Background

Problem 1.Total return maximization under constraint on VaR Deviation

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

Problem 2. VaR Deviation minimization under constraint on total return

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

 

Background

 

This case study is based on the portfolio retail loans dataset provided by  Kukmin Bank, Korea. Default scenarios of bonds are generated at  Kukmin Bank with  CreditMetrics  software from  RiskMetrics Group. For a portfolio of clusters of retail loans the expected return is maximized subject to constraint on VaR deviation. It is assumed that weights for clusters can be rebalanced within 10% and 20% of the original weights.

 

Problem 1

Total return maximization under constraint on VaR Deviation.

 

Simplified Problem Statement

 

Maximize Linear (maximizing total estimated return)

 subject to

Var_dev ≤ Const (internal constraint on credit risk)

Box constraints (upper/lower bounds on exposures)

 

where

 

Var_dev = VaR Deviation for Loss

Box constraints = constraints on individual decision variables

 

Mathematical Problem Statement

 

 

Problem dimension and solving time

 

 

Solution in Run-File Environment

 

 

Input Files to run CS:

 

Output Files:

 

Solution in MATLAB Environment

 

Solved with PSG MATLAB subroutine riskconstrprog and function mpsg_solver (General (Text) Format of PSG in MATLAB):

 

 

Input Files to run CS:

 

 

Problem 2

VaR Deviation minimization under constraint on total return.

 

Simplified Problem Statement

 

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)

 

where

 

Var_dev = VaR Deviation for Loss

Box constraints = constraints on individual decision variables

 

Mathematical Problem Statement

 

 

Problem dimension and solving time

 

 

Solution in Run-File Environment

 

 

Input Files to run CS:

 

Output Files:

 

Solution in MATLAB Environment

 

Solved with PSG MATLAB subroutine riskconstrprog and function mpsg_solver (General (Text) Format of PSG in MATLAB):

 

 

Input Files to run CS: