Initializing help system before first use

Folio - Introductory examples from 'Getting Started'
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(rowstat,colstat)

    # 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")
Parent Topic Getting Started

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