Case study: Portfolio Optimization with Expectiles

Back to main page

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

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

Dataset 1	4	10000	0.00094986	0.06
	# of Variables	# of Scenarios	Objective Value	Solving Time, PC 3.14GHz (sec)
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)nsubject 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 Gai
Box constraints = constraints on individual decision variables ——————————————————————– n

Dataset 1	4	10000	0.02447960	0.01
	# of Variables	# of Scenarios	Objective Value	Solving Time, PC 3.14GHz (sec)
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)nsubject tonexpectile <= Const1 (constraint on the negative expectile risk of the portfolio) Linear = Const2 (budget constraint) Box constraints (box constraints for individual positions) ——————————————————————– Avg_g = Average Gai
Box constraints = constraints on individual decision variables ——————————————————————– n

Data and solution in MATLAB Environmentn

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)nsubject 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 Gai
Box constraints = constraints on individual decision variables ——————————————————————– n

Data and solution in MATLAB Environmentn

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.