Case study: Portfolio Optimization with Expectiles

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PROBLEM 1: maximizing the expected return subject to bounded negative expectile risk

Maximize Avg_g (maximizing the expected return of financial instruments)
subject to
expectile <= Const1 (constraint on the negative expectile risk of the portfolio)
Linear = Const2 (budget constraint)
Box constraints (box constraints for individual positions)
——————————————————————–
Avg_g = Average Gain
Box constraints = constraints on individual decision variables
———————————————————————

# of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec)
Dataset 1 4 10000 0.00094986 0.06
Environments
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Matlab Code Data
R R Code Data

PROBLEM 2: minimizing expectile risk subject to bounded from below expected returns

Minimize expectile (minimize negative expectile risk of the portfolio)
subject to
Avg_g >= Const1 (constraint on the expected return of financial instruments)
Linear = Const2 (budget constraint)
Box constraints (box constraints for individual positions)
——————————————————————–
Avg_g = Average Gain
Box constraints = constraints on individual decision variables
——————————————————————–

# of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec)
Dataset 1 4 10000 0.02447960 0.01
Environments
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Matlab Code Data
R R Code Data

PROBLEM 3: maximizing the expected return subject to bounded negative expectile risk

Maximize Avg_g (maximizing the expected return of financial instruments)
subject to
expectile <= Const1 (constraint on the negative expectile risk of the portfolio)
Linear = Const2 (budget constraint)
Box constraints (box constraints for individual positions)
——————————————————————–
Avg_g = Average Gain
Box constraints = constraints on individual decision variables
——————————————————————–

Data and solution in MATLAB Environment

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 3.50GHz (sec)
Dataset Matlab code Data Solution 4 10000 9.49104E-04 0.25
PROBLEM 4: minimizing expectile risk subject to bounded from below expected returns

Minimize expectile (minimize negative expectile risk of the portfolio)
subject to
Avg_g >= Const1 (constraint on the expected return of financial instruments)
Linear = Const2 (budget constraint)
Box constraints (box constraints for individual positions)
——————————————————————–
Avg_g = Average Gain
Box constraints = constraints on individual decision variables
——————————————————————–

Data and solution in MATLAB Environment

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 3.50GHz (sec)
Dataset Matlab code Data Solution 4 10000 2.52517E-02 0.72
CASE STUDY SUMMARY
This case study demonstrates portfolio optimization problem when risk is measured by negative expectile risk. Two cases of formulation when risk is minimized and bounded subject to expected return of financial instruments are considered. Results are obtained using PSG external functions interface in MATLAB.