# Are Corporate Bond Defaults Contagious across Sectors?

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Past Research: Defining and Testing for Contagion and the Problem of Time-Varying Bias

_{t}] = 0, E [ε

_{t}

^{2}] < ∞, E [x

_{t}, ε

_{t}] = 0 and also (for simplicity) that |β| < 1. Now suppose that the variance of x

_{t}changes over the sample period so that it is lower in one part of the sample (l) and higher in the second part of the sample (h). Since by assumption the error and explanatory (x

_{t}) variables are orthogonal, the consistent and efficient ordinary least squares (OLS) estimator will return the same parameter estimates across samples: β

^{h}= β

^{l}. By assumption, we also know that σ

^{h}

_{xx}> σ

^{l}

_{xx}which, when combined with the standard definition of β, implies that σ

^{h}

_{xy}> σ

^{l}

_{xy}: the covariance between x and y will be higher in the second period. Since the residual variance is constant by construction and |β| < 1, we know that:

## 3. Sectoral Bond Defaults: Inspecting the Data

## 4. Testing for Contagion across Sectors

## 5. Conclusions

## Funding

## Conflicts of Interest

## Appendix A. Numerical Listing of Corporate Sectors

S01 | Aerospace and Defense |

S02 | Automotive |

S03 | Beverage, Food and Tobacco |

S04 | Capital Equipment |

S05 | Chemicals, Plastics and Rubber |

S06 | Construction and Building |

S07 | Consumer goods: Durable |

S08 | Consumer goods: Non-durable |

S09 | Containers, Packaging and Glass |

S10 | Energy: Electricity |

S11 | Energy: Oil and Gas |

S12 | Environmental Industries |

S13 | FIRE: Finance |

S14 | FIRE: Insurance |

S15 | FIRE: Real Estate |

S16 | Forest Products and Paper |

S17 | Healthcare and Pharmaceuticals |

S18 | High Tech Industries |

S19 | Hotel, Gaming and Leisure |

S20 | Media: Advertising, Printing and Publishing |

S21 | Media: Broadcasting and Subscription |

S22 | Media: Diversified and Production |

S23 | Metals and Mining |

S24 | Retail |

S25 | Services: Business |

S26 | Services: Consumer |

S27 | Telecommunications |

S28 | Transportation: Cargo |

S29 | Transportation: Consumer |

S30 | Utilities: Electric |

S31 | Utilities: Oil and Gas |

S32 | Utilities: Water |

S33 | Wholesale |

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**Figure 2.**Corporate default rates across different sectors. Note that the exhibit presents sectoral default rates for 33 non-financial corporate sectors; each sector is shown in a different colour. The vertical axis was deliberately limited to 50% to illustrate volatility within and across sectors relative to lower default rates in some time periods. Source: Moody’s.

**Figure 3.**Cross-sector correlation coefficients for sectoral corporate defaults. Source: Author’s calculations. Note: Sectors are defined numerically for ease of presentation; see Appendix A for further details.

**Figure 4.**Sectoral default rates around the late 2000s’ deterioration in credit conditions. Source: Author’s calculations and Moody’s. Note that the exhibit presents sectoral default rates for 33 non-financial corporate sectors. The vertical axis was deliberately limited to 50% to illustrate volatility within and across sectors relative to lower default rates in some time periods. The “media and publications” sector is highlighted in red, as it was the first sector that saw its default rate jump sharply during the course of 2007.

**Figure 5.**Sectoral default rates around the early 2000s downturn in credit conditions. Source: Author’s calculations and Moody’s. Note that the exhibit presents sectoral default rates for 33 non-financial corporate sectors. The vertical axis was deliberately limited to 50% to illustrate volatility within and across sectors relative to lower default rates in some time periods. The “environmental services” sector is highlighted in red, as it is the first sector that saw its default rate jump sharply and persist higher during the course of 1999/2000.

**Figure 6.**Sectoral default rates around the late 1980s downturn in credit conditions. Source: Author’s calculations and Moody’s. Note that the exhibit presents sectoral default rates for 33 non-financial corporate sectors. The vertical axis was deliberately limited to 50% to illustrate volatility within and across sectors relative to lower default rates in some time periods. The “hotels and gaming” sector is highlighted in red, as it is the first sector that saw its default rate jump sharply and persist higher during the course of 1998/1999.

**Table 1.**Biased and adjusted correlation coefficients for contagion tests in August 2007. Source: Author’s calculations. Note: Contagion tests based on statistical tests for differences in correlation coefficients calculated in “stress period” (defined as January 2008 until January 2011) compared with correlation coefficients calculation between February 2003 and January 2011.

Sector | Correlation in Stress Period (Unadjusted) | Evidence of Contagion? | Correlation in Stress Period (Adjusted) | Evidence of Contagion? |
---|---|---|---|---|

Aerospace and Defense | 0.806 | N | 0.225 | N |

Automotive | 0.948 | Y | 0.453 | N |

Beverage, Food and Tobacco | 0.604 | Y | 0.128 | N |

Capital Equipment | 0.946 | Y | 0.444 | N |

Chemicals, Plastics and Rubber | 0.875 | Y | 0.294 | N |

Construction and Building | 0.267 | N | 0.047 | N |

Consumer goods: Durable | 0.933 | Y | 0.403 | N |

Consumer goods: Non-durable | 0.688 | Y | 0.159 | N |

Containers, Packaging and Glass | 0.712 | Y | 0.170 | N |

Energy: Electricity | −0.577 | N | −0.119 | N |

Energy: Oil and Gas | 0.860 | Y | 0.276 | N |

Environmental Industries | −0.249 | N | −0.044 | N |

FIRE: Finance | 0.889 | Y | 0.313 | N |

FIRE: Insurance | −0.614 | N | −0.131 | Y |

FIRE: Real Estate | 0.914 | N | 0.358 | N |

Forest Products and Paper | 0.433 | N | 0.081 | N |

Healthcare and Pharmaceuticals | 0.637 | Y | 0.139 | N |

High Tech Industries | 0.887 | Y | 0.311 | N |

Hotel, Gaming, and Leisure | 0.921 | Y | 0.372 | N |

Media: Advertising, Printing and Publishing | 0.883 | Y | 0.306 | N |

Media: Diversified and Production | 0.310 | N | 0.055 | N |

Metals and Mining | 0.985 | Y | 0.691 | N |

Retail | −0.265 | N | −0.047 | N |

Services: Business | 0.781 | Y | 0.208 | N |

Services: Consumer | 0.121 | N | 0.021 | N |

Telecommunications | 0.926 | Y | 0.385 | N |

Transportation: Cargo | 0.285 | N | 0.051 | N |

Transportation: Consumer | −0.332 | N | −0.060 | N |

Wholesale | 0.721 | Y | 0.174 | N |

Summary: All Sectors | 16/29 | 1/29 |

**Table 2.**Percentage of sectors exhibiting contagion compared with “leading” sector. Source: Author’s calculations. Note that the sectors with negative “stress” correlation coefficients were excluded from the percentages presented. The contagion tests were calculated as specified in Table 1 using the sample periods specified in the main text.

Credit Downturn Cycle | Leading Sector | Ordinary (Biased) Correlations | Adjusted (Unbiased) Correlations |
---|---|---|---|

1988 | Hotel and gaming | 3% | 0% |

1999 | Environment | 27% | 10% |

2008 | Media and publications | 48% | 0% |

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**MDPI and ACS Style**

Ellis, C.
Are Corporate Bond Defaults Contagious across Sectors? *Int. J. Financial Stud.* **2020**, *8*, 1.
https://doi.org/10.3390/ijfs8010001

**AMA Style**

Ellis C.
Are Corporate Bond Defaults Contagious across Sectors? *International Journal of Financial Studies*. 2020; 8(1):1.
https://doi.org/10.3390/ijfs8010001

**Chicago/Turabian Style**

Ellis, Colin.
2020. "Are Corporate Bond Defaults Contagious across Sectors?" *International Journal of Financial Studies* 8, no. 1: 1.
https://doi.org/10.3390/ijfs8010001