Case 2 | Case 1 | Case 3 | Case 4 | Case 1 | Case 5 | ||

Parameters | |||||||

Initial Liability: L0 | 100 | 100 | 100 | 100 | 100 | 100 | |

Initial Asset: w0 | 70 | 70 | 70 | 70 | 70 | 70 | |

Liabiilty growth ratio | 2% | 2% | 2% | 2% | 2% | 2% | |

risk free interest rate | 1% | 1% | 1% | 1% | 1% | 1% | |

γ of Utility | 5.650 | 1.411 | 0.627 | 0.353 | 1.6 | 3.170 | |

Risky Asset’s return: μ | 5% | 5% | 5% | 3% | 5% | 7% | |

Risky Asset’s volatility: σ | 10% | 20% | 30% | 20% | 20% | 20% | |

Risky Asset’s Sharpe Ratio | 0.40 | 0.20 | 0.13 | 0.10 | 0.20 | 0.30 | |

periods (years) | 20 | 20 | 20 | 20 | 20 | 20 | |

Characteristics | |||||||

Risky Asset weight | 71% | 70.9% | 71% | 142% | 63% | 47% | |

Portfolio return | 3.8% | 3.8% | 3.8% | 3.8% | 3.5% | 3.8% | |

Portfolio risk | 7.1% | 14.2% | 21.3% | 28.3% | 12.5% | 9.5% | |

Portfolio Sharpe Ratio | 0.40 | 0.20 | 0.13 | 0.10 | 0.20 | 0.30 | |

Initial Funding Ratio | 70% | 70% | 70% | 70% | 70% | 70% | |

Liability Value at the end of the period | 149 | 149 | 149 | 149 | 149 | 149 | |

Necessary returns calculated from initial Funding Ratio | 3.8% | 3.8% | 3.8% | 3.8% | 3.8% | 3.8% | |

Simulation Results | |||||||

Ratio of CC is superior to STD | 19.3% | 46.5% | 58.9% | 67.5% | 46.5% | 30.3% |