# CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Drawdown Definition

#### 2.2. CoCDaR Definitions

#### 2.3. State Variables

#### 2.4. Estimation of CoCDaR

#### 2.5. Institutional Drawdown-at-Risk

#### 2.6. Sytemic Risk Contribution

#### 2.7. mCoCDaR Definition

#### 2.8. Estimation of mCoCDaR

#### 2.9. Sytemic Risk Contribution using mCoCDaR

#### 2.10. Advantages of mCoCDaR and mCoCVaR

#### 2.11. mCoCDaR Versus mCoCVaR

## 3. Case Studies

#### 3.1. Financial Institutions

- JP Morgan Chase & Company (JPM)
- Bank of America (BAC)
- Citigroup Inc (C)
- Wells Fargo & Company (WFC)
- The Bank of New York Mellon Corporation (BK)
- US Bancorp (USB)
- Capital One Financial Corporation (COF)
- PNC Financial Services Group Inc (PNC)
- State Street Corporation (STT)
- The BB&T Corporation (BBT)

#### 3.2. CoCVaR Calculation Results

1. WFC: 0.03608 | 6. STT: 0.02905 |

2. BBT: 0.03210 | 7. COF: 0.02776 |

3. PNC: 0.03089 | 8. BK : 0.02740 |

4. JPM: 0.03077 | 9. USB: 0.02341 |

5. BAC: 0.03063 | 10. C : 0.00187 |

#### 3.3. CoCDaR Calculation Results

1. WFC: 0.27695 [1] | 6. BK: 0.03564 [8] |

2. BAC: 0.22285 [5] | 7. PNC: 0.02558 [3] |

3. BBT: 0.07073 [2] | 8. JPM: 0.02306 [4] |

4. COF: 0.06107 [7] | 9. STT: 0.00242 [6] |

5. USB: 0.05502 [9] | 10. C: –0.01390 [10] |

#### 3.4. mCoCVaR Calculation Results

1. BBT: 0.00813 [2] | 6. STT: 0.00463 [8] |

2. BAC: 0.00721 [5] | 7. WFC: 0.00306 [1] |

3. BK: 0.00619 [8] | 8. COF: 0.00266 [7] |

4. JPM: 0.00598 [4] | 9. USB: 0.00149 [9] |

5. PNC: 0.00494 [3] | 10. C: 0.00062 [10] |

#### 3.5. mCoCDaR Results

1. BAC: 0.20572 [2] | 6. BK: 0.01548 [6] |

2. BBT: 0.02964 [3] | 7. C: 0.00434 [10] |

3. USB: 0.02485 [5] | 8. PNC: –0.01353 [7] |

4. STT: 0.02011 [9] | 9. JPM: –0.01353 [8] |

5. COF: 0.01749 [4] | 10. WFC: –0.06106 [1] |

#### 3.6. Comparative Summary of the Proposed Methods

## 4. mCoCDaR Application to Style Classification

## 5. On Portfolio Optimization with mCoCDaR and mCoCVaR

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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3. | Portfolio Safeguard (PSG) is a product of American Optimal Decisions: http://aorda.com |

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**Figure 1.**Drawdown example: the solid line is the uncompounded cumulative rate of return, which at time t is the sum of rates of return over periods $1,\dots ,t$. Here, $\tau =6$. For $t=5$, ${\xi}_{5}=0.5\%$, whereas the maximum of ${\xi}_{t}$ over time moments preceding $t=5$ occurs at $t=2$ with ${\xi}_{2}=1.5\%$. Consequently, ${y}_{5}=1.5\%-0.5\%=1\%$. The instrument maximum drawdown over time period $[0,6]$ occurs at $t=5$.

mCoCDaR | CoCDaR | mCoCVaR | CoCVaR | |
---|---|---|---|---|

JPM | 9 | 8 | 4 | 4 |

BAC | 1 | 2 | 2 | 5 |

C | 7 | 10 | 10 | 10 |

WFC | 10 | 1 | 7 | 1 |

STT | 4 | 9 | 6 | 6 |

PNC | 8 | 7 | 5 | 3 |

USB | 3 | 5 | 9 | 9 |

COF | 5 | 4 | 8 | 7 |

BK | 6 | 6 | 3 | 8 |

BTT | 2 | 3 | 1 | 2 |

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**MDPI and ACS Style**

Ding, R.; Uryasev, S.
CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions. *J. Risk Financial Manag.* **2020**, *13*, 270.
https://doi.org/10.3390/jrfm13110270

**AMA Style**

Ding R, Uryasev S.
CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions. *Journal of Risk and Financial Management*. 2020; 13(11):270.
https://doi.org/10.3390/jrfm13110270

**Chicago/Turabian Style**

Ding, Rui, and Stan Uryasev.
2020. "CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions" *Journal of Risk and Financial Management* 13, no. 11: 270.
https://doi.org/10.3390/jrfm13110270