Abstract : This paper explores the application of Harry Markowitz’s Modern Portfolio Theory (MPT) through two distinct computational lenses: stochastic Monte Carlo simulations and deterministic mathematical optimization. Using a portfolio comprising major technology and hardware equities: Apple (AAPL), Cisco (CSCO), IBM, and Amazon (AMZN). This study evaluates the risk-return trade-offs during a specific historical period. We analyse the construction of the Efficient Frontier and identify the Optimal Risky Portfolio based on the maximization of the Sharpe Ratio.

Keyword : Efficient Frontier, Log Returns, Modern Portfolio Theory, Monte Carlo Simulation, Portfolio Optimization, Sharpe Ratio.