Implementation of machine learning in \(\ell _{\infty }\)-based sparse Sharpe ratio portfolio optimization: a case study on Indian stock market

Constructing the optimal portfolio by determining and selecting the best combinations of multiple portfolios is computationally challenging due to its exponential complexity. This paper considers the above issue and demonstrates an efficient portfolio selection method based on the sparse minimax Sharpe ratio model involving pre-selected stocks by an unsupervised machine learning approach. Different clustering techniques, such as k-means, fuzzy c-means, and ward linkage, have been used to cluster the stock market data into a finite number of clusters created based on their return rates and related risk levels. Several validity indices have been applied to arrive at the most appropriate number of groups to opt into the portfolio. Further, the sparse minimax Sharpe ratio model is implemented for the selection of the most efficient portfolio. Finally, the efficacy of the developed technique is justified and validated by illustrating a numerical example based on the historical dataset taken from the Bombay stock exchange (BSE), India.