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A Comprehensive Approach for Calculating Banking Sector Risks^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

- CCA for Households (HH) and Non-Financial Corporations (NFC) sectors and CDS valuation for the Government (GVT) sector.
- a new approach based on sectors balance sheet interconnections is adopted to detect the banking sector proximity to distress.

#### 2.1. The Standard CCA Approach

#### 2.2. The Application of CCA Approach to NFC and HH Sectors

#### 2.2.1. Non-Financial Corporations

#### 2.2.2. Households

- the net financial worth of the aggregated households balance sheet as E;
- the volatility of the ten years government bond as ${\sigma}_{E}$6;
- the whole liabilities of households as B.

#### 2.3. The Government Sector

#### 2.4. The Comprehensive Approach for the Banking Sector

- assets with a domestic counterpart (issuer) (${A}^{D}$);
- assets with counterpart (issuer) from the Euro Area (except the reference country)(${A}^{EA}$);
- assets with non-Euro counterpart (issuer) (${A}^{EX}$);
- other assets without a counterpart (for instance gold) (K)11.

#### 2.5. Sensitivity Analysis

## 3. Data

- when it comes to evaluate the domestic area (D), we consider as ${\widehat{D}}_{j,i}$ of the unknown counterpart the simple mean of the risky debt of the sectors in S of c21:$${A}_{c}^{D,u}={A}_{c,l}^{D,u}\frac{{\sum}_{s}{\widehat{D}}_{c,s}}{\left|S\right|}+{A}_{c,ds}^{D,u}\frac{{\sum}_{\tilde{s}}{\widehat{D}}_{c,\tilde{s}}}{|S\setminus \{HH\left\}\right|},\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}s\in S,\tilde{s}\in S\setminus \left\{HH\right\}$$
- when it comes to evaluate the Euro Area (EA), we consider as ${\widehat{D}}_{j,i}$ the simple mean of the risky debt of the sectors of all the countries, except the domestic one:$${A}_{c}^{EA,u}={A}_{c,l}^{EA,u}\frac{{\sum}_{g}{\sum}_{s}{\widehat{D}}_{g,s}}{|C\setminus \{c\left\}\right|+\left|S\right|}+{A}_{c,ds}^{EA,u}\frac{{\sum}_{g}{\sum}_{\tilde{s}}{\widehat{D}}_{g,\tilde{s}}}{|C\setminus \{c\left\}\right|+|S\setminus \{HH\left\}\right|},\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}g\in C\setminus \left\{c\right\},s\in S,\tilde{s}\in S\setminus \left\{HH\right\}$$
- when it comes to evaluate the Extra Euro area (EX), we consider as ${\widehat{D}}_{j,i}$ the simple mean of the risky debt of the sectors of all the countries:$${A}_{c}^{EX,u}={A}_{c,l}^{EX,u}\frac{{\sum}_{g}{\sum}_{s}{\widehat{D}}_{g,s}}{\left|C\right|+\left|S\right|}+{A}_{c,ds}^{EX,u}\frac{{\sum}_{g}{\sum}_{\tilde{s}}{\widehat{D}}_{g,\tilde{s}}}{\left|C\right|+|S\setminus \{HH\left\}\right|},\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}g\in C,s\in S,\tilde{s}\in S\setminus \left\{HH\right\}$$

## 4. Results

^{TM}), uses empirical data (for instance, historical defaults) to create a reliable map to the real $PD$s (Crosbie and Bohn 2003) in its effort to get fatter tails. In addition, since $N(\xb7)$ is a strictly monotonic increasing function, it preserves the ranking provided by the distance to default and therefore does not return any new information to the comparative analysis (Jessen and Lando 2015). For these reasons, we devote our full attention to the distance to default as a risk metric. This section is divided as follows: first we show the results of our methodology comparing, for each country, the $DtD$s of the four sectors. Then, we compare our findings with the ones obtained through the usual CCA applied to the banking sector. Finally, we present a static stress exercise to give a hint of how a sudden shock hitting GTV, NFC and HH affect the banking sector.

#### 4.1. A Comparison of Sectoral Distance to Distress

#### 4.2. The Alternative versus the CCA Approach

#### 4.3. Effects of a Shock

## 5. Conclusions and Future Directions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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1. | In this paper, the terms “banking sector”, “credit institutions sector” and “financial sector” are used interchangeably although understandably the financial sector is more broad since it includes financial companies that do not provide credit. |

2. | Although for banks actual default depends also on the regulatory environment which seems to be more protective the recent years due to the central role of banks for the economy. |

3. | Simulations have shown that when the put is at the money then the system is unstable and even small differences in the initial conditions produce large output deviations. |

4. | To define a representative volatility for the whole sector two methodologies were employed. The first one is the average of each corporation volatility weighted according to its market capitalization relevance on the aggregated one, ignoring equity correlations. The second one enriches the weighted average with the correlations. The results show that the second methodology, producing a lower volatility, leads to higher $DtD$ values. In the results section we chose to show the $DtD$s obtained through the latter approach, since it seems more reasonable to assume that the volatility of the whole sector is softened by the negative correlations of the firms in it. Nevertheless, the application of both the methodologies reveal similar final results. |

5. | The mainstream empirical practice is followed and $\alpha $ is set to 0.5. |

6. | Instead of using a mixture of resale price index volatility and private residential index volatility as in Lai (2016), the volatility of ten-year government bond is used as a proxy for the HH equity volatility. This was chosen because it was felt that the ten-year yield volatility represents a better proxy for the future HH volatility. We follow Castrén and Kavonius (2009), and we consider two main justifications for this assumption. First, European banks’ market portfolio is composed by 25% of domestic bonds, which therefore represent a crucial component of banks’ profitability. Hence, higher volatility in sovereign debt securities leads to increasing risk on credit institutions’ asset side, which is in turn transmitted to loan rates (directly hitting households’ assets). Secondly, 10-year government bonds mirror structural features of each economy, as expected inflation and growth, being a gauge of country soundness. Therefore, we can assume that the market perceived level of uncertainty of households’ assets is significantly represented by the volatility of long-term sovereign securities. |

7. | Given that the level of global interest rates is extremely low (sometimes near zero for the time period we analyze), this leads to a zero or negative put which, in turn, results in either no solution or an instable solution for our system of equations. |

8. | $CDS$ is in basis points so s is defined as $\frac{CD{S}_{s}}{\mathrm{10,000}}$. |

9. | See also Duffie (1999); O’Kane and Turnbull (2003), and Izzi et al. (2012) in support of the claim that the analysis of the CDS relies on a risk-neutral world which is, hence, comparable to the one seen for the other sectors. |

10. | Throughout the paper, the recovery rate for the government sector debt is assumed to be 40%. We rely on the empirical evidence presented in Singh and Bilal (2012). |

11. | We assume that for K the book value and the market value coincide. |

12. | $j,i$ denote a quantity from counterpart sector i in j area and if superscript $tot$ exist denotes the total quantity of this. |

13. | The shocks were under the assumption of 1% risk-free rate. |

14. | The methodology can be applied to the most recent available data. |

15. | Bloomberg L.P. |

16. | The weights are chosen with respect to each firm market capitalization contribution to the total E. |

17. | This database contains the aggregated balance sheet data of macro sectors for the EU countries. |

18. | Where ten-year sovereign bond volatility is not available, the volatility of the ICE 10-year sovereign bond index is used. |

19. | Loans (l) and debt securities (ds). |

20. | Where $C=\{AT,BE,DE,ES,FR,IE,IT,NL,PT,SL\}$ is the country set. |

21. | Subscripts and superscripts in A should be self-explanatory. For instance ${A}_{c,l}^{EX,u}$ denotes a non-Euro loan in country c issued by an unknown counterpart u. |

22. | The weights are the market value contributions of each asset to ${A}_{mkt}$. |

23. | To measure the annual risk-free return, we use a 1 year rate. Furthermore, we rely on the interbank deposit rate as monetary authorities are assumed to act as lender of last resort to support these exposures, supporting the assumption of risk-freeness of the rate. |

24. | To visually distinguish the different sectors in these graphs we opted for a log-scale, since the extremely high levels of households’ $DtD$ would otherwise make the comparison hard. Sectors where $log\left(DtD\right)<0$ are considered to be in high stress. |

25. | Countries data can be provided by the authors upon request. |

26. | Irish banks suffered extremely from the global financial crush mainly due to heavy exposure to the EA and to the rest of the world. |

27. | Bloomberg L.P. |

**Figure 1.**Effect on the Sensitivities of D. The left and right panels show the impact of a shock in equity and volatility of euqity (respectively) on the market value of the debt. The shock is applied on different touples of euqity and volatility of equity (from 0 to 5 for E and from 0 to 1 for ${\sigma}_{E}$).

**Figure 2.**Banking sectors $DtD$s. The chart shows the level of aggregate banks’ $DtD$ in the analysed countries (AT, BE, DE, ES, FR, IE, IT, NL, PT, SL) from 2005 to end 2017. The y-axis expresses this measure in standard deviations.

**Figure 3.**Sectors $DtD$. The panels show the level of $DtD$ for each sector considered in the analysis for each country (NFCs in blue, HH in yellow, GVT in red and CI in green). The y-axis expresses the $DtD$ measure in standard deviations (log-scale).

**Figure 4.**Banking sector $DtD$s comparison between CCA and non-CCA approach. The panels show the level of $DtD$ for the CI sector of each country given the two possible approaches to compute it: the yellow line refers to the usual use of CCA while the blue line refers to the new methodology proposed in the paper. The y-axis expresses the $DtD$ measure in standard deviations.—For Slovenia, the comparison was not possible due to lack of market data for the banks.

**Figure 5.**Sectors Shocks to banks $DtD$. The panels present the variation in $DtD$ given a shock in one of the analysed counterparty sectors (HH, NFC, GVT). For the first two sectors we employed a 20% shock on E and ${\sigma}_{E}$ (negative to the former, positive to the latter). For the government sector we employ a 200 basis points positive shock on the CDS spead. The shock is separately applied on each sector and for each point in time (each quarter from beginning 2005 to end 2017). The blue line represents the shock from NFC, the yellow line the impact of a variation in HH and, lastly, the red line represents the impact of a shock in GVT CDS spreads.

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**MDPI and ACS Style**

Salleo, C.; Grassi, A.; Kyriakopoulos, C.
A Comprehensive Approach for Calculating Banking Sector Risks. *Int. J. Financial Stud.* **2020**, *8*, 69.
https://doi.org/10.3390/ijfs8040069

**AMA Style**

Salleo C, Grassi A, Kyriakopoulos C.
A Comprehensive Approach for Calculating Banking Sector Risks. *International Journal of Financial Studies*. 2020; 8(4):69.
https://doi.org/10.3390/ijfs8040069

**Chicago/Turabian Style**

Salleo, Carmelo, Alberto Grassi, and Constantinos Kyriakopoulos.
2020. "A Comprehensive Approach for Calculating Banking Sector Risks" *International Journal of Financial Studies* 8, no. 4: 69.
https://doi.org/10.3390/ijfs8040069