Portfolio Optimization using Genetic Algorithm: Application to CAC40

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[...] Mutation: Small, random changes are introduced to some individuals in the population, promoting diversity and preventing convergence to local optima. ? Generation Update: The new offspring and mutated individuals form the next generation, and the process iterates. ? Project Objective This project aims to implement and apply Genetic Algorithms (GAs) for the optimization of investment portfolios, focusing on top 15 CAC40 assets. The primary objective is to leverage the adaptive nature of GAs to efficiently explore the solution space, generating diverse and innovative portfolio allocations that balance returns and risk. [...]

[...] Genetic Algorithm 3.1 Population Initialization - Initial Generation of Portfolios and Weight Initialization The Genetic Algorithm kicks off with the creation of an initial population, which consists of portfolios, each containing the same set of 15 assets. These assets represent the largest companies by market capitalization in the French stock market (CAC40), as sourced from TradingView. The individual assets within the portfolios have fixed returns and volatilities based on the market data for the year 2023. Here is the table of the assets chosen, their individual returns and volatility : Name of the asset Asset number Weight Return Volatility LVMH 1 w1 11.85% 1.95% L'Oreal 2 w2 11.89% 1.52% Hermes INTL 3 w3 23.71% 1.59% TotalEnergies 4 w4 5.79% 1.43% Sanofi 5 w5 6.97% 1.29% Airbus 6 w6 3.31% 1.46% Dior 7 w7 5.00% 1.96% Hermes 8 w8 6.73% 1.44% Schneider Electric 9 w9 6.45% 1.21% EssilorLuxotica 10 w10 3.79% 1.82% Safran 11 w11 6.75% 1.43% BNP Paribas 12 w12 0.30% 1.64% AXA 13 w13 0.95% 1.27% Vinci 14 w14 4.08% 1.16% Stellantis 15 w15 10.38% 1.81% Each portfolio is characterized by a distribution of weights, determining the proportion of each asset's contribution to the overall portfolio. [...]

[...] This selection process ensures that well-performing portfolios have a higher chance of passing their characteristics to subsequent generations, ultimately guiding the algorithm toward convergence to optimal or near-optimal solutions. 4. Parameters and Iterations 4.1 Parameters - Choice of Parameters such as Population Size, Mutation Rate, and Number of Generations The effectiveness of the Genetic Algorithm in portfolio optimization relies on the careful selection of key parameters that influence its behavior. Three crucial parameters are the population size, the mutation rate, and the number of generations. [...]

[...] Rationale: Customizing the objective function allows tailoring the optimization process to specific financial objectives. 7. Elitism: ? Incorporation: Implemented elitism to preserve a percentage of the best-performing individuals without changes in each generation. ? Rationale: Elitism safeguards successful solutions, preventing their loss in subsequent generations. 8. Dynamic Parameters: ? Adaptability: Investigated adaptive mechanisms to dynamically adjust parameters based on the algorithm's performance. ? Rationale: Dynamic parameter adaptation enhances the algorithm's ability to respond to changing conditions during the optimization process. [...]

[...] Selection: The selected portfolios, based on their fitness, undergo crossover and mutation operations, introducing genetic variations and generating new portfolios (offspring). 4. Crossover and Mutation: The selected portfolios undergo crossover and mutation operations, introducing genetic variations and generating new portfolios (offspring). 5. Termination: The generational loop continues for a predefined number of iterations (generations) or until a termination criterion is met, such as reaching a satisfactory level of portfolio performance. By iteratively applying these steps, the GA refines the portfolio population, allowing it to explore diverse weight configurations and converge towards portfolios with improved performance characteristics. [...]