Getting started guide - Python examples


Type:	Portfolio optimization
Rating:	2 (easy-medium)
Description:	Simple tasks for formulating and solving a portfolio optimization problem: inputting an LP problem from data arrays (Folio.py) inputting a MIP problem - binary variables (FolioMIP1.py) inputting a MIP problem - semicontinuous variables (FolioMIP2.py) inputting a QC problem (FolioQC.py) inputting a QP problem (FolioQP.py) inputting a problem using heuristics (FolioHeuristic.py)
File(s):	Folio.py, FolioMIP1.py, FolioMIP2.py, FolioQC.py, FolioQP.py, FolioHeuristic.py
Data file(s):	foliocppqp.csv

Folio.py

# Modeling a small LP problem to perform portfolio optimization.
#
# (C) 2025 Fair Isaac Corporation

import xpress as xp

# Problem data
NSHARES = 10
RET = [5, 17, 26, 12, 8, 9, 7, 6, 31, 21]
RISK = [1, 2, 3, 8, 9]
NA = [0, 1, 2, 3]

p = xp.problem(name="Folio")

# VARIABLES.
frac = p.addVariables(NSHARES, ub=0.3, name="frac")

# CONSTRAINTS.
# Limit the percentage of high-risk values.
p.addConstraint(xp.Sum(frac[i] for i in RISK) <= 1/3)

# Minimum amount of North-American values.
p.addConstraint(xp.Sum(frac[i] for i in NA) >= 0.5)

# Spend all the capital.
p.addConstraint(xp.Sum(frac) == 1)

# Objective: maximize total return.
p.setObjective(xp.Sum(frac[i] * RET[i] for i in range(NSHARES)), sense=xp.maximize)

# Solve.
p.optimize()

# Print problem status.
print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
    {p.attributes.solstatus.name}")

# Solution printing.
print("Total return:", p.attributes.objval)
sol = p.getSolution(frac)
for i in range(NSHARES):
    print(f"{frac[i].name} : {sol[i]*100:.2f} %")

FolioMIP1.py

# Modeling a small MIP problem to perform portfolio optimization.
# - Limiting the total number of assets.
#
# (C) 2025 Fair Isaac Corporation

import xpress as xp

# Problem data
MAXNUM = 4
NSHARES = 10
RET = [5, 17, 26, 12, 8, 9, 7, 6, 31, 21]
RISK = [1, 2, 3, 8, 9]
NA = [0, 1, 2, 3]

p = xp.problem(name="Folio")

# VARIABLES.
frac = p.addVariables(NSHARES, ub=0.3, name="frac")
buy = p.addVariables(NSHARES, vartype=xp.binary, name="buy")

# CONSTRAINTS.
# Limit the percentage of high-risk values.
p.addConstraint(xp.Sum(frac[i] for i in RISK) <= 1/3)

# Minimum amount of North-American values.
p.addConstraint(xp.Sum(frac[i] for i in NA) >= 0.5)

# Spend all the capital.
p.addConstraint(xp.Sum(frac) == 1)

# Limit the total number of assets.
p.addConstraint(xp.Sum(buy) <= MAXNUM)

# Linking the variables.
p.addConstraint(frac[i] <= buy[i] for i in range(NSHARES))

# Objective: maximize total return.
p.setObjective(xp.Sum(frac[i] * RET[i] for i in range(NSHARES)), sense=xp.maximize)

# Solve.
p.optimize()

# Print problem status.
print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
    {p.attributes.solstatus.name}")

# Solution printing.
print("Total return:", p.attributes.objval)
sol = p.getSolution(frac)
for i in range(NSHARES):
    print(f"{frac[i].name} : {sol[i]*100:.2f} %")

FolioMIP2.py

# Modeling a small MIP problem to perform portfolio optimization.
# - Imposing a minimum investment per share.
#
# (C) 2025 Fair Isaac Corporation

import xpress as xp

# Problem data
MAXNUM = 4
NSHARES = 10
RET = [5, 17, 26, 12, 8, 9, 7, 6, 31, 21]
RISK = [1, 2, 3, 8, 9]
NA = [0, 1, 2, 3]

p = xp.problem(name="Folio")

# VARIABLES.
frac = p.addVariables(NSHARES, vartype=xp.semicontinuous, threshold=0.1, ub=0.3, name="frac")

# CONSTRAINTS.
# Limit the percentage of high-risk values.
p.addConstraint(xp.Sum(frac[i] for i in RISK) <= 1/3)

# Minimum amount of North-American values.
p.addConstraint(xp.Sum(frac[i] for i in NA) >= 0.5)

# Spend all the capital.
p.addConstraint(xp.Sum(frac) == 1)

# Objective: maximize total return.
p.setObjective(xp.Sum(frac[i] * RET[i] for i in range(NSHARES)), sense=xp.maximize)

# Solve.
p.optimize()

# Print problem status.
print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
    {p.attributes.solstatus.name}")

# Solution printing.
print("Total return:", p.attributes.objval)
sol = p.getSolution(frac)
for i in range(NSHARES):
    print(f"{frac[i].name} : {sol[i]*100:.2f} %")

FolioQC.py

# Modeling a small QC problem to perform portfolio optimization.
# - Maximize return with limit on variance.
#
# (C) 2025 Fair Isaac Corporation

import xpress as xp
import csv

# Read the CSV file and store each row as a 2D list
file_path = 'Data/foliocppqp.csv'
VAR = []
with open(file_path, 'r') as file:
    reader = csv.reader(file)
    for row in reader:
        VAR.append([float(value) for value in row])

# Problem data
MAXVAR = 0.55
MAXNUM = 4
NSHARES = 10
RET = [5, 17, 26, 12, 8, 9, 7, 6, 31, 21]
NA = [0, 1, 2, 3]

p = xp.problem(name="Folio")

# VARIABLES.
frac = p.addVariables(NSHARES, ub=0.3, name="frac")

# CONSTRAINTS.
# Minimum amount of North-American values.
p.addConstraint(xp.Sum(frac[i] for i in NA) >= 0.5)

# Spend all the capital.
p.addConstraint(xp.Sum(frac) == 1)

# Limit variance.
variance = [frac[s]*frac[t]*VAR[s][t] for s in range(NSHARES) for t in range(NSHARES)]
p.addConstraint(xp.Sum(variance) <= MAXVAR)

# Objective: maximize total return.
p.setObjective(xp.Sum(frac[i] * RET[i] for i in range(NSHARES)), sense=xp.maximize)

# Solve.
p.optimize()

# Print problem status.
print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
    {p.attributes.solstatus.name}")

# Solution printing.
print(f"With a max variance of {MAXVAR} total return is {p.attributes.objval}")
sol = p.getSolution(frac)
for i in range(NSHARES):
    print(f"{frac[i].name} : {sol[i]*100:.2f} %")

FolioQP.py

# Modeling a small QP problem to perform portfolio optimization.
# 1. QP: minimize variance.
# 2. MIQP: limited number of assets.
#
# (C) 2025 Fair Isaac Corporation

import xpress as xp
import csv

# Read the CSV file and store each row as a 2D list
file_path = 'Data/foliocppqp.csv'
VAR = []
with open(file_path, 'r') as file:
    reader = csv.reader(file)
    for row in reader:
        VAR.append([float(value) for value in row])

# Problem data
TARGET = 9
MAXNUM = 4
NSHARES = 10
RET = [5, 17, 26, 12, 8, 9, 7, 6, 31, 21]
NA = [0, 1, 2, 3]

# *******FIRST PROBLEM: UNLIMITED NUMBER OF ASSETS********
p = xp.problem(name="Folio")

# VARIABLES.
frac = p.addVariables(NSHARES, ub=0.3, name="frac")

# CONSTRAINTS.
# Minimum amount of North-American values.
p.addConstraint(xp.Sum(frac[i] for i in NA) >= 0.5)

# Spend all the capital.
p.addConstraint(xp.Sum(frac) == 1)

# Target yield.
p.addConstraint(xp.Sum(frac[i] * RET[i] for i in range(NSHARES)) >= TARGET)

# Objective: minimize mean variance.
variance = [frac[s]*frac[t]*VAR[s][t] for s in range(NSHARES) for t in range(NSHARES)]
p.setObjective(xp.Sum(variance))

# Solve.
p.optimize()

# Print problem status.
print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
    {p.attributes.solstatus.name}")

# Solution printing.
print(f"With a target of {TARGET} minimum variance is {p.attributes.objval}")
sol = p.getSolution(frac)
for i in range(NSHARES):
    print(f"{frac[i].name} : {sol[i]*100:.2f} %")

# *******SECOND PROBLEM: LIMIT NUMBER OF ASSETS********
buy = p.addVariables(NSHARES, vartype=xp.binary, name="buy")

# CONSTRAINTS.
# Minimum amount of North-American values.
p.addConstraint(xp.Sum(frac[i] for i in NA) >= 0.5)

# Limit the total number of assets.
p.addConstraint(xp.Sum(buy) <= MAXNUM)

# Linking the variables.
p.addConstraint(frac[i] <= buy[i] for i in range(NSHARES))

# Solve.
p.optimize()

# Print problem status.
print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
    {p.attributes.solstatus.name}")

# Solution printing.
print(f"With a target of {TARGET} minimum variance is {p.attributes.objval}")
sol = p.getSolution(frac)
for i in range(NSHARES):
    print(f"{frac[i].name} : {sol[i]*100:.2f} %")

FolioHeuristic.py

# Using a heuristic solution to perform portfolio optimization.
#
# (C) 2025 Fair Isaac Corporation

import xpress as xp

# Problem data
MAXNUM = 4
NSHARES = 10
RET = [5, 17, 26, 12, 8, 9, 7, 6, 31, 21]
RISK = [1, 2, 3, 8, 9]
NA = [0, 1, 2, 3]

def printSolution(prob, name):
    # Solution printing.
    print(f"Total return {name}:", prob.attributes.objval)
    sol = prob.getSolution()
    for i in range(NSHARES):
        print(f"{frac[i].name} : {sol[i] * 100:.2f} %")

def solveHeuristic(prob):
    # Disable automatic cuts.
    prob.controls.cutstrategy = 0
    # Switch presolve off.
    prob.controls.presolve = 0
    prob.controls.mippresolve = 0
    # Get feasibility tolerance.
    tol = prob.controls.feastol

    prob.lpOptimize()

    # Save the current basis.
    rowstat, colstat = prob.getBasis()

    # Fix all variables 'buy' for which `frac' is at 0 relatively close to 1
    fsol = prob.getSolution(frac)      # get the solution values of `frac'
    for i in range(NSHARES):
        if fsol[i] < tol:
            buy[i].lb = 0
            buy[i].ub = 0
        elif fsol[i] > 0.2 - tol:
            buy[i].lb = 1
            buy[i].ub = 1

    prob.mipOptimize()

    print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
        {p.attributes.solstatus.name}")

    printSolution(prob, "Heuristic solution")

    # Reset variables to their original bounds.
    for i in range(NSHARES):
        if fsol[i] < tol or fsol[i] > 0.2 - tol:
            buy[i].lb = 0
            buy[i].ub = 1

    # Load basis.
    prob.loadBasis(rowstat, colstat)

    # Set cutoff to the best known solution.
    prob.controls.mipabscutoff = prob.attributes.objval - tol

p = xp.problem(name="Folio")

# VARIABLES.
frac = p.addVariables(NSHARES, ub=0.3, name="frac")
buy = p.addVariables(NSHARES, vartype=xp.binary, name="buy")

# CONSTRAINTS.
# Limit the percentage of high-risk values.
p.addConstraint(xp.Sum(frac[i] for i in RISK) <= 1/3)

# Minimum amount of North-American values.
p.addConstraint(xp.Sum(frac[i] for i in NA) >= 0.5)

# Spend all the capital.
p.addConstraint(xp.Sum(frac) == 1)

# Limit the total number of assets.
p.addConstraint(xp.Sum(buy) <= MAXNUM)

# Linking the variables.
p.addConstraint(frac[i] <= buy[i] for i in range(NSHARES))

# Objective: maximize total return.
p.setObjective(xp.Sum(frac[i] * RET[i] for i in range(NSHARES)), sense=xp.maximize)

# Solve with heuristic.
solveHeuristic(p)

# Solve original problem.
p.optimize()

# Print problem status.
print(f"Problem status: \n\t Solve status: {p.attributes.solvestatus.name} \n\t Sol status: \
    {p.attributes.solstatus.name}")

printSolution(p, "Exact Solve")

© 2001-2025 Fair Isaac Corporation. All rights reserved. This documentation is the property of Fair Isaac Corporation (“FICO”). Receipt or possession of this documentation does not convey rights to disclose, reproduce, make derivative works, use, or allow others to use it except solely for internal evaluation purposes to determine whether to purchase a license to the software described in this documentation, or as otherwise set forth in a written software license agreement between you and FICO (or a FICO affiliate). Use of this documentation and the software described in it must conform strictly to the foregoing permitted uses, and no other use is permitted.

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Getting started guide - Python examples