Portfolio optimisation with multi-objective genetic algorithms

This repository includes all the files and scripts to reproduce the project of investment portfolio optimisation.

Requisites

• R is required for reproducing the analysis. Further documentation here.
  • The eaf library is needed to produce the algorithms' comparison plots. More information here.
• Python is required for reproducing the analysis. Further documentation here.
  • The pandas package is required for data manipulation and to get real time data.
  • The datetime package is used for selecting time frames when downloading real market data.
  • The numpy package is required for mathematical formulations.
  • The pymoo package is required. This is the package used specifically for modeling and solving the applied genetic algorithms.
  • The scipy package is used for performing statistical tests.
  • The lzma package is required for formatting the results correctly for the eaf library.

Real market data

The financial data used as input for the two algorithms has been sourced from Yahoo Finance.

The stocks_info.py inside code folder contains the method utilized to download real market data of $20$ stocks considered important inside the UK.

The stocks_info.py file performs the following:

• Using the datetime package, the stocks data was delimited between $5$ October $2019$ and $5$ October $2022$.

• The risk free rate was setted to $0.00$. The returns were annualized and the sharpe ratio was computed as a percentage delta and the volatility based on $250$ trading days.

• Finally the formatted data is exported to stocks_info.csv inside data.

Both alg1.py and alg2.py source to the stocks_info.csv dataset as the source of market information employed as input.

Reproducibility

In order to reproduce the analysis, it is necessary to follow the subsecuent steps:

1. Run both algorithms
2. Run the analysis and creation of plots

Run both algorithms

As this work icompare two portfolio optimisation algorithms with different settings, the user should run both algorithms. The order in which they are performed is unimportant.

Algorithm 1 Algorithm contained inside alg1 folder within code. alg1 contains two files:

• alg1.py: stores the complete implementation of the genetic algorithm and exportation of results.
• algorithm_1_results_formating.py: formats the first algorithm's results.

For running and saving the findings of the first algorithm first excecute alg1.py for running the genetic algorithm and exporting results. Then, run algorithm_1_results_formatin.py, for generating an exported dataset of the results saved inside the alg1 folder within results.

Algorithm 2

Algorithm contained inside alg2 folder within code. alg2 contains two files:

• alg2.py: stores the complete implementation of the genetic algorithm and exportation of results.
• algorithm_2_results_formating.py: formats the second algorithm's results.

For running and saving the findings of the second algorithm first excecute alg2.py for running the genetic algorithm and exporting results. Then, run algorithm_2_results_formatin.py, for generating an exported dataset of the results saved inside the alg2 folder within results.

Run the analysis and creation of plots

Results from both algorithms are stored inside results folder, divided correspondingly into two subfolders: alg1 and alg2. For comparing the GA's open the analysis folder inside code, there will be three files:

• algs_boxplots.R: creates a box plot comparing the objective values of the two GA's. Exports boxplot.pdf to figures folder.
• algorithm_comparison_figures.R: creates a eaf plot for each of the two algorithms and a eaf comparison plot between both algorithms. Exports A1.pdf, A2.pdf and A1_vs_A2.´df to figures folder.
• analysis_test.py: performs a Mann-Whitney U Test between the two algorithms' results. Exports mann_whitney_tests.txt to results.

Report

Report available as report.pdf inside report folder. To replicate it please download and unzip report.zip, then compile it using LaTex. Due to report.pdf's high resolution plots, there is a high probability of user issues when opening the file. For this reason, a compressed version can be found here.