The HW-Frontier

The HW-Frontier is a full-stack quantitative finance application. It leverages Modern Portfolio Theory (MPT) and Convex Optimization to solve for the efficient frontier, helping users allocate capital across volatile assets based on historical risk-adjusted returns.

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The Mathematical Model

As math-focused developers, we moved away from simple heuristics and implemented a rigorous Mean-Variance Optimization engine.

1. Data Processing & Statistical Grounding

To maintain statistical integrity, we transform raw price data into Log Returns. This ensures time-additivity and better handles the compounding nature of financial assets: $$r_t = \ln\left(\frac{P_t}{P_{t-1}}\right)$$

We then calculate the Annualized Expected Return Vector ($\mu$) and the Annualized Covariance Matrix ($\Sigma$) assuming $N=252$ trading days: $$\mu_{ann} = E[r] \times 252$$ $$\Sigma_{ann} = \text{Cov}(r) \times 252$$

2. Quadratic Programming (QP)

The engine solves a Convex Optimization problem using the CVXPY library. Given a risk-aversion parameter $\gamma$ (mapped from the UI slider), we maximize the risk-adjusted return:

$$ \begin{aligned} \text{maximize} \quad & w^T \mu - \gamma (w^T \Sigma w) \\ \text{subject to} \quad & \sum_{i=1}^{n} w_i = 1 \\ & w_i \ge 0.05 \\ & w_i \le 0.45 \end{aligned} $$

3. Numerical Stability

To ensure the solver always finds a global minimum, we implemented Tychonov Regularization. By adding a small $\epsilon$ ($10^{-6}$) to the diagonal of $\Sigma$, we ensure the matrix is strictly positive definite: $$\Sigma_{stable} = \Sigma + \epsilon I$$

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Tech Stack

Frontend (Client)

• React (Vite + TypeScript): For a type-safe, high-performance user interface.
• Tailwind CSS: Modern, responsive design with a financial "Glassmorphism" aesthetic.
• Recharts: Dynamic SVG-based Donut charts for asset weight visualization.
• Axios: Asynchronous API communication with the Python backend.

Backend (Server)

• FastAPI: High-speed ASGI web framework for serving the optimization logic.
• CVXPY: A specialized library for formulating and solving convex optimization problems.
• Pandas & NumPy: For heavy-duty data manipulation and linear algebra operations.
• Uvicorn: Lightning-fast ASGI server implementation.

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Installation & Setup

1. Clone the Repository

git clone https://github.com/Arya125-droid/Fin_opt.git
cd Fin_opt