  Portfolio optimization has been a broad and intense area of interest for
quantitative and statistical finance researchers and financial analysts. It is
a challenging task to design a portfolio of stocks to arrive at the optimized
values of the return and risk. This paper presents an algorithmic approach for
designing optimum risk and eigen portfolios for five thematic sectors of the
NSE of India. The prices of the stocks are extracted from the web from Jan 1,
2016, to Dec 31, 2020. Optimum risk and eigen portfolios for each sector are
designed based on ten critical stocks from the sector. An LSTM model is
designed for predicting future stock prices. Seven months after the portfolios
were formed, on Aug 3, 2021, the actual returns of the portfolios are compared
with the LSTM-predicted returns. The predicted and the actual returns indicate
a very high-level accuracy of the LSTM model.
