Computational Finance Project – Exam Version C

This repository contains the full implementation of the Computational Finance project for the course examination (Version C).
The project develops and compares multiple portfolio optimization methodologies — classical, robust, factor-based, diversification-based, and deep-learning driven — using a universe of 16 synthetic equity indices.

All results are generated through the main MATLAB script: Comp_Fin_Group9

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📌 Project Overview

The project is structured into five main exercises, each addressing a different quantitative finance technique:

1. Constrained Mean–Variance Frontier and Robust Frontier via resampling
2. Black–Litterman Model with equilibrium returns and investor views
3. Diversification-Based Portfolios (Maximum Diversification Ratio & Maximum Entropy)
4. PCA-Based Risk Modelling and CVaR Optimization
5. Personal Deep-Learning Allocation Strategy

All models are estimated in-sample (2018–2022) and evaluated with out-of-sample analysis (2023–2024 where applicable).

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🔧 Requirements

This project requires MATLAB R2021a or later, with:

• Optimization Toolbox
• Statistics & Machine Learning Toolbox
• Deep Learning Toolbox (for Exercise 5)

No Python dependencies are used — the project is entirely MATLAB-based.

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▶️ How to Run

1. Open MATLAB
2. Set the project root folder as the current directory
3. Run:

Comp_Fin_Group9

The script will automatically: • load data • run Exercises 1–5 • print portfolio summaries • generate all figures in separate windows

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Exercise Summary

Exercise 1 — Mean–Variance & Robust Frontier

•	Constrained efficient frontier (A–B)
•	Robust frontier using 200 resampled scenarios (C–D)

Exercise 2 — Black–Litterman Model

•	Reverse optimization to compute equilibrium returns
•	3 investor views
•	Posterior returns and updated frontier (E–F)

Exercise 3 — Diversification-Based Portfolios

•	Maximum Diversification Ratio (G)
•	Maximum Entropy in Risk Contributions (H)
•	Sector exposure constraints enforced

Exercise 4 — PCA & CVaR Optimization

•	PCA reconstruction of the covariance matrix
•	Portfolio I: PCA-based maximum Sharpe (with volatility cap)
•	Portfolio J: Minimum CVaR with target volatility 10% (shown to be infeasible → solved at the volatility boundary)

Exercise 5 — Personal Strategy

A deep-learning allocator based on: • 600-day rolling window of returns • Feed-forward neural network • Softmax-constrained weights • Objective: maximize risk-adjusted returns with regularization • Tested out-of-sample on 2023–2024

file to run:

main_py

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Output

Running the project generates: • Efficient frontiers (standard + robust) • Black–Litterman posterior returns and portfolios • MDR and Entropy frontiers • PCA explained variance plots • CVaR-optimized portfolio • Formatted tables summarizing: • expected return • volatility • Sharpe ratio • concentration metrics • top asset exposures

All figures can optionally be saved inside the Plots/ directory.

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Authors

This project was developed by:

• Giacomo Kirn
• Riccardo Girgenti
• Filippo Cuoghi
• Francesco Ligorio
• Luigi Di Gregorio

Computational Finance – Exam Version C
MSc Mathematical Engineering
Politecnico di Milano – 2025