# Case Study: VaR Optimization Retail Portfolio of Bonds

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
——————————————————————–

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 0.022744275053 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.