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Purpose: The present study aims to test the Quadratic Programming model for Optimal Portfolio selection empirically.

Need for the Study: All the investors who buy financial products are motivated to obtain higher profits or, in other words, to maximise their returns. However, the high returns are often accompanied by higher risks, and avoiding such risks has become the primary concern for all investors. There is a great need for such a model to maximise profits and minimise risk, which can help design an investment portfolio with minimum risk and maximum return. The Quadratic Programming model is one such model which can be applied for selected shares to build an optimised portfolio.

Methodology: This study optimises the stock samples using a two-level screening of correlation coefficient and coefficient of variation. The monthly closing prices of the NSE-listed Indian pharmaceutical stocks from December 2019 to January 2022 have been used as sample data. The Lagrange Multiplier method is used to apply the model to achieve the optimal portfolio solution. Based on the market reality, the transaction costs have also been considered. The Quadratic programming model is further optimised to achieve the optimal portfolio for the select stocks.

Findings: The traditional portfolio theory and the modified quadratic model gives similar and consistent results. In other words, the modified quadratic model asserts the accuracy of the conventional portfolio model. The portfolio constructed in the present study gives a return much higher than the return of the benchmark portfolio of Nifty Fifty, indicating the usefulness of applying the Quadratic Programming model.

Practical Implications: The construction of an optimal portfolio using the traditional or modified Quadratic model can help investors make rational investment decisions for better returns with lower risks.