INTERNATIONAL JOURNAL OF ENGINEERING MANAGEMENT AND
SOCIAL SCIENCES

Portfolio Optimization using Modern Portfolio Theory

In a world of countless investment choices and ever-present risk, the scientific construction of efficient, diversified portfolios is one of the most important tasks in investment management. Modern Portfolio Theory (MPT), developed by Harry Markowitz, provides the foundational framework for this task by showing how the combination of imperfectly correlated assets can reduce risk for a given level of return. The present study applies this framework to the securities of three leading financial-sector companies — Goldman Sachs, HSBC, and HDFC Bank — to construct and evaluate an optimised portfolio. The study adopts an analytical and quantitative research design based on secondary data, namely the annual returns of the three stocks over the five-year period 2021 to 2025. Average returns, variances, standard deviations, covariances, and correlations of the stocks were computed, and mean-variance optimization was applied to construct the minimum-risk and maximum-Sharpe (optimal) portfolios and the efficient frontier, with performance evaluated using the Sharpe ratio. The findings reveal that Goldman Sachs gave the highest average return (32.34%) but also the highest risk, while HDFC Bank, with a low correlation to the other stocks, served as an effective diversifier. The equal-weighted diversified portfolio achieved a risk of 13.27%, significantly lower than the weighted-average risk of the individual stocks (16.64%), and the optimal portfolio achieved the best risk-adjusted return with a Sharpe ratio of 1.19. The hypothesis test confirmed that optimization significantly reduced risk, leading to rejection of the null hypothesis. The study concludes that portfolio optimization using Modern Portfolio Theory is an effective tool for constructing efficient portfolios, and offers suggestions on diversification, risk-adjusted selection, and use of the efficient frontier for investors.