Background

Problem. Portfolio with return dominating the benchmark portfolio return in the second order and having maximum expected return

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

References

 

Background

This case study finds a portfolio with return dominating the benchmark portfolio return in the second order and having maximum expected return. Mean-risk models are convenient from a computational point of view and have an intuitive appeal. In their traditional form, however, they use only two (or a few) statistics to characterize a distribution, and thus may ignore important information. Stochastic dominance, in contrast, takes into account the entire distribution of a random variable. The second-order stochastic dominance is an important criterion in portfolio selection. This case study optimizes a problem with a dataset considered in paper Fabian et al.

 

Problem

 

Simplified Problem Statement

 

Maximize Linear_1

 subject to

Linear_2 ≤ Const  (budget constraint)

PM_Pen_1(Loss) ≤ const_1

...

PM_Pen_1(Loss) < const_J

Box constraints (0 ≤ portfolio weights ≤ 0)

 

where

 

Linear = linear (non-random) function in decision variables

PM_Pen(Loss) = Partial Moment One of random loss function (expected loss in access of benchmark)

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 function tbpsg_run (General (Text) Format of PSG in MATLAB):

 

 

Input Files to run CS:

 

 

References

 

[1]  Fabian, C.I., Mitra, G, Roman, D., and V. Zverovich (2010):  An enhanced model for portfolio choice with SSD criteria: a constructive approach. Quantitative Finance, # 6.

[2]  Rudolf, G., and A. Ruszczynski (2008): Optimization problems with second order stochastic dominance constraints: duality, compact formulations, and cut generation methods, SIAM J. OPTIM, Vol. 19, No. 3, pp. 1326–1343.

[3]  Roman, D.,  Darby-Dowman, K., and G. Mitra (2006): Portfolio construction based on stochastic dominance and target return distributions, Mathematical Programming, Series B, Vol. 108, pp. 541-569.

[4]  Ogryczak,W., and A. Ruszczynski (1999): From stochastic dominance to mean–risk models: Semideviations as risk measures. European Journal of Operational Research, Vol. 116, pp. 33–50.