Case Study: Portfolio Optimization with Drawdown Constraints, Single Path vs Multiple Paths

TEST PROBLEMS
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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_cdar_dev_multiple
Maximize Linear (maximizing average annualized portfolio return)
subject to
Cdarmulti_dev ≤ Const (constraint on CDaR Deviation Multiple (for multiple paths))
Box constraints (lower and upper bounds on weights)
——————————————————————–
Cdarmulti_dev = CDaR Deviation Multiple
Box constraints = constraints on individual decision variables
——————————————————————–

# of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec)
Dataset1 30 12,925 0.240832 0.18
Environments
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Subroutines Matlab Code Data
R R Code Data
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 18 211,618 0.182599 11.52

PROBLEM 2: problem_cdar_dev_single
Maximize Linear (maximizing average annualized portfolio return)
subject to
Cdar_dev ≤ Const (constraint on CDaR Deviation (for united single path))
Box constraints (lower and upper bounds on weights)
——————————————————————–
Cdar_dev = CDaR Deviation
Box constraints = constraints on individual decision variables
——————————————————————–

# of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec)
Dataset1 30 12,925 0.228868 0.12
Environments
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Subroutines Matlab Code Data
R R Code Data
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 18 211,618 0.179377 4.95
CASE STUDY SUMMARY
This case study compares solutions of two optimization problems: (1) maximizing annualized portfolio return on multiple sample paths subject to constraint on CDaR Deviation Multiple; (2) maximizing annualized portfolio return on a single sample path subject to constraint on CDaR Deviation. In the problem (2) the single sample path is the union of multiple sample paths from the problem (1).
Problems (1) and (2) are solved using two datasets each: Dataset1 for “long case study” including 180 sample paths of the underlying instruments and Dataset2 for “short case study” including only 11 sample paths.