  Designing an optimum portfolio that allocates weights to its constituent
stocks in a way that achieves the best trade-off between the return and the
risk is a challenging research problem. The classical mean-variance theory of
portfolio proposed by Markowitz is found to perform sub-optimally on the
real-world stock market data since the error in estimation for the expected
returns adversely affects the performance of the portfolio. This paper presents
three approaches to portfolio design, viz, the minimum risk portfolio, the
optimum risk portfolio, and the Eigen portfolio, for seven important sectors of
the Indian stock market. The daily historical prices of the stocks are scraped
from Yahoo Finance website from January 1, 2016, to December 31, 2020. Three
portfolios are built for each of the seven sectors chosen for this study, and
the portfolios are analyzed on the training data based on several metrics such
as annualized return and risk, weights assigned to the constituent stocks, the
correlation heatmaps, and the principal components of the Eigen portfolios.
Finally, the optimum risk portfolios and the Eigen portfolios for all sectors
are tested on their return over a period of a six-month period. The
performances of the portfolios are compared and the portfolio yielding the
higher return for each sector is identified.
