Pension investment portfolios play a pivotal role in ensuring financial security for retirees. With an aging global population, the importance of optimizing these portfolios to withstand market fluctuations and ensure steady returns becomes paramount. This study delves into the complexities of pension investment portfolios using the time-tested mean-variance model, aiming to strike a balance between risk and expected returns. Focusing on key industries like technology, entertainment, automotive, resources, and air travel, the research critically analyzes a diverse set of stocks. Methods employed include a deep analysis of expected returns, variances, covariances, and the overarching risk-return trade-off. Preliminary results underscore the nuanced nature of portfolio management and the indispensability of incorporating modern portfolio theory in pension fund management. The outcomes of this study not only aid in making informed investment decisions but also shed light on the broader social implications of robust pension fund management, emphasizing its significance in securing retirees' financial futures.