# Bond Yields, Sovereign Risk and Maturity Structure

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Sovereign Risk Proxies

## 4. Hypotheses Formulation

#### 4.1. Relation between Sovereign Risk and Debt Maturity Structure

**Hypothesis**

**1.**

#### 4.2. Diamond’s Model (1991) and Its Application in the Analysis of the Maturity Structure

**Hypothesis**

**2.**

#### 4.3. Stock of Debt Influence on the Relationship between Sovereign Bond Yields, Sovereign Risk and Debt Maturity

**Hypothesis**

**3.**

## 5. Data and Methodology

#### 5.1. Data

- The dependent variable is the ratio of long-term debt to total debt9. The ratio of long-term debt to total debt allows us to analyze the impact of sovereign risk on the maturity structure of sovereign debt. The data for this variable were obtained from the European Central Bank Statistical Data Warehouse, which collects data from the European System of Central Banks (ESCB), Eurostat and national central banks. This ratio represents the volume of long-term debt from all sectors of the economy to the total debt10.
- We included the average maturity of sovereign debt as the main determinant of the sovereign debt maturity structure. This variable represents residual maturity of sovereign debt expressed in years. The data were obtained from the European Central Bank Statistical Data Warehouse. We considered the following control variables as determinants of sovereign debt maturity structure:
- ▪
- Inflation (Missale and Blanchard 1994; Goudswaard 1990; De Haan et al. 1995): This variable was expressed as the increase compared to the previous period. It is expected that the coefficient for this variable has a negative sign because higher inflation increases uncertainty about the long-term bonds. This uncertainty generates a trend toward investing in short-term maturities. The data were obtained from the European Central Bank Statistical Data Warehouse.
- ▪
- Gross Domestic Product (GDP): This variable was used as a proxy for the business cycle (Goudswaard 1990) and to control the size of the economy. It is expected that an increase in GDP leads to an increase in the debt maturity and therefore a lengthening of the maturity structure. The data were obtained from the Eurostat Statistics Database.
- ▪
- Debt/GDP ratio (Missale and Blanchard 1994; De Haan et al. 1995; Bodnaruk 1999): Data for this variable were obtained from European Central Bank Statistical Data Warehouse11.
- ▪
- Borrowing requirements of the public administration: the borrowing requirement covers all financial transactions in government debt instruments. The data were obtained from European Central Bank Statistical Data Warehouse.

- Annual 10-year sovereign bond yields: This proxy was calculated as the average of the monthly bond yields published in the European Central Bank Statistical Data Warehouse. A high value of returns is generally indicative of greater sovereign risk; therefore, we expect to find a negative relationship with the ratio of long-term debt to total debt.
- Spreads (Broner et al. 2013; Perez 2017): This proxy allowed us to measure the default risk of a country. Spreads were calculated as the difference between the 10-year sovereign bond yields and German bond yields of the same maturity, which were both obtained from European Central Bank Statistical Data Warehouse. We also used risk premiums relative to 10-year U.S. bonds (Bernoth et al. 2012) to include Germany in the study and as a robustness test. Data for U.S. bond yields were obtained from the database of the Federal Reserve Bank of St. Louis. A high spread indicates greater risk, and therefore, the expected sign for this variable is negative.
- Sovereign Ratings: We constructed a numerical variable to approximate the Moody’s agency ratings (Remolona et al. 2007). The scale assigned a greater score to ratings with higher risk; therefore, the sign of this variable is expected to coincide with the sign of the rest of sovereign risk proxies. We assigned a value of 1 to the rating Aaa, a value of 2 to Aa1 and so on12. The results are depicted in Figure 1. However, ratings have the disadvantage that their variability is not very high, as they are not frequently reviewed by rating agencies. We expect to find an inverse relation between this proxy and the maturity structure of sovereign debt, as with the other proxies for sovereign risk.

#### 5.2. Methodology

_{it}represents average maturity, X

_{it}is a vector that represents the control variables included in the study as determinants of the maturity structure, Risk

_{it}represents the different proxies for sovereign risk, and its analysis is the fundamental objective of the study to draw conclusions about their relationships with the dependent variables. Finally, ${\delta}_{i}$ represents country fixed effects, δ

_{t}shows time fixed effects and ${\epsilon}_{it}$ is the error term.

## 6. Results and Discussion

#### 6.1. Sovereign Bond Yields, Sovereign Risk and Maturity Structure

#### 6.2. Robustness Tests

#### 6.3. Analysis of the Non-Monotonic Relation between Sovereign Bond Yields, Sovereign Risk and Maturity Structure

#### 6.4. Relation between Sovereign Bond Yields, Sovereign Risk and Maturity Structure Depending on the Indebtedness Level

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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1 | Several papers refer to the countries of the Euro area that are not included within peripheral countries as core countries. See Kalbaska and Gątkowski (2012) in this regard. We consider the following core countries: Germany, Austria, Belgium, Finland, France and the Netherlands. |

2 | See also Hardouvelis et al. (2018) who analyze the effects of uncertainty in Greece and obtain similar results in the context of Greek debt crisis. Namely, they find that uncertainty lead to an increase in sovereign bond yields in Greek bonds. |

3 | See also Hatchondo et al. (2011) for further analysis of the relationship between duration and sovereign default risk. |

4 | The countries more affected by the European debt crisis: Greece, Ireland, Italy, Portugal and Spain. |

5 | We have used a scale to transform Moody’s ratings into numerical values. We assign the value 1 to the higher rating quality (Aaa), 2 for the following ranking (Aa1) and so on. |

6 | In the case of Europe, the difference between the sovereign 10-year bond yields from a European country and that from the same instrument in Germany is used. |

7 | Another measure to quantify the sovereign risk is used by Alesina et al. (1992), who use the ratio of sovereign bond yields to corporate bond yields, as well as the difference between them. |

8 | The proxies used to approximate sovereign risk are selected according to data availability. |

9 | The ECB provides the average maturity of sovereign debt for the period between 1990 and 2013 but does not include Germany and Spain. These data were obtained from the OECD database and the Spanish Treasury. |

10 | The ECB provides the ratio of short and long-term debt over GDP and the volumes of short and long-term debt. To construct the ratio of long-term debt to total debt, we consider total debt to be the sum of short and long-term debt, and we subsequently calculate the ratio. The ECB defines government debt as consolidated gross debt, including all sectors of the economy and excluding financial derivatives and loans. |

11 | The debt/GDP provided by the ECB includes all sectors of the economy, including regional and local debt and social security funds. |

12 | When there is more than one rating during the year, we calculate the average numerical value of the ratings. If there are favorable prospects, we round the value representing the lowest risk and vice versa. |

13 | The values of the Hausman (1978) provide a p-value that leads to the rejection of the null hypothesis in our models. Therefore, we choose to use the fixed effects instead of the random effects estimation. However, the results for the random effects estimation provide similar results to those obtained with the OLS or fixed effects estimation. These results are available upon request to the authors. |

14 | These tests are considered to be the most appropriate when the series does not follow a normal distribution and when the population variances are not equal. |

15 | We also use the Moody’s sovereign rating to measure sovereign risk, but it does not provide significant results, as this variable does not vary much with time. The results for this variable are available upon request to the authors. |

16 | A phenomenon can vary between years for reasons that are not adequately captured by the explanatory variables in the model. Therefore, not controlling for temporal variation may lead to a bias in the results. |

17 | We also use the VSTOXX index to approximate international risk aversion. The results do not vary regarding the presented in Table 5. |

**Figure 6.**Average Marginal Effects with level (95)% Cls. Peripheral and core countries (Yields)(II).

**Figure 7.**Average Marginal Effects with level (95)% Cls. Peripheral and core countries (Spreads)(I).

**Figure 8.**Average Marginal Effects with level (95)% Cls. Peripheral and core countries (Spreads)(II).

**Figure 9.**Average Marginal Effects with level (95)% Cls. Peripheral and core countries (U.S. Spreads)(I).

**Figure 10.**Average Marginal Effects with level (95)% Cls. Peripheral and core countries (U.S. Spreads)(II).

Hypotheses | Effect of Sovereign Risk on the Maturity Structure of Sovereign Debt | |
---|---|---|

If Risk Increases | If Risk Decreases | |

H1: A variation in sovereign bond yields or in sovereign risk modifies the maturity structure of sovereign debt. | The maturity structure of sovereign debt is shortened | The maturity structure of sovereign debt is lengthened |

H2: The relationship between, sovereign bond yields, sovereign risk and the maturity structure differs depending on the country risk level. | The maturity structure is shortened (peripheral countries) | The maturity structure is lengthened (peripheral countries) |

The maturity structure is lengthened (core countries) | The maturity structure is shortened (core countries) | |

H3: The indebtedness level of the countries influences the relationship between debt maturity and sovereign bond yields and sovereign risk. | The maturity structure is shortened (highly indebted countries) | The maturity structure is lengthened (highly indebted countries) |

No relationship (less indebted countries) | No relationship (less indebted countries) |

Variables | Long-Term Debt to Total Debt Ratio | |
---|---|---|

Maturity | Average maturity | + |

Control Variables | Inflation | + |

GDP | – | |

Debt/GDP | – | |

Borrowing requirements | – | |

Long-term sovereign bond returns | Yields | – |

Sovereign risk proxies | Spread | – |

Spread USA | – | |

Ratings | – |

**Table 3.**Panel data regression of maturity structure on sovereign bond yields and on sovereign risk.

Dependent Variable: Long-Term Debt to Total Debt Ratio | OLS Estimation | Fixed Effects Estimation | ||||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |

Average maturity | 0.0207 *** | 0.0248 *** | 0.0231 *** | 0.0224 * | 0.0222 * | 0.0229 ** |

(0.00297) | (0.00309) | (0.00300) | (0.0100) | (0.0101) | (0.00995) | |

GDP (in logs) | −0.0301 *** | −0.0357 *** | −0.0245 *** | −0.0736 | −0.0342 | −0.0421 |

(0.0109) | (0.00971) | (0.00901) | (0.0496) | (0.0457) | (0.0452) | |

Debt/GDP | 0.00673 | 0.0210 | 0.0129 | 0.0157 | 0.0386 | 0.0312 |

(0.0247) | (0.0243) | (0.0243) | (0.0654) | (0.0726) | (0.0717) | |

Inflation | 0.00156 | 0.00317 | 0.00286 | 0.00418 | 0.00343 | 0.00432 |

(0.00334) | (0.00338) | (0.00337) | (0.00486) | (0.00538) | (0.00518) | |

Borrowing requirements | −0.00364 *** | −0.00295 ** | −0.00249 ** | −0.00305 * | −0.00319 * | −0.00262 * |

(0.00115) | (0.00124) | (0.00126) | (0.00146) | (0.00146) | (0.00136) | |

Yields | −0.296 * | −0.599 * | ||||

(0.171) | (0.266) | |||||

Spread | −0.574 ** | −0.552 * | ||||

(0.232) | (0.292) | |||||

Spread USA | −0.603 *** | −0.660 ** | ||||

(0.220) | (0.249) | |||||

Constant | 1.173 *** | 1.181 *** | 1.062 *** | 1.725 ** | 1.162 * | 1.271 ** |

(0.143) | (0.122) | (0.116) | (0.613) | (0.555) | (0.555) | |

Country fixed effect | No | No | No | Yes | Yes | Yes |

Observations | 196 | 181 | 196 | 196 | 181 | 196 |

R-squared | 0.263 | 0.274 | 0.276 | 0.283 | 0.277 | 0.286 |

**Table 4.**Panel data regression of maturity structure on sovereign bond yields and sovereign risk with time dummy variables and a time trend.

Dependent Variable: Long-Term Debt to Total Debt Ratio | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 |
---|---|---|---|---|---|---|

Average maturity | 0.0239 ** | 0.0250 ** | 0.0237 * | 0.0228 * | 0.0239 ** | 0.0242 ** |

(0.0106) | (0.00994) | (0.0108) | (0.0104) | (0.0106) | (0.0100) | |

GDP (in logs) | 0.0620 | 0.0438 | 0.0381 | 0.000112 | 0.0620 | 0.0358 |

(0.146) | (0.133) | (0.167) | (0.143) | (0.146) | (0.134) | |

Debt/GDP | 0.0658 | 0.0599 | 0.0679 | 0.0496 | 0.0658 | 0.0583 |

(0.0955) | (0.102) | (0.0936) | (0.0990) | (0.0955) | (0.101) | |

Inflation | 0.00712 | 0.00475 | 0.00762 | 0.00326 | 0.00712 | 0.00418 |

(0.00472) | (0.00482) | (0.00508) | (0.00511) | (0.00472) | (0.00506) | |

Borrowing requirements | −0.000913 | −0.00252 | −0.000871 | −0.00314 * | −0.000913 | −0.00250 |

(0.00205) | (0.00146) | (0.00207) | (0.00152) | (0.00205) | (0.00139) | |

Yields | −0.696 ** | −0.735 ** | ||||

(0.306) | (0.255) | |||||

Spread | −0.713 ** | −0.550 * | ||||

(0.305) | (0.292) | |||||

Spread USA | −0.696 ** | −0.666 ** | ||||

(0.306) | (0.253) | |||||

Constant | −0.0262 | 0.230 | 0.210 | 0.730 | −0.0858 | 0.276 |

(1.850) | (1.710) | (2.090) | (1.820) | (1.853) | (1.722) | |

Time fixed effects | Yes | No | Yes | No | Yes | No |

Trend | No | Yes | No | Yes | No | Yes |

Observations | 196 | 196 | 181 | 181 | 196 | 196 |

R-squared | 0.429 | 0.305 | 0.278 | 0.283 | 0.429 | 0.295 |

**Table 5.**Panel data regression of maturity structure on sovereign bond yields and on sovereign risk (robustness test).

Dependent Variable: Long-term Debt to Total Debt Ratio | Model 1 | Model 2 | Model 3 |
---|---|---|---|

Average maturity | 0.00313 | 0.00274 | 0.00313 |

(0.00299) | (0.00281) | (0.00299) | |

GDP (in logs) | 0.121 | 0.105 | 0.121 |

(0.0844) | (0.111) | (0.0844) | |

Debt/GDP | 0.0363 | 0.0391 | 0.0363 |

(0.0564) | (0.0541) | (0.0564) | |

Inflation | 0.0118 ** | 0.0121 ** | 0.0118 ** |

(0.00407) | (0.00443) | (0.00407) | |

Borrowing requirements | −0.000651 | −0.000574 | −0.000651 |

(0.00171) | (0.00174) | (0.00171) | |

Yields | 0.172 | ||

(0.330) | |||

Spread | 0.142 | ||

(0.340) | |||

Spread USA | 0.172 | ||

(0.330) | |||

VIX | −0.00196 | −0.00203 | −0.00195 |

(0.00118) | (0.00129) | (0.00117) | |

LTROs (in logs) | −0.0275 ** | −0.0264 ** | −0.0275 ** |

(0.00938) | (0.0105) | (0.00943) | |

Constant | −0.208 | 0.00442 | −0.194 |

(1.065) | (1.327) | (1.071) | |

Time fixed effects | Yes | Yes | Yes |

Observations | 144 | 132 | 144 |

R-squared | 0.439 | 0.423 | 0.440 |

Group of Countries | Mean | Median |
---|---|---|

Peripheral countries | 0.029 | 0.010 |

Core countries | 0.004 | 0.002 |

Wilcoxon rank-sum test | 0.000 *** | |

K-sample equality-of-medians test | 0.000 *** |

**Table 7.**Panel data regression of maturity structure on sovereign bond yields and on sovereign risk distinguishing between peripheral and core countries.

Dependent Variable: Long-term Debt to Total Debt Ratio | Model 1 | Model 2 | Model 3 |
---|---|---|---|

Average maturity | 0.0296 *** | 0.0358 *** | 0.0330 *** |

(0.00548) | (0.00592) | (0.00501) | |

GDP (in logs) | −0.0111 | −0.0297 *** | −0.0160 |

(0.0131) | (0.00920) | (0.0132) | |

Debt/GDP | −0.0176 | −0.0105 | −0.0208 |

(0.0503) | (0.0461) | (0.0489) | |

Inflation | 0.0154 | 0.0126 | 0.00887 |

(0.0132) | (0.0121) | (0.0127) | |

Borrowing requirements | 0.00109 | 0.000554 | 0.00125 |

(0.00216) | (0.00204) | (0.00228) | |

Yields | 1.456 *** | ||

(0.492) | |||

Spread | 0.320 | ||

(1.556) | |||

Spread USA | 0.133 | ||

(1.384) | |||

Peripheral | 0.0229 | −0.0429 * | −0.0597 ** |

(0.0221) | (0.0243) | (0.0240) | |

PeripheralxYields | −1.918 *** | ||

(0.546) | |||

PeripheralxSpread | −0.976 | ||

(1.374) | |||

PeripheralxSpreadUSA | −0.571 | ||

(1.126) | |||

Constant | 0.683 *** | 1.010 *** | 0.879 *** |

(0.197) | (0.138) | (0.156) | |

Time fixed effects | Yes | Yes | Yes |

Observations | 196 | 181 | 196 |

R-squared | 0.484 | 0.389 | 0.377 |

**Table 8.**Panel data regression of maturity structure on sovereign bond yields and on sovereign risk distinguishing by the debt level.

Dependent Variable: Long-term Debt to Total Debt Ratio | Model 1 | Model 2 | Model 3 |
---|---|---|---|

Average maturity | 0.0237 * | 0.0258 * | 0.0252 ** |

(0.0105) | (0.0114) | (0.0109) | |

GDP (in logs) | 0.0851 | 0.0400 | 0.0672 |

(0.151) | (0.174) | (0.150) | |

Inflation | 0.00583 | 0.00518 | 0.00499 |

(0.00427) | (0.00503) | (0.00477) | |

Borrowing requirements | −0.00123 | −0.00180 | −0.00173 |

(0.00183) | (0.00180) | (0.00175) | |

Yields | 1.191 | ||

(0.878) | |||

Spread | 1.425 | ||

(1.412) | |||

Spread USA | −1.206 | ||

(0.793) | |||

Debt/GDP | 0.180 ** | 0.0995 | 0.0900 |

(0.0773) | (0.0895) | (0.0908) | |

Debt/GDPxYields | −1.436 ** | ||

(0.547) | |||

Debt/GDPxSpread | −1.464 | ||

(0.891) | |||

Debt/GDPxSpreadUSA | −1.206 | ||

(0.793) | |||

Constant | −0.506 | 0.128 | −0.197 |

(1.916) | (2.175) | (1.907) | |

Time fixed effects | Yes | Yes | Yes |

Observations | 196 | 181 | 196 |

R-squared | 0.482 | 0.456 | 0.451 |

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**MDPI and ACS Style**

González-Fernández, M.; González-Velasco, C.
Bond Yields, Sovereign Risk and Maturity Structure. *Risks* **2018**, *6*, 109.
https://doi.org/10.3390/risks6040109

**AMA Style**

González-Fernández M, González-Velasco C.
Bond Yields, Sovereign Risk and Maturity Structure. *Risks*. 2018; 6(4):109.
https://doi.org/10.3390/risks6040109

**Chicago/Turabian Style**

González-Fernández, Marcos, and Carmen González-Velasco.
2018. "Bond Yields, Sovereign Risk and Maturity Structure" *Risks* 6, no. 4: 109.
https://doi.org/10.3390/risks6040109