# Exercise Solution 14.8

- Exceedence
data is calculated from the data of Exhibit 14.13 and presented in Exhibit s1 below.^{t}i

time | ^{t}i | time | ^{t}i | time | ^{t}i | time | ^{t}i | time | ^{t}i |
---|---|---|---|---|---|---|---|---|---|

t | at t | t | at t | t | at t | t | at t | t | at t |

-124 | 0 | -99 | 0 | -74 | 0 | -49 | 0 | -24 | 0 |

-123 | 0 | -98 | 0 | -73 | 0 | -48 | 0 | -23 | 0 |

-122 | 0 | -97 | 0 | -72 | 0 | -47 | 0 | -22 | 0 |

-121 | 0 | -96 | 0 | -71 | 0 | -46 | 0 | -21 | 0 |

-120 | 0 | -95 | 1 | -70 | 0 | -45 | 0 | -20 | 0 |

-119 | 0 | -94 | 0 | -69 | 0 | -44 | 0 | -19 | 0 |

-118 | 0 | -93 | 1 | -68 | 0 | -43 | 0 | -18 | 1 |

-117 | 0 | -92 | 0 | -67 | 0 | -42 | 0 | -17 | 0 |

-116 | 0 | -91 | 0 | -66 | 0 | -41 | 0 | -16 | 0 |

-115 | 0 | -90 | 0 | -65 | 0 | -40 | 0 | -15 | 0 |

-114 | 0 | -89 | 0 | -64 | 0 | -39 | 0 | -14 | 0 |

-113 | 0 | -88 | 0 | -63 | 0 | -38 | 0 | -13 | 0 |

-112 | 0 | -87 | 0 | -62 | 0 | -37 | 0 | -12 | 0 |

-111 | 0 | -86 | 0 | -61 | 0 | -36 | 0 | -11 | 0 |

-110 | 0 | -85 | 0 | -60 | 0 | -35 | 0 | -10 | 0 |

-109 | 0 | -84 | 1 | -59 | 0 | -34 | 0 | -9 | 0 |

-108 | 0 | -83 | 0 | -58 | 0 | -33 | 0 | -8 | 0 |

-107 | 0 | -82 | 0 | -57 | 0 | -32 | 0 | -7 | 0 |

-106 | 0 | -81 | 0 | -56 | 0 | -31 | 0 | -6 | 0 |

-105 | 0 | -80 | 0 | -55 | 0 | -30 | 0 | -5 | 0 |

-104 | 0 | -79 | 0 | -54 | 0 | -29 | 0 | -4 | 0 |

-103 | 0 | -78 | 0 | -53 | 0 | -28 | 0 | -3 | 0 |

-102 | 0 | -77 | 0 | -52 | 1 | -27 | 0 | -2 | 1 |

-101 | 0 | -76 | 0 | -51 | 0 | -26 | 0 | -1 | 0 |

-100 | 0 | -75 | 0 | -50 | 0 | -25 | 0 | 0 | 0 |

Exhibit s1: Exceedence

*data calculated from the data of Exhibit 14.13. A 1 indicates an exceedence occurred. A 0 indicates one did not.*^{t}ib.

- To apply our recommended standard coverage test, we need
- the quantile of loss the value-at-risk measure is intended to measure:
*q*= 0.99, - the number of observations: α + 1 = 125, and
- the number of exceedences, from Exhibit s1 above:
*x*= 6.

In Exhibit 14.3, we find that our recommended standard coverage test’s non-rejection interval for

*q*= 0.99 and α + 1 = 125 is [0, 3]. Since our number of exceedances falls outside this interval, we reject the value-at-risk measure. - the quantile of loss the value-at-risk measure is intended to measure:
- In Exhibit 14.4, we find that the PF test’s non-rejection interval for
*q*= 0.99 and α + 1 = 125 is [0, 4]. Since our number of exceedances falls outside this interval, we reject the value-at-risk measure. - We cannot use the Basel Committee’s Trafic Light coverage test because the test applies only if there are α + 1 = 250 observations.