Background

Problem. Optimization problem setup with the Omega objective function

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

References

 

Background

 

A fund of funds blends the risk-return profiles of various fund managers/strategies to meet investor requirements. The performance of the fund of funds is described by the Omega function. This case study demonstrates an optimization problem setup with the Omega objective function. Optimization is done using two different approaches:

 

Problem

 

Simplified Problem Statement

 

Minimize Pm_pen

 subject to

Avg ≤ Const1 (loss constraint)

Linear = Const2 (budget constraint)

Const3 ≥ Linear ≤ Const4 (constraints on allocations to strategies)

Const5 ≥ X ≤ Const6 (constraints on allocations to individual managers)

Box constraints (box constraints for individual positions)

 

where

 

Avg_g = Average Gain

Pm_pen = Partial Moment Penalty 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 riskratioprog:
 

 

Input Files to run CS:

 

Note. MATLAB problem statement differs from Run-File problem statement.

 

 

References

 

[1]  Keating, C., and W. Shadwick (2002): A Universal Performance Measure. The Journal of Performance Measurement v. 6 #3.

[2]  Mauser, H., Saunders, D., and L. Seco (2006): Optimizing Omega. Risk, November, pp. 88-92.

[3]  Avouyi-Dovi, S., Morin, A., and D. Neto (2004)” Optimal asset allocation with omega function, tech. report, Banque de France. Research Paper.

[4]  Passow, A. (2005): Omega portfolio construction with Johnson distributions. Risk, April, pp. 85–90.