A PCA-DEA framework for stock selection in Indian stock market

Portfolio optimization is the process of making an investment decision on a set of assets to realize high returns with low risk. It has three major stages: asset selection, asset weighting and asset management. Asset selection is an important phase because it influences asset allocation and ultimately affects the returns of a portfolio. Today, there is an increase in the number of listings on a stock exchange. Therefore, it is important for an investor to screen and select stocks for investment. This study focuses on the first stage of the portfolio optimization problem, namely, asset selection. The purpose of this study is to evaluate and select profitable stocks quoted on National Stock Exchange (NSE) for portfolio optimization.

Financial ratios are considered as the input and output parameters for evaluating the financial performance of the firms. This study adopts a hybrid principal component analysis (PCA) and data envelopment analysis (DEA) approach to evaluate the efficiency of the firms. Based on the efficiency scores, the firms are selected for the investment process.

The model helps to determine the relative efficiencies of the firms. The efficient firms are considered to be the potential stocks for investment. It helps the investors to screen the stocks from a large number of stocks quoted on NSE.

One of the limitations of the standard DEA model is that it fails to discriminate the firms when the number of input and output parameters are larger than the number of firms. To overcome this problem, either a parameter can be ignored or weight-restricted DEA can be applied. When an input/output parameter is dropped, the information in that variable is lost. Weight-restricted DEA model uses expert opinion for measuring the relative importance of input and output parameters. Expert opinion is subjective and might be biased. The PCA-DEA model helps to identify the efficient firms by improving the discriminatory power of standard DEA without any loss of information and without the need for expert opinion, which might be biased.

Asset selection is an important stage in the investment process. Selection of stocks based on the efficiency score is an easier option available to the investors. But the misclassification of firms either due to biased expert opinion or discrimination inability of DEA can be costly to an investor. The PCA-DEA model overcomes both these limitations. Investors can select the potential candidates for asset allocation based on the efficiency scores obtained using the PCA-DEA model. Further, the relative efficiencies obtained can help the firms to benchmark their performance against the best performing firms within their industry.

This paper is one of few papers to adopt the PCA-DEA framework to select stocks in the Indian stock market.