In order to evaluate the relative magnitude and estimation uncertainty of 99% VaR vs. 97.5% we calculated these risk forecasts for a range of stocks. The table below shows the average and standard error of the risk forecasts, daily data from 2000 until November 2013, estimation window 1000 days and estimation methods historical simulation and GARCH.

The results indicate that the GARCH ES(97.5%) and VaR(99%) are almost exactly the same, which is expected given the analytical analysis. The picture is not as clear for historical simulation, the two numbers ES(97.%) and VaR(99%) are generally quite close, with one or the other slightly dominating. However, the standard errors of ES(97.%) usually, but not always, are larger than those for VaR(99%).

These results are in-line with the Monte Carlo results.

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | ^gspc | 64.37 | 69.85 | 53.82 | 54.08 |

se | 10.81 | 16.90 | 14.50 | 14.57 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | IBM | 45.95 | 45.25 | 29.68 | 29.82 |

se | 10.70 | 10.06 | 11.82 | 11.87 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | JPM | 77.08 | 79.96 | 50.82 | 51.07 |

se | 31.16 | 32.88 | 42.25 | 42.46 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | GS | 73.88 | 72.14 | 50.32 | 50.57 |

se | 33.28 | 29.54 | 32.57 | 32.73 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | BA | 54.59 | 54.20 | 40.58 | 40.78 |

se | 13.05 | 12.71 | 15.01 | 15.09 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | CVX | 44.49 | 49.07 | 34.55 | 34.72 |

se | 10.58 | 14.49 | 18.23 | 18.32 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | TRV | 54.46 | 58.29 | 38.90 | 39.09 |

se | 14.85 | 18.30 | 24.27 | 24.39 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | MSFT | 52.34 | 54.82 | 35.37 | 35.55 |

se | 14.25 | 13.72 | 15.01 | 15.09 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | KO | 34.19 | 36.67 | 25.12 | 25.24 |

se | 7.52 | 7.44 | 12.04 | 12.10 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | PG | 33.06 | 35.20 | 23.81 | 23.93 |

se | 7.94 | 9.33 | 8.07 | 8.11 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | WMT | 37.26 | 38.04 | 26.39 | 26.52 |

se | 7.59 | 7.74 | 8.56 | 8.60 |

asset | HS VaR(99%) | HS ES(97.5%) | GARCH VaR(99%) | GARCH ES(97.5%) | |
---|---|---|---|---|---|

mean | AAPL | 64.37 | 69.85 | 53.82 | 54.08 |

se | 10.81 | 16.90 | 14.50 | 14.57 |

© All rights reserved, Jon Danielsson, 2018