I need help creating and LP or GRG model for the testing of a portfolio as per attached word file or instructions below. Excel file contains the dataset for modelling purposes.Data from excel is also below. Conceptual Understanding:

A "6-pack portfolio" typically refers to a diversified investment portfolio consisting of six different asset classes, securities, or investment types. The idea is to balance risk and return by spreading investments across various sectors or categories.

Objective:

• Develop an optimal trading strategy leveraging Linear or nonlinear programming techniques to maximize risk-adjusted expected returns while adhering to specific constraints.

Data Collection:

• Obtain historical returns data for a selection of assets and TSX index serving as benchmark:
• SPTSX Index (benchmark)
• Financial - RY CN Equity
• Utility - FTS CN Equity
• Telecom - T CN Equity
• Industrial - CNR CN Equity
• Real Estate - IIP-U CN Equity
• Energy - ENB CN Equity

Model Formulation:

• Define the decision variables: Allocation percentages for each asset class.
• Objective function: Maximize the Sharpe ratio (risk-adjusted return).
• Constraints:
  • Budget constraint: Sum of allocation percentages = 100%.
  • Risk tolerance: Define a maximum acceptable portfolio variance.
  • Non-negativity: Allocation percentages must be non-negative.
  • Diversification constraints: Set minimum and maximum allocation limits for each asset class to ensure diversification.

Mathematical Representation:

Let ; represent the allocation to asset i. . Objective: Maximize Ro-Rf , where R is the portfolio return, Ry is the risk-free rate, and Op is the portfolio standard deviation. Constraints: Didi = 1 Up . max 20 C mini - Ci max. for each asset