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Designing an optimum portfolio that allocates weights to its constituentstocks in a way that achieves the best trade-off between the return and therisk is a challenging research problem. The classical mean-variance theory ofportfolio proposed by Markowitz is found to perform sub-optimally on thereal-world stock market data since the error in estimation for the expectedreturns adversely affects the performance of the portfolio. This paper presentsthree approaches to portfolio design, viz, the minimum risk portfolio, theoptimum risk portfolio, and the Eigen portfolio, for seven important sectors ofthe Indian stock market. The daily historical prices of the stocks are scrapedfrom Yahoo Finance website from January 1, 2016, to December 31, 2020. Threeportfolios are built for each of the seven sectors chosen for this study, andthe portfolios are analyzed on the training data based on several metrics suchas annualized return and risk, weights assigned to the constituent stocks, thecorrelation heatmaps, and the principal components of the Eigen portfolios.Finally, the optimum risk portfolios and the Eigen portfolios for all sectorsare tested on their return over a period of a six-month period. Theperformances of the portfolios are compared and the portfolio yielding thehigher return for each sector is identified.

Optimum Risk Portfolio and Eigen Portfolio: A Comparative Analysis Using Selected Stocks from the Indian Stock Market