This repo accompanies our paper.
The cptopt package can be installed using pip as follows
pip install git+https://github.com/cvxgrp/cptopt.gitWe 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.weightsIf you want to reference our paper in your research, please consider citing us by using the following BibTeX:
@article{luxenberg2024cptopt,
title={Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization},
author={Luxenberg, Eric and Schiele, Philipp and Boyd, Stephen},
journal={Computational Economics},
pages={1--21},
year={2024},
doi = {https://doi.org/10.1007/s10614-024-10556-x},
publisher={Springer},
url = {https://web.stanford.edu/\%7Eboyd/papers/pdf/cpt_opt.pdf},
}
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