# A Simple Traffic Light Approach to Backtesting Expected Shortfall

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## Abstract

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## 1. Introduction

## 2. Review of the VaR Traffic Light Test

## 3. Derivation of the Expected Shortfall Traffic Light Test

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Table 1.**Traffic Light zone boundaries are computed assuming $\alpha =1\%$ and $N=250$ observations.

Basel Traffic Light Approach to VaR | ||
---|---|---|

Zone | Breach Value | Cumulative Probability |

Green | 0 | 8.11% |

1 | 28.58% | |

2 | 54.32% | |

3 | 75.81% | |

4 | 89.22% | |

Yellow | 5 | 95.88% |

6 | 98.63% | |

7 | 99.60% | |

8 | 99.89% | |

9 | 99.97% | |

Red | more than 10 | 99.99% |

**Table 2.**Expected Shortfall Traffic Light zone boundaries are computed assuming $\alpha =2.5\%$ and $N=250$ observations.

Traffic Light Approach to Expected Shortfall | ||
---|---|---|

Zone | Generalized Breach Value | Cumulative Probability |

Green | 0 | 0.18% |

1.3929 | 10% | |

2.1131 | 25% | |

3.0276 | 50% | |

4.0520 | 75% | |

5.0622 | 90% | |

5.7049 | 95% | |

Yellow | 5.7049 | 95% |

6.9844 | 99% | |

8.5285 | 99.9% | |

9.8833 | 99.99% | |

Red | more than 9.8833 | 99.99% |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Costanzino, N.; Curran, M.
A Simple Traffic Light Approach to Backtesting Expected Shortfall. *Risks* **2018**, *6*, 2.
https://doi.org/10.3390/risks6010002

**AMA Style**

Costanzino N, Curran M.
A Simple Traffic Light Approach to Backtesting Expected Shortfall. *Risks*. 2018; 6(1):2.
https://doi.org/10.3390/risks6010002

**Chicago/Turabian Style**

Costanzino, Nick, and Michael Curran.
2018. "A Simple Traffic Light Approach to Backtesting Expected Shortfall" *Risks* 6, no. 1: 2.
https://doi.org/10.3390/risks6010002