# Case Study: VaR Optimization Retail Portfolio of Bonds

** Case study background and problem formulations**

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

**PROBLEM 1: problem_1_Korea_retail**

Maximize Linear (maximizing total estimated return)

subject to

Var_dev ≤ Const (internal constraint on credit risk)

Box constraints (upper/lower bounds on exposures)

——————————————————————–

Var_dev = VaR Deviation for Loss

Box constraints = constraints on individual decision variables

——————————————————————–

Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
---|---|---|---|---|---|---|---|

Dataset1 | Problem Statement | Data | Solution | 23 | 10,000 | 0.022744275053 | 0.19 |

Dataset2 | Problem Statement | Data | Solution | 23 | 100,000 | 0.023516910907 | 10.73 |

Dataset3 | Problem Statement | Data | Solution | 23 | 10.000 | 0.023496175110 | 0.25 |

Dataset4 | Problem Statement | Data | Solution | 23 | 100,000 | 0.023515769798 | 11.86 |

Data and solution in MATLAB Environment

Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|

Dataset1 | Matlab code | Data | Solution | 23 | 10,000 | 0.0227443 | 0.19 |

Dataset2 | Matlab code | Data | Solution | 23 | 100,000 | 0.0235145 | 11.11 |

Dataset3 | Matlab code | Data | Solution | 23 | 10.000 | 0.023496175110 | 0.25 |

Dataset4 | Matlab code | Data | Solution | 23 | 100,000 | 0.0235145 | 11.16 |

**PROBLEM 2: problem_2_Korea_retail**

Miminize Var_dev (minimizing portfolio VaR DEVIATION)

subject to

Linear ≥ Const (constraint on the portfolio rate of return)

Box constraints (upper/lower bounds on exposures)

——————————————————————–

Var_dev = VaR Deviation for Loss

Box constraints = constraints on individual decision variables

——————————————————————– Data and solution in Run-File Environment

Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
---|---|---|---|---|---|---|---|

Dataset1 | Problem Statement | Data | Solution | 23 | 10,000 | 0.009467421776 | 0.14 |

Dataset2 | Problem Statement | Data | Solution | 23 | 100,000 | 0.009077285759 | 12.17 |

Dataset3 | Problem Statement | Data | Solution | 23 | 10.000 | 0.009095559339 | 0.16 |

Dataset4 | Problem Statement | Data | Solution | 23 | 100,000 | 0.009077417243 | 14.69 |

Data and solution in MATLAB Environment

Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|

Dataset1 | Matlab code | Data | Solution | 23 | 10,000 | 0.00946742 | 0.2 |

Dataset2 | Matlab code | Data | Solution | 23 | 100,000 | 0.00907742 | 14.76 |

Dataset3 | Matlab code | Data | Solution | 23 | 10.000 | 0.00909556 | 0.16 |

Dataset4 | Matlab code | Data | Solution | 23 | 100,000 | 0.00907742 | 14.7 |

**CASE STUDY SUMMARY**

The case study is conducted with the portfolio retail loans dataset provided by the Kukmin Bank, Korea. Default scenarios of bonds are generated at the Kukmin Bank with the CreditMetrix software from RiskMetrics Group. Scenarios data are imported to PSG format by the Converter_VaR_Optimizaion intended for processing the outputs from the CreditMetrix. This converter can be downloaded after installation of PSG from the AORDA client website. Two credit risk portfolio optimization problems are considered for the portfolio of clusters of retail loans. It is assumed that weights for clusters can be rebalanced within 10% and 20% of original weights. Problem 1: The expected return is maximized subject to constraint on VaR deviation of loss and bounds on weights. Problem 2: VaR deviation of loss is minimized subject to the constraint on the expected return and bounds on instrument weights.

Problems 1 and 2 are solved with 4 datasets:

• Dataset1 for “short case study” including matrix of scenarios with 10,000 scenarios and weights for clusters rebalanced within 10% original weights;

• Dataset2 for “long case study” including matrix of scenarios with 100,000 scenarios and weights for clusters rebalanced within 10% original weights;

• Dataset3 for “short case study” including matrix of scenarios with 10,000 scenarios and weights for clusters rebalanced within 20% original weights;

• Dataset4 for “long case study” including matrix of scenarios with 100,000 scenarios and weights for clusters rebalanced within 20% original weights.

• Dataset1 for “short case study” including matrix of scenarios with 10,000 scenarios and weights for clusters rebalanced within 10% original weights;

• Dataset2 for “long case study” including matrix of scenarios with 100,000 scenarios and weights for clusters rebalanced within 10% original weights;

• Dataset3 for “short case study” including matrix of scenarios with 10,000 scenarios and weights for clusters rebalanced within 20% original weights;

• Dataset4 for “long case study” including matrix of scenarios with 100,000 scenarios and weights for clusters rebalanced within 20% original weights.