portfolio.md

Portfolio example

The goal in portfolio optimization is to maximize profit by choosing a number of assets in which to invest a given amount of money.

Nominal version

Parameters of the problem are the returns r for each asset. Each variable x[i] indicates the fraction of the available money which is invested in asset i. The only constraint ensures that all of the money is invested.

m = pe.ConcreteModel()
m.cons = pe.ConstraintList()

r = [0.1, 0.3, 0.5, 0.7, 0.4]

m.x = pe.Var(range(5), bounds=(0, 1))

m.cons = pe.Constraint(expr=sum([m.x[i] for i in index]) == 1)
m.obj = pe.Objective(expr=sum([r[i]*m.x[i] for i in index]),
                     sense=pe.maximize)

Robust version

Future returns are usually not known explicitly. It therefore makes sense to consider r to be uncertain and to optimize the worst case profit.

m = pe.ConcreteModel()
m.cons = pe.ConstraintList()

r = [0.1, 0.3, 0.5, 0.7, 0.4]

m.x = pe.Var(range(5), bounds=(0, 1))

# Construct uncertainty set and uncertain parameter
m.U = ro.uncset.EllipsoidalSet(r,
                               [[0.0005, 0, 0, 0, 0],
                               [0, 0.0005, 0, 0, 0],
                               [0, 0, 0.0005, 0, 0],
                               [0, 0, 0, 0.0005, 0],
                               [0, 0, 0, 0, 0.0005]])
m.r = ro.UncParam(range(5), uncset=m.U, nominal=r)

# Add constraint and objective
m.cons = pe.Constraint(expr=sum([m.x[i] for i in index]) == 1)
m.obj = pe.Objective(expr=sum([m.r[i]*m.x[i] for i in index]),
                     sense=pe.maximize)

Running the example

The portfolio optimization example is available as part of ROmodel and can be used as follows:

import romodel.examples as ex
import pyomo.environ as pe

m = ex.Portfolio()

solver = pe.SolverFactory('romodel.cuts')
solver.solve(m)

The full code is available here.