any country, except for in the total period estimation where it shows a light correlation with the United Kingdom.

3.6. Variable impact

Each variable is regressed separately on the yield spread rate to evaluate the impact each variable individually has. All the variables were estimated using Least Squares. The data is presented in table 16, this table has a different layout than the tables before because each variable-country combination represents a separate estimation. The first number is the adjusted R-Squared of the estimation, the second the coefficient of the independent variable, the third is the probability of the independent variable. 35 of the 44 variables have a significant impact in the single variable estimations, 22 of those 35 variables have the same sign as expected. Japan had the most significant variables with only liquidity not being significant. But many of those significant variables have a different sign then is expected. This can perhaps be explained by the fact that Japan is the only country that has a trend in its yield spread, as can be seen in graph 1 till 4 on page 23. The impact a variable has can be seen form the adjusted R-Squared, which is a measure of how well the model fits the real data. Since there is only one variable it represents how well that variable is able to fit the bond yield or yield spread. The variable that has most impact for all countries is the policy rate, its adjusted R-squared ranges from 64% for the US to 82% for Japan. This was expected because the policy rate can be interpreted as a risk free rate from which the bond yield emerges.

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Table 16 – Single variable estimations Sample (adjusted): 1992Q1 – 2013Q4

Dependent Variable: 10Y Bond yield – Policy Rate or (1) 10Y Bond yield Method: Least Squares

United States

United

Kingdom

Japan

Germany

Variables Adjusted R-Squared (Coefficient) [probability] Adjusted R-Squared (Coefficient) [probability] Adjusted R-Squared (Coefficient) [probability] Adjusted R-Squared (Coefficient) [probability] Economic Growth 0.011852 (0.041999) [0.1565] 0.096846*** (-0.051380) [0.0018] 0.046073** (0.010290) [0.0250] 0.127924*** (0.073386) [0.0004] Inflation 0.086530*** (-0.358409) [0.0031] -0.011579 (-0.006637) [0.9486] 0.260728*** (-0.306401) [0.0000] 0.557612*** (-0.556398) [0.0000] Interest Expenditures -0.011615 (-0.006098) [0.9732] -0.004195 (0.224628) [0.4272] 0.244104*** (0.418956) [0.0000] -0.011301 (-0.046225) [0.8680] M1 0.017632 (0.009328) [0.1132] 0.068968*** (0.012451) [0.0077] 0.299128*** (-0.010568) [0.0000] -0.010796 (-0.001096) [0.7908] M3 0.006211 (0.006633) [0.2174] 0.108851*** (0.016844) [0.0010] 0.295888*** (-0.029422) [0.0000] -0.011274 (0.000674) [0.8627] Policy Rate(1) 0.640734*** (0.569134) [0.0000] 0.680102*** (0.650732) [0.0000] 0.815151*** (0.996357) [0.0000] 0.708648*** (0.682931) [0.0000] Reserves 0.050366** (243.2666) [0.0201] 0.141067*** (80.46472) [0.0002] 0.263190*** (-3.586561) [0.0000] -0.002968 (-10.38049) [0.3913] National Saving 0.414002*** (-0.003544) [0.0000] 0.543466*** (-0.041779) [0.0000] 0.225779*** (1.31E-05) [0.0000] 0.096870*** (-0.006634) [0.0018] Primary Surplus 0.345383*** -0.206923) [0.0000] 0.587288*** (-0.305561) [0.0000] 0.037625** (0.040848) [0.0388] 0.172123*** (-0.247406) [0.0000] Debt to GDP 0.123689*** (0.026145) [0.0005] 0.278031*** (0.045613) [0.0000] 0.300772*** (-0.006573) [0.0000] 0.146099*** (0.057187) [0.0001] Net trade 0.029619* (0.176159) [0.0592] 0.001530 (-0.084082) [0.2900] 0.136191*** (0.143280) [0.0002] -0.008752 (0.028839) [0.6217] Liquidity 0.396157*** (35.13102) [0.0000] 0.027170* (52.55978) [0.0675] -0.006012 (1.287872) [0.4903] 0.041184** (35.76344) [0.0323] -*,**,*** represent significance at a 10%, 5%, or 1% -Estimated using EViews.

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 92 94 96 98 00 02 04 06 08 10 12 JAPAN_YIELD-JAPAN_PR Graph 1, 2, 3 and 4:

3.7. Analysis of monetary policy

As can be seen from the graphs 6, 7, 8 and 9 (on page 24), countries have had very different developments of their money supply, especially since the credit crisis. Clearly visible is the dramatic rise in M1 in the United States graph since 2008, while in the UK both M1 and M3 show a stagnation since then. Over all the different period estimations M1 is significant 12 out of 16 times. Of those 12 it is negative 10 times and positive twice. M3 is significant 11 times and it is positive 9 times. Both M1 and M3 have two occasions where the sign differs from the norm, one of those is in the United States total estimation (table 1) where M1 and M3 have a different sign from all the other countries. The other is in the crisis period estimation where Germany and Japan both have one money supply definition as significant. In 9 occasions M1 is negative and M3 is positive. We can see in table 15 that both M1 and M3 show no significant relationship with the yield spread over the entire period. In table 7 it is visible that M1 has a negative effect and M3 has a positive effect during the crisis period for the United States. Since both variables use the same index basis, the coefficients can be compared and since M3 is bigger than M1, the monetary policy has an increasing effect on the bond spread. For the UK both definitions of money supply are significant in all estimations, with M1 negative and M3 positive. In 3 of those cases M3 has the bigger coefficient, only during the 90s period M1 is bigger. Monetary policy does not affect the yield spread in the Japan most of the time. During the 90s and pre-crisis period both definitions of money supply are insignificant. During the crisis period only M3 is negative, overall however both M1 and M3 are significant. In the German estimations only M1 is significant in the crisis and pre-crisis periods, being positive during the crisis and negative in pre-crisis. In the total estimation and during the 90s both money supply definitions are

significant with M1 negative and M3 positive.

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Overall the money supply had a positive influence on the bond spread except in Germany, where M3 is only slightly larger than M1. Both the US and UK had M1 negative and M3 positive during the crisis, with M3 being larger than M1. They have however completely different monetary policies. Where UK stagnates the growth of money, the US increases it drastically.

The mostly positive effect of money supply on the bond spread is either caused by an increase in inflation or because it is successful in stimulating the economy and thus raising overall expected future returns on assets. Table 17 shows the results of regressions of both definitions of money supply on the expected inflation. Although the adjusted R-squares are relatively low for most countries, all the coefficients are significant. When we regress both definitions of money supply on the PMI’s the results are significant for all country’s but Japan. The money supply affects the economy of a country on different area’s including inflation and economic growth. Which both causes the yield spread to go up, and on the other hand it increases the demand for bonds which causes the yield spread to go down.

There is no solid indication that quantitative easing in the United States have significantly reduced the yield spread. The measures have not been taken in the UK or Germany (in the period of this research) but the yields have a similar progression.

Graph 5, on the left here shows the development of the yield, the spread, the policy rate, M1 and M3 of the United States during the crisis. The starting dates of the three quantative easing programs are marked QE1, QE2 and QE3. The effect on M1 is clearly visible, but effects on either the yield or the spread are less apparent. Markets do not appear to react in any way to the QE programs.

Graph 6, 7, 8 and 9: 20 40 60 80 100 120 140 160 92 94 96 98 00 02 04 06 08 10 12 US_M1 US_M3 0 20 40 60 80 100 120 92 94 96 98 00 02 04 06 08 10 12 UK_M1 UK_M3 30 40 50 60 70 80 90 100 110 120 0 20 40 60 80 100 120 -2 -1 0 1 2 3 4 5 6 7 70 80 90 100 110 120 130 140 150 160 2006 2007 2008 2009 2010 2011 2012 2013

US_YIELD Policy Rate US_YIELD-US_PR US_M1 US_M3

QE1

QE2

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Table 17 – Inflation and money supply

Dependent Variable: Inflation expectation

Variables Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Coefficient (S.E) [p-value] Constant 3.255855 (0.424170) [0.0000] 2.055211 (0.341020) [0.0000] 2.744819 (1.255592) [0.0316] 2.322819 (0.384726) [0.0000] M1 -0.041050*** (0.012915) [0.0021] -0.080003** (0.039744) [0.0473] 0.041501*** (0.006843) [0.0000] 0.097965** (0.041567) [0.0207] M3 0.038099*** (0.011760) [0.0017] 0.106101** (0.043977) [0.0180] -0.041640** (0.019152) [0.0325] -0.097201** (0.039190) [0.0151] Adjusted R-squared 0.091084 0.145917 0.716961 0.052084 -*,**,*** represent significance at a 10%, 5%, or 1% -Estimated using EViews.

Table 18 – Expected economic growth and money supply

Dependent Variable: Expected economic growth (PMI’s)

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3.8. Comparison to volatility

Graph 10 (on the left) shows the residuals of Germany and the United states for the crisis period and a VIX (as a barometer of risk in the market). The VIX used is the Chicago Board Option Exchange SPX volatility index. The Generally periods with high volatility are associated with high amounts of uncertainty. You would expect that the residuals of both Germany and the US will drop below zero in times of high volatility. For the United States there is a large drop at the first peak of volatility, which is most probably caused by the large drop in policy rate at that time , Germany shows no clear drop (perhaps because its overall variance in the residuals appears to be less than that of the US). Because of the large drops in the policy rate it cannot be said whether there was a flight to quality during the first volatility peak. The other two peaks in volatility do seem to coincide with small downward deviations of the residuals, with this time Germany being a little more clear than the United States. The second peak is the euro crisis, the third coincides with the US debt ceiling crisis.

3.9 Net national savings

Because this variable has not been used in any earlier research I could find, there will be a deeper analysis of this variable. In the total period estimation and the single variable estimation net savings is shown to have a

significant impact on the yield spread. During the crisis however this significant relation disappears from the estimations. In graph 10 until 13 however it seems that the relationship is actually stronger during the crisis then at any other moment, especially for the United States, United Kingdom and Germany where the extremes fit almost perfectly over each other. The absence of the net savings variable in table 7 is probably because it is being dominated by other variables. At the start of the financial crisis net savings makes a steep drop for all countries, probably caused by unemployment and a lack of income indexation which stimulated people to eat their savings in order to keep a steady wealth level. When the economy starts recovering people start saving again, the savings drop a second time for Germany and the United Kingdom due to the euro crisis. Graph 11, 12, 13 and 14 show the yield spread (blue) and the net national savings (red) across time.

-1 0 1 2 3 4 5 -400 -200 0 200 400 600 800 92 94 96 98 00 02 04 06 08 10 12

US_YIELD-US_PR National Savings

-3 -2 -1 0 1 2 3 4 -40 -20 0 20 40 60 80 100 92 94 96 98 00 02 04 06 08 10 12

UK_YIELD-UK_PR National Savings

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4 Conclusion

There is evidence of irrational connections between the yields of long term government bonds. In this paper the rational is separated from the irrational by estimating the yield spread using a variety of economic variables. This is then what the yield spread should be given the average of the connection between the yield spread and the economic variables. The difference between this and the actuals are then regressed on the those of other countries. Over the whole time frame this gave correlations between the UK and the US, the UK and Germany, and a very light one between the UK and Japan. Across time the UK loses all its irrational connections with the other countries, where in the 90s it correlated with both Germany and the US, during the crisis it had no correlations. Germany and the United States are the only countries whose residuals correlate during the crisis. This probably due to the fact that they are both considered ‘safe havens’ to investors. This shared thought that these two countries are safer than others causes them both to have a lower yield spread then what is to be expected based on economic circumstances. Because of the correlation in the earlier periods one could argue that the United Kingdom also (partially) belonged to this safe haven group, but that its perception as safe has since been diminished. Japan is in a whole other group, it appears that investors never make the consideration between a Japanese government bond and that of one of the other three countries. There is some light evidence for a flight to quality during times of high volatility. But because of large measures taken with regard to the policy rate in Germany and the United States the effects on the yield spread are not conclusive. The correlation in residuals appears to be more caused by relative value in which investors weigh German and US bonds against each other because they are generally considered safe.

The other part of this paper was the estimation of bond yields with the use of economic variables. One of observations is that the relevant variables change a lot over time, as can be seen from table 15, where the green (meaning that the variable was significant once) is the dominant color. Nonetheless there are some interesting results from the estimations. Expected future economic growth, even though it decreases the risk of default, increases the yield spread because it indicates a large future growth of other assets, which bonds have to compete with. This forces governments to offer a higher yield on their sovereign bonds. Inflation gives mixed results, probably due to its correlation with the money supply which affects a country’s economy in different ways. Interest expenditures show a negative correlation in most cases. Does not serve as a good proxy for the risks of current debts. Debt to GDP ratio generally serves as a good indication of the risk of debt, higher ratio means a higher yield spread. Japan forms an exception to this. A country’s debt as a percentage of total debt in the OECD is not a good measure of bond liquidity. Net national savings are a good indication of demand for government bonds, the net in or outflow of savings negatively correlates with the yield spread, best illustrated by graph 11 until 14. Decreasing the bond yield for all country’s (japans’ single variable estimation has a positive coefficient, but this is due to both having a largely downward trend over time). Net national savings is not a good proxy in distressed economic times, it disappears from the estimations during the crisis. However when looked at it separately it appears that the relationship between net national savings and the yield spread only becomes stronger. Other variables apparently have a more dominant influence during that time which causes saving to drop for all countries. Net trade balance appears to have different effects depending on whether the country runs a surplus or deficit. The primary surplus is a good indication of the state of current government’s finances. Money supply influences the bond yield in different ways. Directly by increasing demand for bonds and thus lowering the yield, indirectly by its correlation with inflation and economic growth.

4.2 Discussion

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