This paper compares a series of contemporary portfolio construction approaches by employing ten U.S. stocks (TSLA, WMT, BAC, GS, LLY, MRK, GOOG, META, AAPL and XOM) in a time frame from September 2023 to December 2025. The paper explores both basic mean-variance optimization, constrained optimization, Fama French five factor regression modeling, Monte Carlo simulation, and the Black-Litterman model to determine how constraints to a solution, risk factors to a strategy, simulated approximations, and specific market views may all impact the outcome of portfolio allocation, performance and stability. Overall, the results show that standard optimization may result in highly concentrated portfolios, while constrained optimization leads to changes in portfolio allocations by altering the efficient frontier, five factor regression models suggest that a basic investment style of defensive large value and profitability exposure, Monte Carlo approximation is a viable technique to arrive at mean-variance optimal portfolios provided the simulations are high enough especially under a box constraint, the Black Litterman portfolio approach produces more economically intuitive allocations and greater stability compared to standard mean-variance optimization as the approach balances equilibrium returns with investor views.
