What influence does liquidity have on government bond yields?

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Section 1: Introduction

Nowadays liquidity of asset markets is an important topic. Daily liquidity of mutual funds and index trackers are offered while there is probably a lack of buyers when there are a lot of sellers due to uncertainty and market stress. Given the current interest in liquidity as an important topic in financial markets, this paper will explore how liquidity affects government bonds and what the interaction is between liquidity and aggregate risk in the market and their impact on government yields. The main aim is to see whether an earlier proposed and tested model of Favero, Pagano and Von Thadden (2010) holds looking at more recent data and controlling for sovereign risk.

Liquidity can be defined as how easy an asset can be converted into cash without sacrificing its price. By definition, cash is the most liquid asset. Beningno and Nasticò (2013) consider liquidity as the property of an asset to be exchanged for goods. What this paper wants to investigate is: ‘How liquidity affects the yield premium in government bonds.’ As will be shown later on, a lot of previous research has been done about this topic. The difference between this paper and previous papers, except the paper from Favero et al. (2010), is that we take a closer look at how transaction costs and aggregate risk influence the yield premium. This paper will especially focus on the interaction affect between the transaction costs and aggregate risk, which is different than most previous papers. The paper from Favero et al. (2010) has already investigated the interaction affect between the transaction costs and aggregate risk. This paper has a data set from after/during the final crisis, while Favero et al. (2010) have a data set from right after the introduction off the Euro. Mimicking their methods, this paper will investigated whether their findings hold with a data set that includes influences from the global financial crisis of 2008. If they do not hold, how they have changed, ten years later.

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and bank borrowing still rose levels previously seldom observed (Ivashina and Scharfstein, 2010). In the same period, the yield of the Treasury bond dropped dramatically due to high levels of investor demand for those securities, as well as quantitative easing policies that saw the central bank increase its holdings of government bonds (Krishnamurthy, 2010). Research has shown that multiple factors play a role in constructing the overall yield. This paper will address the most commonly used factors in constructing the yield: aggregate risk, solvency risk, bonds’ return distribution, liquidity, other investment opportunities and trading costs. Bonds’ return distribution and liquidity play a role in constructing the yield (Chen, L., Lesmond, D. A., & Wei, J., 2007), but further research needs to be done on how these two determinants react to each other and in what way. The bonds of the countries that are in the European Monetary Union (EMU) offer a great platform to investigate these determinants since there are no currencies and bond convention changes that have to be taken into account. Since the introduction of the Euro, there has been correlation between the bonds of the EMU participants but differences in yields have remained. For instance, a bond of Spain is not a good substitution for a German Bund. Bonds with the same AAA-rating still have a different yield and are not seen as a perfect hedge to each other. If we look at the yield differentials, solvency risk is one of the factors that investors see (Gryglewicz, S., 2011). Solvency risk is perceived differently for each country, even with the Stability Pact made by the countries that are in the EMU. A different factor can be liquidity. Liquidity can also play a role in constructing the yield according to Codogno, L., Favero, C., and Missale, A., (2003).

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factor explaining the yield differentials. Other factors must have an influence on the differentials, as well. Solvency risk and other investment opportunities are likely the other factors that have influential power. If we look at comparable bonds within the Euro-area with the same default risk relative to the German Bund, an increase in global risk perception can influence the yield differentials to co-move collectively. But this still does not give the full story. If we compare two AAA-rated Euro-countries, such as Finland and Germany, there is an average difference of 23 basis points (bp) that is higher for the bond of Finland compared to that of the German Bund. Meaning that default risk does not paint the complete picture. Showing that liquidity most likely does play a part in constructing the yield. Our theoretical analysis is based on the fact that liquidity is accounted for in pricing. We follow Favero et al. (2010) in the belief that liquidity interacts with aggregate risk factors which is not commonly used if we look at the traditional capital asset pricing model (CAPM). Vayanos (2004) has made a model that produces results which are contrary to the paper of Favero et al. (2010) and what this paper will produce. This will be explained more thoroughly in the literature section.

The model we will use is based on the model of Favero et al. (2010). Their model is constructed around the thought that the demand for liquidity depends on two factors. The first variable is: How large are the trading cost being incurred by investors? Obviously if trading costs are high, investors make less of a return on their money if they trade frequently. The second variable looks at if there are other investment opportunities that investors want to exploit. The investor rather holds on to their securities if no good alternative investment opportunities show themselves, which influences their liquidity. This paper assumes that when aggregate risk increases the need of investors to go into liquid securities decreases and therefore the premium declines.

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6 aggregated risk increases. The influence of transaction costs on yields is positive, but this weight declines if aggregate risk increases. For our research, we have collected daily data on yields and liquidity variables from the years 2012 and 2013. For aggregate risk we have used the yield difference between the U.S. government bonds on the corresponding maturity and the U.S. fixed interest rate on swaps. So aggregate risk is the U.S. swap rate minus the U.S. government yield. We have used daily data about a couple of EMU countries. Similar to what Favero et al. (2010) have done just after the introduction of the Euro. This paper wants to investigate if their results still hold, with a dataset that is almost exactly ten years older than theirs. Therefore, this paper will have a similar theoretical framework. This is needed so that a good comparison can be made between the result from Favero et al. (2010) and this paper. In addition to Favero et al. (2010), this paper is going to do extra regressions which include credit defaults swap (CDS) spreads to see how an extra factor of risk perception influences the results.

We have collected daily data from most Euro-area countries for the years 2012 and 2013. This data will be used in comparison with our benchmark country, Germany. We find that there is a negative interaction affect between the risk factor (which we measure through the difference between the U.S. swaps and U.S. yield) and the bid-ask spread (what we use to measure liquidity).

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Both papers have concluded that transaction cost has a direct effect on the yield premium, but they see this in the opposite way. Vayanos model looks at fund managers that need to sell their assets because their assets fall below a binding margin. These liquidations mostly happen when there is high volatility and are sold through the cheapest channels, meaning the most liquid assets. Because of these mutual runs to the cheapest channels Vayanos finds that there is a higher demand for liquidity and this increases the liquidity premium. The liquidity premium is defined as the difference between a forward interest rate and the market's expectation of the corresponding future spot rate (McCulloch, J. H., 1975). In other words, it is an extra return demanded by investors for holding assets that have the same characteristics but may be more difficult to convert into cash. Contrary to Vayanor’s paper this paper assumes that when aggregate risk increases the need of investors to go into liquid securities decreases and therefore the premium declines. Favero et al. Aggregate risk Search for Liquidity Yield premium Sensitive to trading costs Vayanos Aggregate risk Search for Liquidity Yield premium Not sensitive to trading costs The empirical implication of the model used in this paper is, while both increases in risk and illiquidity should decrease asset prices and increase their future returns, their interaction needs to have the opposite sign, meaning that assets prices should increase while the increased required return should be reduced (Favero et al., 2010).

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Beber et al. (2009) investigate the spreads between long-term bond yields and the Euro-area swap rate using CDS premium as a proxy for credit quality and trading-based liquidity measures like bid-ask spreads or market depth. They found that in times of market stress, investors chase liquidity (Beber et al., 2009). Schwartz (2011) has produced a model of Euro-area sovereign yield spreads over German bonds that used CDS spreads as a credit measure and an agency-government spread as a liquidity measure. A more recent study by Ejsing et al. (2015) looks at disentangled credit and liquidity premium in highly rated and very liquid sovereign markets, where they control directly for credit risk by using government-guaranteed agency bond yields. They find that there is no evidence of any systematic pattern between credit and liquidity factors. We will look at the U.S. Treasury-swap spread as a global credit risk factor and bid-ask spreads for liquidity.

To give this paper extra depth, we will include CDS spreads into our regressions. CDS spreads represent payments that must be paid by the buyer of CDS to the seller for the contingent claim in the case of a credit event, in this case non-payment (or forced restructuring) of sovereign debt, and is therefore an excellent proxy for market-based default risk pricing (Aizenman, J., Hutchison, M., and Jinjarak, Y., 2013). CDS spread correlates a lot with the yield of our government bonds. We therefore are interested in how our regressions react with the inclusion of the CDS spreads.

The main questions of this paper are the hypothesis. We want to tests these hypothesis and see in what why they differ or confirm the results from Favero et al. (2010). The hypotheses for this paper are:

Hypothesis 1. The yield differential is insensitive to aggregate risk if aggregate risk affects bonds of different fundamental value identically. It is increasing in aggregate risk if the fundamentals of riskier bonds react more to aggregate risk than those of less risky ones.

Hypothesis 2. The yield differential between the two bonds depends positively on their transaction cost differential.

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Section 3: Data

The data that we have collected for this paper is about the EMU countries: Austria, Belgium, Finland, France, Germany, Italy, the Netherlands, Portugal, and Spain. We have left out Greece and Ireland because we want to look if the results from Favero et al. (2010) still hold or in what way are different. And since they did not include these countries it is useless to include them in our paper. Favero et al. (2010) left Greece and Ireland out of their sample because there was not suitable data about these countries when they began their study. We have collected daily data from Bloomberg between the period of January 2, 2012 (we start at the second of January because the first was a Sunday) till January 6, 2014. We have also collected the 5-year credit default spread (CDS) about the same period. We only use the 5-year CDS spreads because these are most commonly used. We calculate the average 5-day spread between the bid and ask prices. The data is about the daily bid and ask prices. We calculate the average 5-day spread between the bid and ask prices. We have taken Germany’s Bund as our benchmark because it is has an AAA-ratings and because of the high trading volume. As said earlier Finland is also an AAA-rated bond but because of higher turnover in the German Bund we will use this as our benchmark.

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12 Euro-area government bonds. Table 1 also includes the CDS spreads, which we will use later to see if it can correct for differences in solvency. Table 1 Table 1 shows in Panel A the yield differentials (in basis point) between the government bonds and the German Bund for the 5- and 10-year bonds. Panel B shows the bid-ask spread minus the German Bund bid-ask Spread also for the 5- and 10-year bonds. Panel C shows the CDS differentials of the 5-year government benchmark bonds. The calculations have been based on data from January 2, 2012 till December 31, 2013. Panel A. Yield differentials 10-Year Bonds 5-Year Bonds

Mean Median Std. Dev. Mean Median Std. Dev.

Austria 62.05 46.90 29.22 38.16 22.30 33.51 Belgium 106.82 86.50 45.78 87.13 57.26 57.87 Finland 22.75 18.40 12.53 22.63 17.50 13.44 France 69.34 57.10 29.86 63.16 48.10 31.86 Italy 326.81 310.20 77.39 288.65 269.40 96.70 Netherlands 27.63 26.40 9.66 22.97 18.90 12.27 Portugal 673.29 552.40 248.51 783.65 663.20 258.55 Spain 367.22 353.90 94.86 328.12 300.50 119.35 Panel B. Bid-Ask Spreads 10-Year Bonds 5-Years Bonds

Mean Median Std. Dev. Mean Median Std. Dev.

Austria 1.90 1.40 1.32 3.29 2.00 2.96 Belgium 1.61 0.90 1.32 2.89 1.40 3.27 Finland 1.00 0.80 0.63 1.81 1.20 1.53 France 0.82 0.60 0.52 1.32 0.80 0.96 Italy 1.72 1.30 1.20 2.80 2.30 2.17 Netherlands 0.60 0.50 0.39 1.08 0.70 0.88 Portugal 34.07 23.30 27.65 44.72 30.10 39.59 Spain 3.66 3.00 2.21 6.29 4.90 4.40 Panel C: Euro-area CDS Differentials 5-Year Benchmark Bonds

Mean Median Std. Dev.

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Figure 1 shows the 5-day average bid-ask spreads of the Euro-area government bonds minus the 5-day average bid-ask spread of the German Bund. Graph B shows the spread of Portugal compared to the German Bund, we can see that in the beginning of the year 2012 the spread was astonishing high compared to the other bid-ask spreads in the graph A and C. For Portugal it starts the period with a little more than 130 bp compared to the German Bund. If you compare this to the maximum of Spain of almost 10 bp is it clear that there is a big spillover from the Greece crisis at that moment. The graph is interesting to look at because it shows that after about a year, so around the start of 2013, the spread has dropped to around 15 bp. If we take a closer look at graph A and C we can see that there is a reasonable high level of correlation and that the spreads are quite steady over time. Graph B gives a good illustration that for Spain shocks have a much higher impact on their spreads. Figure 1 Figure 1 shows 5-day average bid-ask spreads of the Euro-area government bonds minus the 5-day average bid-ask spread of the German Bund. The calculations have been based on data from January 2, 2012 till January 6, 2014 about the 10-year government bonds. On the vertical axe it shows the spread (in basis point) and the time is given on the horizontal axe. Graph A. the Netherlands, French and Finland -0,5 0 0,5 1 1,5 2 2,5 3 02-01-12 02-04-12 02-07-12 02-10-12 02-01-13 02-04-13 02-07-13 02-10-13 02-01-14 Bid-Ask Spread Minus German Bund

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14 Graph B. Portugal Graph C. Belgium, Austria, Spain and Italy In Figure 2 we can see the risk factor for the 5- and 10-year risk factor, which we measure through the difference between the U.S. swaps and U.S. yield differentials. Table 2 and table 3 show the correlation between the yield differentials of 10-year government bonds and the bid-ask spread of the 10 year government bonds, respectively. Table 2 shows that there is high correlation between the government bonds in the Euro-area except for Spain, which has an average correlation of around 0.55. For the bid-ask spreads shown in table 3 the correlations is slightly lower than the correlations for the yields. Indicating that 0 20 40 60 80 100 120 140 02-01-12 02-04-12 02-07-12 02-10-12 02-01-13 02-04-13 02-07-13 02-10-13 02-01-14 Bid-Ask Spread Minus German Bund Portugal 0 2 4 6 8 10 02-01-12 02-04-12 02-07-12 02-10-12 02-01-13 02-04-13 02-07-13 02-10-13 02-01-14 Bid-Ask Spread Minus German Bund

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15 Figure 2 Figure 2 shows the 5- and 10-years risk factor, which we measure through the difference between the U.S. swaps and U.S. yield differentials. The data is based on the period January 2, 2012 till January 6, 2014. On the vertical axe it shows the yield and the time is given on the horizontal axe. .0 .1 .2 .3 .4 I II III IV I II III IV 2012 2013

Risk Factor 10-Year Risk Factor 5-Year

Y ie ld Years the liquidity indicator, the bid-ask spread, behave differently than the yield in the Euro-area. This different movement is better observable when looking at correlation tables. France for instance has very high correlation with almost all other countries for the yield, but a much lower correlation when looking at the bid-ask spread. In case of Spain the opposite is happening. Table 2 Table 2 shows the correlation matrix of the yields for the 10-year benchmark bonds. The data is based on the period January 2, 2012 till December 31, 2013. 10-Year Yield Benchmark Bonds Correlation Matrix

_France France _1.00 Netherlands Spain _- _- Portugal Italy _- _- Austria _- Belgium _- Finland _-

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16 Table 3 Table 3 shows the correlation matrix for the bid-ask spreads of the 10-year benchmark bonds minus the 10-year German Bund. The data is based on the period January 2, 2012 till December 31, 2013. 10-Year Bid-Ask Spread Benchmark Bonds – German Bund Correlation Matrix

France Netherlands Spain Portugal Italy Austria Belgium Finland

France 1.00 - - - - Netherlands 0.69 1.00 - - - - Spain 0.73 0.74 1.00 - - - - - Portugal 0.69 0.40 0.65 1.00 - - - - Italy 0.72 0.65 0.82 0.77 1.00 - - - Austria 0.72 0.51 0.68 0.89 0.79 1.00 - - Belgium 0.75 0.53 0.73 0.89 0.83 0.92 1.00 - Finland 0.77 0.66 0.80 0.82 0.83 0.83 0.87 1.00

Section 4 Theoretical framework

This model will be based on the theoretical model of Favero et al. (2010) for good comparison of the results. Like them we have constructed a model with three dates, t = 0, 1, 2. 2 bonds can be traded, bond A and bond B, and there is a separate riskless asset that yields a return of r per period. Bond i = A,B pay face value V with probability 𝑞! and pays 0

with probability 1 − 𝑞! at date 2. At date 1 there is no pay out. We assume that A is bigger

than B giving 𝑞! ≤ 𝑞! and we take bond A as our benchmark. There is a common factor, 𝛼,

that has influence on the repayment probability for both bonds. When 𝛼 increases, both bonds are less likely to repay 𝑑𝑞!/𝑑𝛼 ≤ 0. The price of the bond 𝑝!! in the beginning of the

period, so time 0. At date 1 there is an opportunity to trade the bonds at a bid price of 1 − 𝑡_! 𝑝_!! and ask price of 𝑝!!, where 𝑡! is a proportional transaction cost.

There is an endless amount of investors ℎ ∈ 0,1 that want to invest at the beginning of the period. In this model we assume that investors are risk neutral and want to have the highest return on investment at date 2. The investors may have better investment prospects at date 1 and can sell their bonds to invest in these other opportunities, which included nonmarketable private equity and human capital. Favero et al. (2010): ‘The expected return of these other investments are negatively affected by the aggregate factor 𝛼:

1) 𝑟 − 𝑒!_𝛼,

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where 𝑟 > 0 is the maximal expected return and 𝑒! _{∈ 0, 𝑒 is a person-specific parameter}

that shows the investors exposure to the aggregate factor.’ Where the aggregate factor, in this setting, influences the return of these other investments opportunities in a negative way while in the same time declining the creditworthiness of marketable debt. The person specific parameter 𝑒!_{stands for how large the other investment opportunities are}

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18 equilibrium implying: 5) 𝜋! = 𝐺 _!!− _{! !! !}!!! ! . We need to discount the value and we take a constant discount rate between years 0-1 and 1-2. The expected payoff of bond i at period 0 therefore is: 6) 𝑝!! = 𝜋! !!!_!!!! !!!+ 1 − 𝜋! _!!!!!!! = !!!!!!!!! !!! ! .

We expect that investors already have rational expectations over their future decision to either sell (which occurs with probability 𝜋!) or hold on to the bond (which occurs with

probability 1 − 𝜋!). So the bond’s pledged yield to maturity is: 7) 1 + 𝑌! =_!! !! = !!! ! !!!!!! !!. The yield ratio between the two bonds is simpler to calculate than the yield differential. It is given by: 8) !!!! !!!!= !!!!!! !!!!!! !! !!

By using the approximation ln 1 + 𝑥 ≈ 𝑥 the yield differential at period 0 can be approximated by:

9) Δ𝑌 = 𝑌_!− 𝑌_! ≈ 𝜋_!𝑡_!− 𝑞_!− 𝜋_!𝑡_!+ 𝑞_!.

If we take a closer look at expression 8 we can see that there is direct positive impact on transaction costs. Because if 𝜋! is constant, then transaction costs would drive up yields.

Therefore a higher form of liquidity would be associated with lower required yields. This is because investors take into account that if they want to trade at period 1, this will bring transaction cost that need to be accounted for. Another quality of expression 8 is that the yield differential increases if fundamental risk increases. So if bond B has a high risk of default, the required yield for bond B will also go up compared to bond A. Beber et al. (2009) find in their paper this same impact of fundamental risk and of liquidity costs on yield spreads.

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how changes in liquidity and risk behave when the probability of liquidation is endogenous. Meaning that the probability itself reacts to changes in both transaction costs and other investment opportunities.

Liquidation of the bonds in period 1 depends on how high the transaction costs are and if there are any other good investment opportunities. Higher transaction costs automatically means that selling your bond at period 1 is less attractive. Similar to that, if there are no good other investment opportunities, investors are more inclined to hold on to their bonds. Taking this into account we can explore how risk and liquidity affect bond yields in our simple model: 10) !∆!_!" ! = 𝜋!+ !"! !"!𝑡!, 11) !∆!_!" =!"! !" 𝑡!− !"! !" 𝑡!+ ! !!!!! !" , If we take a closer look at equation 10 we can see that there is a positive and a negative term meaning that the sign is vague. This is because there are two effects that play a role: direct and indirect effects. Higher transaction costs have a direct effect on driving up the price by a factor 𝜋! and because this model works with endogenous liquidation probabilities

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we want to investigated is the sign between the derivatives.

Taking all this into account we have formed hypotheses that test the measures of illiquidity through transaction cost differential ∆𝑡 and changes in 𝑡! are mirror images of

those in 𝑡!. These will be the same as the paper of Favero et al. (2010). Here they are again

to freshen up the memory:

Hypothesis 1. The yield differential is insensitive to aggregate risk if aggregate risk affects bonds of different fundamental value identically. It is increasing in aggregate risk if the fundamentals of riskier bonds react more to aggregate risk than those of less risky ones: 12) !∆!_!" ≥ 0.

Hypothesis 2. The yield differential between the two bonds depends positively on their transaction cost differential:

13) !∆!_!∆! > 0.

Hypothesis 3. The positive effect of transaction costs on the yield differential is dampened by aggregate risk:

14) _!∆!"#!!∆! < 0.

To test these hypotheses we follow Favero et al. (2010) who make use of an approach that is built on the estimation of a simultaneous equation model for yield differentials with all different maturities. We will also measure the aggregate risk factor by the spread between j-year fixed interest rates on U.S. swaps, 𝑅_!"#!,!! , and the yield on j-year U.S. government bonds, 𝑅_!",!! just like Favero et al.(2010). They have opted for this measure because of its high correlation with all U.S.-based measures of risk and because of its availability at different maturities. They have developed the following dynamic partial adjustment model for yield differentials:

𝑌_!,! − 𝑌_!,! = 𝑝_! 𝑌_!,!!!− 𝑌_!,!!! + 1 − 𝑝_! 𝑌_!,!− 𝑌_!,! ∗+ 𝑢_!,!,

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theory-consistent long-run equilibrium value for yield differentials.

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stationary, then it can be proven that the standard assumptions for asymptotic analysis will not be valid. In other words, the usual “t-ratios” will not follow a t-distribution, so we cannot validly undertake hypothesis tests about the regression parameters2. We have checked this using unit root tests. We have used a group unit root test for the variables that differ across the countries and have used the ADF unit root test for the risk factors. The actual test results can be found in the Appendix and will be further explained hereafter. From the unit root test results we can see that in general we reject the null hypothesis of common unit root process and therefore we can conclude that the variables jointly are stationary. The risk factor for 10 years has a unit root, however if we look for the common unit root process we can reject the null hypothesis that there is a common unit root process. This indicates that, as a group, the data is stationary. These results show that we can use our data and assume that standard rules apply. Table 4 illustrates the estimation outputs of the seemingly unrelated regression as mentioned in the previous sector. We estimated 4 different equations put into 2 different models. Both models have a 10-year and 5-year equation but they differ in that model 2 also has the CDS differential factor within the equation. This gives us the following: Model 1: Panel A: 10-year yield differentials Panel B: 5-year yield differentials Model 2: Panel C: 10-year yield differentials with CDS differential Panel D: 5-year yield differentials with CDS differential From the table we can see that all of the coefficients are statistically highly significant. The 10-year yield differentials own lagged coefficients in the first model (Panel A) range from 0.97-0.99. For all countries this coefficient is close to 1, which is a sign of strong persistence of yield differentials, and means that today’s yield differentials in these countries are highly dependent on the previous period`s yield differentials. The coefficients do not change significantly when we also control for CDS differentials (Panel C). For this model the own lag coefficients range from 0.93-0.98. For the 5-year yield differentials they

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differentials, the bid-ask spread coefficients are now negative for the stronger rated countries but are positive for Italy, Spain and Portugal. It’s remarkable but not immediately clear why these results differ so much from the 10-year coefficients. Perhaps for stronger rated countries the 5-year bonds are considered a relative liquid substitute for the 5-year German government bonds and investors are not stopped by a somewhat higher trading cost. If we look at a regression of the yield differentials solely on bid-offer spreads in table 4 we find positive coefficients so the inclusion of aggregate risk and the interaction effect changes the relationship. Table 4 Table 4 show the result of a regression of the yield differentials solely on bid-offer spreads for the 5-year yield differentials. This regression was made on daily observations from January 2, 2012 to December 31, 2013. Standard errors are reported within parentheses below the coefficient estimates. ***, ** and * indicate that the corresponding coefficient is significantly different from 0 at the 1%, 5% and 10% levels, respectively.

Constant Own Lag Bid-Ask Spread

Austria 0.000 0.983*** 0.127*** (0.002) (0.005) (0.003) Belgium 0.002 0.985*** 0.22*** (0.003) (0.003) (0.006) Finland 0.001 0.985*** 0.091*** (0.001) (0.006) (0.003) France -0.001 0.995*** 0.299*** (0.002) (0.004) (0.003) Italy -0.007 0.995*** 0.566*** (0.008) (0.004) (0.000) Netherlands 0.002 0.982*** 0.166*** (0.001) (0.007) (0.006) Portugal 0.093*** 0.954*** 0.502*** (0.023) (0.008) (0.007) Spain 0.005 0.994*** 0.18*** (0.008) (0.004) (0.004)

When we look at the coefficient of the bid-offer spread in table 5, when this is negative we see that the coefficient of the interaction effect is positive. So still the impact of the 2 factors and their interaction is dampened due to the negative sign of the bid-offer spread. So Hypothesis 2 can be accepted for 10-year yield differentials and but not for 5-year yield differentials. More study is advised on the difference between 5- and 10-spread. So Hypothesis 2 can be accepted for 10-year yield differentials and but not for 5-year yield differentials.

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The results we find are very much in line with our Hypothesis 3, that the interaction between liquidity and aggregate risk factor has a negative influence on the yield differentials. Which is in line with the paper of Favero et al. (2010).

In models 2 we have implemented the CDS differential. The coefficients for CDS spread range from 0.00-0.09 for 10-year yield differentials and 0.00-0.32 for the 5-year yield differentials and have in most cases a small positive effect. This means that the increase in CDS differential with respect to the benchmark country, gives an increase in yield differentials. If we look at the R-squared, within the Appendix, we can see that almost all the R-squared are much bigger for the equation with CDS differentials involved. Meaning that if we include the CDS spread, the yield differentials can be explained better than without the CDS spreads included. Table 5

The equations are estimated by the seemingly unrelated regression (SUR) method on a sample of daily observations from January 2, 2012 to December 31, 2013. Panel A shows the coefficient estimates for the 10-year maturity. Benchmark country for all results is the German Bund 5/10 year accordingly. Panel B shows coefficients estimates results for the 5-year maturity. Panel C and D are the results of respective models where we additionally control for CDS differentials. Standard errors are reported within parentheses below the coefficient estimates. ***, ** and * indicate that the corresponding coefficient is significantly different from 0 at the 1%, 5% and 10% levels, respectively.

Variable Constant Own Lag Bid-Ask Spread Risk Factor Interaction

CDS differential Panel A. 10-Year Yield Differentials (model 1)

Austria -0.001 0.973*** 0.607*** 0.07*** -1.889*** (0.002) (0.005) (0.02) (0.002) (0.172) Belgium -0.002 0.979*** 0.873*** 0.104*** -3.117*** (0.002) (0.004) (0.028) (0.002) (0.232) Finland -0.001 0.978*** 0.284*** 0.018*** -0.499*** (0.001) (0.006) (0.013) (0.001) (0.12) France -0.001 0.983*** 0.923*** 0.042*** -2.434*** (0.002) (0.004) (0.031) (0.002) (0.28) Italy -0.004 0.988*** 1.44*** 0.196*** -6.706*** (0.005) (0.005) (0.034) (0.003) (0.303) Netherlands 0.000 0.969*** 0.717*** 0.052*** -3.66*** (0.001) (0.008) (0.029) (0.001) (0.249) Portugal -0.003 0.969*** 0.513*** 0.919*** -2.187*** (0.01) (0.007) (0.011) (0.019) (0.102) Spain -0.001 0.992*** 0.633*** 0.165*** -3.249*** (0.006) (0.004) (0.016) (0.004) (0.148)

Panel B. 5-Year Yield Differentials (model 1)

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26 (0.002) (0.008) (0.029) (0.003) (0.087) Belgium -0.005* 0.947*** -0.023 0.217*** 1.051*** (0.002) (0.006) (0.025) (0.003) (0.083) Finland -0.001* 0.961*** -0.102*** 0.048*** 0.416*** (0.001) (0.008) (0.016) (0.001) (0.049) France -0.002 0.951*** -0.074 0.156*** 0.791*** (0.002) (0.007) (0.058) (0.002) (0.186) Italy -0.005 0.984*** 0.775*** 0.184*** -1.809*** (0.006) (0.007) (0.03) (0.003) (0.107) Netherlands -0.001 0.934*** -0.318*** 0.087*** 0.898*** (0.001) (0.011) (0.048) (0.001) (0.16) Portugal -0.022* 0.941*** 0.489*** 1.485*** -0.6*** (0.013) (0.01) (0.025) (0.028) (0.074) Spain -0.002 0.987*** 0.366*** 0.17*** -1.123*** (0.006) (0.005) (0.017) (0.004) (0.084)

Panel C. 10-Year Yield Differentials (model 2)

Austria 0.000 0.937*** 0.944*** 0.162*** -5.345*** 0.041*** (0.002) (0.008) (0.03) (0.003) (0.244) (0.001) Belgium -0.001 0.942*** 1.035*** 0.2*** -5.946*** 0.04*** (0.002) (0.008) (0.053) (0.004) (0.368) (0.001) Finland -0.001 0.98*** 0.32*** 0.015*** -0.722*** 0.001*** (0.001) (0.006) (0.014) (0.001) (0.125) (0.001) France -0.001 0.947*** 0.545*** 0.036*** -0.735*** 0.044*** (0.002) (0.008) (0.081) (0.004) (0.484) (0.001) Italy 0.001 0.906*** 3.016*** 0.357*** -18.144*** 0.089*** (0.005) (0.01) (0.177) (0.021) (1.171) (0.001) Netherlands 0.000 0.963*** 0.789*** 0.041*** -3.017*** 0.011*** (0.001) (0.009) (0.036) (0.002) (0.309) (0.001) Portugal -0.002 0.931*** 0.253*** 0.593*** -1.738*** 0.064*** (0.01) (0.011) (0.027) (0.039) (0.157) (0.001) Spain 0.004 0.928*** 1.117*** 0.39*** -10.956*** 0.077*** (0.005) (0.007) (0.099) (0.022) (0.683) (0.001)

Panel D. 5-Year Yield Differentials (model 2)

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27 (0.012) (0.023) (0.059) (0.103) (0.152) (0.005) Spain -0.001 0.894*** 0.736*** -0.197*** -3.406*** 0.136*** (0.006) (0.011) (0.058) (0.026) (0.275) (0.002) 5.1 Robustness check To check the robustness of the models we also re-estimated the models with shorter periods (since 01/01/2013) and compared the estimation outputs. The year 2013 is after the famous words of Draghi (“Whatever it takes …”) and is a period of tightening yield differentials. The results are given below.

Table 5

The equations are estimated by the seemingly unrelated regression (SUR) method on a sample of daily observations from January 1, 2013 to December 31, 2013. Panel A shows the coefficient estimates for the 10-year maturity. Benchmark country for all results is the German Bund 5/10 year accordingly. Panel B shows coefficients estimates results for the 5-year maturity. Panel C and D are the results of respective models where we additionally control for CDS differentials. Standard errors are reported within parentheses below the coefficient estimates. ***, ** and * indicate that the corresponding coefficient is significantly different from 0 at the 1%, 5% and 10% levels, respectively.

Variable Constant Own Lag Bid-Ask Spread Risk Factor Interaction

CDS differential Panel A. 10-Year Yield Differentials (model 1)

Austria 0.000 0.972*** 0.533*** 0.077*** -3.43*** (0.001) (0.008) (0.016) (0.002) (0.145) Belgium 0.001 0.972*** 1.273*** 0.13*** -6.9*** (0.001) (0.006) (0.044) (0.004) (0.419) Finland 0.000 0.965*** 0.16*** 0.038*** -1.334*** (0.001) (0.011) (0.025) (0.001) (0.244) France 0.000 0.983*** 0.909*** 0.041*** -4.02*** (0.001) (0.006) (0.034) (0.002) (0.258) Italy -0.002 0.981*** 3.159*** 0.322*** -19.245*** (0.005) (0.007) (0.104) (0.008) (1.107) Netherlands 0.001 0.96*** 0.591*** 0.073*** -5.338*** (0.001) (0.009) (0.045) (0.002) (0.508) Portugal -0.001 0.976*** 0.47*** 0.6*** -2.159*** (0.009) (0.01) (0.013) (0.013) (0.097) Spain -0.005 0.986*** 1.301*** 0.246*** -7*** (0.005) (0.006) (0.039) (0.008) (0.416)

Panel B. 5-Year Yield Differentials (model 1)

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28 (0.001) (0.012) (0.099) (0.003) (0.661) Italy -0.003 0.964*** 1.426*** 0.443*** -4.488*** (0.005) (0.01) (0.15) (0.008) (1.162) Netherlands 0.000 0.929*** -1.19*** 0.083*** 6.167*** (0.001) (0.013) (0.117) (0.002) (0.725) Portugal -0.001 0.973*** 0.383*** 0.687*** -1.763*** (0.009) (0.01) (0.025) (0.018) (0.171) Spain -0.007 0.975*** 0.713*** 0.338*** -3.1*** (0.005) (0.007) (0.059) (0.007) (0.413)

Panel C. 10-Year Yield Differentials (model 2)

Austria 0.000 0.964*** 0.731*** 0.092*** -4.669*** 0.028*** (0.001) (0.01) (0.02) (0.002) (0.182) (0.002) Belgium 0.000 0.968*** 1.084*** 0.103*** -6.037*** 0.024*** (0.001) (0.007) (0.083) (0.007) (0.623) (0.003) Finland 0.000 0.964*** 0.307*** 0.041*** -2.512*** 0.003*** (0.001) (0.011) (0.027) (0.001) (0.255) (0.001) France -0.001 0.973*** 0.328*** 0.004*** -0.737*** 0.028*** (0.001) (0.008) (0.078) (0.004) (0.495) (0.001) Italy -0.001 0.885*** 4.396*** 0.155*** -30.181*** 0.133*** (0.005) (0.016) (0.445) (0.043) (3.557) (0.003) Netherlands 0.000 0.954*** 0.795*** 0.064*** -6.558*** 0.014*** (0.001) (0.01) (0.054) (0.004) (0.549) (0.002) Portugal 0.000 0.9*** 0.897*** 0.845*** -4.588*** 0.085*** (0.008) (0.018) (0.052) (0.06) (0.298) (0.003) Spain -0.004 0.93*** 2.156*** 0.157*** -14.752*** 0.09*** (0.005) (0.012) (0.147) (0.03) (1.157) (0.002)

Panel D. 5-Year Yield Differentials (model 2)

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29 From the results of table 5, about only the year 2013, we can assess that in general all the coefficients have about the same pattern as with the model that we have used for the whole time period. It is interesting to see that the interaction differentials, for this smaller period, are more extreme. For instance the 10-year coefficient for Italy is -19.35 while this was only -6.71 for the whole period. If we look at the graphs in section 3 we can see that this might have to do with that in the beginning, almost the whole year 2012, there is a lot of volatility. So now that we have taken the period 2012, out of the equation, the data becomes more closely packed together. Therefore giving more extreme results when small changes happen.

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30

accept higher trading costs and buy less liquid assets that promise a higher return. Therefore the yield differential declines.

The prediction of the constructed model was that the yield differentials would increase in both liquidity and aggregate risk, but the interaction between liquidity and aggregate risk should be negative. Looking into the results we can conclude that the risk factor is always significant. The results show that our predictions about the interaction effect where correct. They were indeed always negative and always highly significant.

If we compare the bid-ask spread coefficients of 5-year differentials and the 10-year differentials we get totally different results. The 10-year differentials all show to be positive but for the 5-year this is different, only 3 out of 8 are positive. The stronger rated countries are negative while Portugal, Italy and Spain are positive. To explain this more research needs to be conducted.

Comparing the results of Favero et al. (2010) to ours, we find very similar results for the 10-year differentials. Our results are more extreme than theirs but this can be contributed to the fact that their data set was just after the introduction of the Euro. Therefore the coefficients of most countries were still highly correlated. Nowadays there are bigger differences in what are considered safe and risky bonds to invest in and consequently there are bigger differences.

A shortcoming of our data is that we cannot conclude cross-sectional differences between countries and therefore we cannot conclude on what the influences are of macroeconomic conditions and/or policies of different countries. For this we have just too little variables included and this might be interesting to investigate in future research. Also different years of investigation might give different result as we see for the whole period and only for the year 2013. The variable maturity we have left out because of perfect multicollinearity. We do not think this has caused any big changes in the results but this should be investigated in additional research.

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31

A message for investors is that liquidity can affect the risk sensitivity of the assets they are holding, but this depends on how the liquidity costs and the aggregate risk are correlated.

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35

Appendix

Unit root tests 10-year yield differentials Group unit root test: Summary Series: YIELD10_AU, YIELD10_BE, YIELD10_FI, YIELD10_FR, YIELD10_IT, YIELD10_NL, YIELD10_PO, YIELD10_SP Date: 02/18/16 Time: 16:54 Sample: 1/02/2012 1/06/2014 Exogenous variables: Individual effects Automatic selection of maximum lags Automatic lag length selection based on SIC: 0 to 4 Newey-West automatic bandwidth selection and Bartlett kernel _Cross-

Method Statistic Prob.** sections Obs

Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -2.16692 0.0151 8 4188 Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -1.25360 0.1050 8 4188 ADF - Fisher Chi-square 19.5053 0.2433 8 4188 PP - Fisher Chi-square 17.9414 0.3273 8 4192 ** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality. Unit root tests 5-year yield differentials Group unit root test: Summary Series: YIELD5_AU, YIELD5_BE, YIELD5_FI, YIELD5_FR, YIELD5_IT, YIELD5_NL, YIELD5_PO, YIELD5_SP Date: 02/18/16 Time: 16:58 Sample: 1/02/2012 1/06/2014 Exogenous variables: Individual effects Automatic selection of maximum lags Automatic lag length selection based on SIC: 0 to 12 Newey-West automatic bandwidth selection and Bartlett kernel _Cross-

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36 Sample: 1/02/2012 1/06/2014 Exogenous variables: Individual effects Automatic selection of maximum lags Automatic lag length selection based on SIC: 3 to 6 Newey-West automatic bandwidth selection and Bartlett kernel _Cross-

Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -5.48788 0.0000 8 4159 Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -5.57426 0.0000 8 4159 ADF - Fisher Chi-square 71.1756 0.0000 8 4159 PP - Fisher Chi-square 176.153 0.0000 8 4192 ** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality. Unit root tests 5-year bid-ask spreads Group unit root test: Summary Series: BID_ASK5_AU, BID_ASK5_BE, BID_ASK5_FI, BID_ASK5_FR, BID_ASK5_IT, BID_ASK5_NL, BID_ASK5_PO, BID_ASK5_SP Date: 02/18/16 Time: 16:59 Sample: 1/02/2012 1/06/2014 Exogenous variables: Individual effects Automatic selection of maximum lags Automatic lag length selection based on SIC: 2 to 6 Newey-West automatic bandwidth selection and Bartlett kernel _Cross-

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37 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RISK10) Method: Least Squares Date: 02/18/16 Time: 17:01 Sample (adjusted): 1/03/2012 1/06/2014 Included observations: 524 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

RISK10(-1) -0.014517 0.007391 -1.964218 0.0500 C 0.001505 0.000947 1.589122 0.1126 R-squared 0.007337 Mean dependent var -0.000186 Adjusted R-squared 0.005435 S.D. dependent var 0.009056 S.E. of regression 0.009031 Akaike info criterion -6.572399 Sum squared resid 0.042578 Schwarz criterion -6.556134 Log likelihood 1723.969 Hannan-Quinn criter. -6.566030 F-statistic 3.858152 Durbin-Watson stat 1.898850 Prob(F-statistic) 0.050035 Unit root tests 5-year risk factor Null Hypothesis: RISK5 has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=18) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.247346 0.1899 Test critical values: 1% level -3.442601 5% level -2.866836 10% level -2.569652 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RISK5) Method: Least Squares Date: 02/18/16 Time: 17:01 Sample (adjusted): 1/03/2012 1/06/2014 Included observations: 524 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

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38 Unit root tests CDS spreads Group unit root test: Summary Series: CDS_AU, CDS_BE, CDS_FI, CDS_FR, CDS_IT, CDS_NL, CDS_PO, CDS_SP Date: 02/18/16 Time: 16:59 Sample: 1/02/2012 1/06/2014 Exogenous variables: Individual effects Automatic selection of maximum lags Automatic lag length selection based on SIC: 0 to 4 Newey-West automatic bandwidth selection and Bartlett kernel _Cross-

Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -1.88770 0.0295 8 4180 Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -0.84295 0.1996 8 4180 ADF - Fisher Chi-square 18.1874 0.3130 8 4180 PP - Fisher Chi-square 34.5883 0.0045 8 4192 ** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality.

Note: the coefficients from the equilibrium model should be multiplied by the 1-lag coefficients to get the coefficients from the tables.

Model 1 for 10 year yield differentials

System: EQ10_1

Estimation Method: Seemingly Unrelated Regression Date: 02/27/16 Time: 15:46

Sample: 1/02/2012 12/31/2013 Included observations: 521

Total system (balanced) observations 4168 Linear estimation after one-step weighting matrix

Coefficient Std. Error t-Statistic Prob.

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39 C(63) -118.9068 8.104856 -14.67105 0.0000 C(71) 16.74292 0.374154 44.74875 0.0000 C(72) 29.95742 0.608746 49.21170 0.0000 C(73) -71.33320 3.328659 -21.43001 0.0000 C(81) 75.04289 1.900032 39.49558 0.0000 C(82) 19.61258 0.431397 45.46297 0.0000 C(83) -385.3610 17.50306 -22.01678 0.0000

Determinant residual covariance 6.46E-13

Equation: YIELD10_AU=C(11)*BID_ASK10_AU+C(12)*RISK10 +C(13) *RISK10*BID_ASK10_AU

Observations: 521

R-squared 0.622270 Mean dependent var 0.622271

Adjusted R-squared 0.620811 S.D. dependent var 0.292898

S.E. of regression 0.180361 Sum squared resid 16.85066

Durbin-Watson stat 0.164750

Equation: YIELD10_BE=C(21)*BID_ASK10_BE+C(22)*RISK10 +C(23) *RISK10*BID_ASK10_BE

Observations: 521

Equation: YIELD10_FI =C(31)*BID_ASK10_FI+ C(32)*RISK10 +C(33) *RISK10*BID_ASK10_FI

Observations: 521

Equation: YIELD10_FR=C(41)*BID_ASK10_FR+C(42)*RISK10 +C(43) *RISK10*BID_ASK10_FR

Observations: 521

Equation: YIELD10_IT =C(51)*BID_ASK10_IT+ C(52)*RISK10 +C(53) *RISK10*BID_ASK10_IT

Observations: 521

Equation: YIELD10_NL=C(61)*BID_ASK10_NL+C(62)*RISK10 +C(63) *RISK10*BID_ASK10_NL

Observations: 521

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40

Observations: 521

Equation: YIELD10_SP=C(81)*BID_ASK10_SP+C(82)*RISK10 +C(83) *RISK10*BID_ASK10_SP

Observations: 521

System: FINAL10_1

C(11) -0.000908 0.001681 -0.540314 0.5890 C(12) 0.972733 0.004748 204.8723 0.0000 C(21) -0.001868 0.002206 -0.847005 0.3970 C(22) 0.979042 0.004158 235.4480 0.0000 C(31) -0.000543 0.000640 -0.848619 0.3961 C(32) 0.978161 0.006151 159.0128 0.0000 C(41) -0.001255 0.001763 -0.712056 0.4765 C(42) 0.982799 0.004455 220.5973 0.0000 C(51) -0.003684 0.004958 -0.743070 0.4575 C(52) 0.988483 0.004646 212.7479 0.0000 C(61) -0.000163 0.000875 -0.186776 0.8518 C(62) 0.969223 0.007626 127.1004 0.0000 C(71) -0.003268 0.010267 -0.318277 0.7503 C(72) 0.969338 0.007080 136.9049 0.0000 C(81) -0.000623 0.005613 -0.110963 0.9117 C(82) 0.991568 0.004140 239.5042 0.0000

Equation: YIELD10_AU=C(11)+C(12)*YIELD10_AU(-1)+(1-C(12)) *YIELD10_AU_0

Observations: 520

Equation: YIELD10_BE=C(21)+C(22)*YIELD10_BE(-1)+(1-C(22)) *YIELD10_BE_0

Observations: 520

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41

Equation: YIELD10_FI =C(31)+C(32)*YIELD10_FI(-1) +(1-C(32)) *YIELD10_FI_0

Observations: 520

Equation: YIELD10_FR=C(41)+C(42)*YIELD10_FR(-1)+(1-C(42)) *YIELD10_FR_0

Observations: 520

Equation: YIELD10_IT =C(51)+C(52)*YIELD10_IT(-1) +(1-C(52)) *YIELD10_IT_0

Observations: 520

Equation: YIELD10_NL=C(61)+C(62)*YIELD10_NL(-1)+(1-C(62)) *YIELD10_NL_0

Observations: 520

Equation: YIELD10_PO=C(71)+C(72)*YIELD10_PO(-1)+(1-C(72)) *YIELD10_PO_0

Observations: 520

Equation: YIELD10_SP=C(81)+C(82)*YIELD10_SP(-1)+(1-C(82)) *YIELD10_SP_0

Observations: 520

System: EQ10_2

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42

C(11) 14.90684 0.478511 31.15257 0.0000 C(12) 2.559937 0.047746 53.61547 0.0000 C(13) -84.40172 3.851475 -21.91413 0.0000 C(14) 0.646269 0.012991 49.74778 0.0000 C(21) 17.96339 0.916593 19.59801 0.0000 C(22) 3.477935 0.069051 50.36744 0.0000 C(23) -103.1703 6.387271 -16.15249 0.0000 C(24) 0.693319 0.013431 51.62173 0.0000 C(31) 15.91511 0.718940 22.13692 0.0000 C(32) 0.758697 0.042435 17.87919 0.0000 C(33) -35.94507 6.214697 -5.783882 0.0000 C(34) 0.025793 0.046899 0.549968 0.5824 C(41) 10.25895 1.520343 6.747791 0.0000 C(42) 0.672262 0.068718 9.782915 0.0000 C(43) -13.84186 9.106184 -1.520051 0.1286 C(44) 0.836723 0.021166 39.53121 0.0000 C(51) 32.12697 1.888010 17.01631 0.0000 C(52) 3.803624 0.228472 16.64810 0.0000 C(53) -193.3050 12.47061 -15.50084 0.0000 C(54) 0.943400 0.013789 68.41823 0.0000 C(61) 21.05691 0.968098 21.75081 0.0000 C(62) 1.090686 0.061251 17.80686 0.0000 C(63) -80.54432 8.263805 -9.746638 0.0000 C(64) 0.293694 0.031669 9.273774 0.0000 C(71) 3.671820 0.386526 9.499549 0.0000 C(72) 8.590180 0.564223 15.22479 0.0000 C(73) -25.17619 2.276926 -11.05710 0.0000 C(74) 0.920996 0.020646 44.60809 0.0000 C(81) 15.52553 1.370421 11.32902 0.0000 C(82) 5.424213 0.306059 17.72274 0.0000 C(83) -152.3500 9.502562 -16.03252 0.0000 C(84) 1.076490 0.017889 60.17576 0.0000

Equation: YIELD10_AU=C(11)*BID_ASK10_AU+C(12)*RISK10 +C(13) *RISK10*BID_ASK10_AU +C(14)*CDS_AU

Observations: 521

Equation: YIELD10_BE=C(21)*BID_ASK10_BE+C(22)*RISK10 +C(23) *RISK10*BID_ASK10_BE +C(24)*CDS_BE

Observations: 521

Equation: YIELD10_FI= C(31)*BID_ASK10_FI+C(32)*RISK10 +C(33) *RISK10*BID_ASK10_FI +C(34)*CDS_FI

Observations: 521

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43 Durbin-Watson stat 0.141757 Equation: YIELD10_FR=C(41)*BID_ASK10_FR+C(42)*RISK10 +C(43) *RISK10*BID_ASK10_FR +C(44)*CDS_FR Observations: 521

Equation: YIELD10_IT= C(51)*BID_ASK10_IT+C(52)*RISK10 +C(53) *RISK10*BID_ASK10_IT +C(54)*CDS_IT

Observations: 521

Equation: YIELD10_NL=C(61)*BID_ASK10_NL+C(62)*RISK10 +C(63) *RISK10*BID_ASK10_NL +C(64)*CDS_NL

Observations: 521

Equation: YIELD10_PO=C(71)*BID_ASK10_PO+C(72)*RISK10 +C(73) *RISK10*BID_ASK10_PO +C(74)*CDS_PO

Observations: 521

Equation: YIELD10_SP=C(81)*BID_ASK10_SP+C(82)*RISK10 +C(83) *RISK10*BID_ASK10_SP +C(84)*CDS_SP

Observations: 521

System: FINAL10_2

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44 C(41) -0.000928 0.001700 -0.545538 0.5854 C(42) 0.946899 0.007784 121.6517 0.0000 C(51) 0.000760 0.004653 0.163362 0.8702 C(52) 0.906137 0.009714 93.27821 0.0000 C(61) -0.000207 0.000869 -0.237726 0.8121 C(62) 0.962548 0.008500 113.2469 0.0000 C(71) -0.001590 0.010061 -0.158036 0.8744 C(72) 0.930969 0.010950 85.01772 0.0000 C(81) 0.004391 0.005332 0.823487 0.4103 C(82) 0.928086 0.007437 124.8008 0.0000

Observations: 520

Equation: YIELD10_IT =C(51)+C(52)*YIELD10_IT(-1) +(1-C(52)) *YIELD10_IT_0

Observations: 520

Equation: YIELD10_NL=C(61)+C(62)*YIELD10_NL(-1)+(1-C(62)) *YIELD10_NL_0

Observations: 520

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45

Equation: YIELD10_PO=C(71)+C(72)*YIELD10_PO(-1)+(1-C(72)) *YIELD10_PO_0

Observations: 520

Equation: YIELD10_SP=C(81)+C(82)*YIELD10_SP(-1)+(1-C(82)) *YIELD10_SP_0

Observations: 520

System: EQ5_1

C(11) -4.631939 0.486033 -9.530099 0.0000 C(12) 1.935633 0.045861 42.20694 0.0000 C(13) 24.40425 1.433021 17.02994 0.0000 C(21) -0.435166 0.476343 -0.913555 0.3610 C(22) 4.071024 0.057913 70.29554 0.0000 C(23) 19.67422 1.547988 12.70954 0.0000 C(31) -2.634749 0.402716 -6.542445 0.0000 C(32) 1.225614 0.021766 56.30804 0.0000 C(33) 10.72761 1.254544 8.551006 0.0000 C(41) -1.516715 1.204848 -1.258843 0.2082 C(42) 3.209421 0.048931 65.59050 0.0000 C(43) 16.29202 3.832200 4.251350 0.0000 C(51) 48.43954 1.902227 25.46465 0.0000 C(52) 11.50850 0.184947 62.22580 0.0000 C(53) -113.0024 6.683447 -16.90780 0.0000 C(61) -4.835981 0.727017 -6.651809 0.0000 C(62) 1.328478 0.021994 60.40129 0.0000 C(63) 13.64187 2.428416 5.617602 0.0000 C(71) 8.316393 0.418153 19.88840 0.0000 C(72) 25.26765 0.481142 52.51603 0.0000 C(73) -10.21931 1.259728 -8.112313 0.0000 C(81) 29.00947 1.314170 22.07436 0.0000 C(82) 13.51470 0.336798 40.12707 0.0000 C(83) -89.00855 6.661845 -13.36095 0.0000

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46

Observations: 521

Equation: YIELD5_BE=C(21)*BID_ASK5_BE+C(22)*RISK5 +C(23)*RISK5 *BID_ASK5_BE

Observations: 521

Equation: YIELD5_FI=C(31)*BID_ASK5_FI+C(32)*RISK5 +C(33)*RISK5 *BID_ASK5_FI

Observations: 521

Equation: YIELD5_FR=C(41)*BID_ASK5_FR+C(42)*RISK5 +C(43)*RISK5 *BID_ASK5_FR

Observations: 521

Equation: YIELD5_IT=C(51)*BID_ASK5_IT+C(52)*RISK5 +C(53)*RISK5 *BID_ASK5_IT

Observations: 521

Equation: YIELD5_NL=C(61)*BID_ASK5_NL+C(62)*RISK5 +C(63)*RISK5 *BID_ASK5_NL

Observations: 521

Equation: YIELD5_PO=C(71)*BID_ASK5_PO+C(72)*RISK5 +C(73)*RISK5 *BID_ASK5_PO

Observations: 521

Equation: YIELD5_SP=C(81)*BID_ASK5_SP+C(82)*RISK5 +C(83)*RISK5 *BID_ASK5_SP

Observations: 521

(47)

47

System: FINAL5_1

C(11) -0.003515 0.001804 -1.948722 0.0514 C(12) 0.939456 0.007716 121.7586 0.0000 C(21) -0.005296 0.002151 -2.461906 0.0139 C(22) 0.946579 0.005578 169.6967 0.0000 C(31) -0.001211 0.000684 -1.769706 0.0768 C(32) 0.961184 0.007861 122.2707 0.0000 C(41) -0.002370 0.001715 -1.381878 0.1671 C(42) 0.951478 0.007401 128.5653 0.0000 C(51) -0.005356 0.005579 -0.960017 0.3371 C(52) 0.983994 0.006888 142.8652 0.0000 C(61) -0.001036 0.000940 -1.103124 0.2700 C(62) 0.934166 0.010680 87.46983 0.0000 C(71) -0.021544 0.012950 -1.663585 0.0963 C(72) 0.941243 0.010332 91.10103 0.0000 C(81) -0.002189 0.006175 -0.354502 0.7230 C(82) 0.987388 0.004578 215.6971 0.0000

Observations: 520