Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization

This repo accompanies our paper.

Installation

The cptopt package can be installed using pip as follows

pip install git+https://github.com/cvxgrp/cptopt.git

Minimum working example

We are unable to provide the full data set used in the paper for licensing reasons. We, therefore, give a minimum working example using simulated data below.

import numpy as np
from scipy.stats import multivariate_normal as normal

from cptopt.optimizer import MinorizationMaximizationOptimizer, ConvexConcaveOptimizer, \
    MeanVarianceFrontierOptimizer, GradientOptimizer
from cptopt.utility import CPTUtility

# Generate returns
corr = np.array([
    [1, -.2, -.4],
    [-.2, 1, .5],
    [-.4, .5, 1]
])
sd = np.array([.01, .1, .2])
Sigma = np.diag(sd) @ corr @ np.diag(sd)

np.random.seed(0)
r = normal.rvs([.03, .1, .193], Sigma, size=100)

# Define utility function
utility = CPTUtility(
    gamma_pos=8.4, gamma_neg=11.4,
    delta_pos=.77, delta_neg=.79
)

initial_weights = np.array([1/3, 1/3, 1/3])

# Optimize
mv = MeanVarianceFrontierOptimizer(utility)
mv.optimize(r, verbose=True)

mm = MinorizationMaximizationOptimizer(utility)
mm.optimize(r, initial_weights=initial_weights, verbose=True)

cc = ConvexConcaveOptimizer(utility)
cc.optimize(r, initial_weights=initial_weights, verbose=True)

ga = GradientOptimizer(utility)
ga.optimize(r, initial_weights=initial_weights, verbose=True)

The optimal weights can then be accessed via the weights property.

mv.weights
mm.weights
cc.weights
ga.weights

Citing

If you want to reference our paper in your research, please consider citing us by using the following BibTeX:

@misc{luxenberg2022cptopt,
  author = {Luxenberg, Eric and Schiele, Philipp and Boyd, Stephen},
  doi = {10.48550/ARXIV.2209.03461},
  title = {Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization},
  url = {https://arxiv.org/abs/2209.03461},
  year = {2022}
}