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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 |

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 |

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.