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Sectoral portfolio optimization by judicious selection of financial ratios via PCA

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Abstract

Embedding value investment in portfolio optimization models has always been a challenge. In this paper, we attempt to incorporate it by employing principal component analysis (PCA) to filter out dominant financial ratios from each sector and thereafter, use the portfolio optimization model incorporating second-order stochastic dominance (SSD) criteria to derive an optimal investment. We consider 11 financial ratios corresponding to each sector representing four categories of ratios, namely liquidity, solvency, profitability, and valuation. PCA is then applied over 10 years to extract dominant ratios from each sector in two ways, one from the component solution and the other from each category on the basis of their communalities. The two-step sectoral portfolio optimization (SPO) model is then utilized to build an optimal portfolio. The strategy formed using the formerly extracted ratios is termed PCA-SPO(A) and the latter PCA-SPO(B). The results obtained from the proposed strategies are compared with those from mean-variance, minimum variance, SPO, and nominal SSD models, with and without financial ratios. The empirical performance of proposed strategies is analyzed in two ways, viz., using a rolling window scheme and on different market scenarios for the S &P BSE 500 (India) and S &P 500 (U.S.) indices. We observe that the proposed strategy PCA-SPO(B) outperforms all other models in terms of downside deviation, CVaR, VaR, Sortino, Rachev, and STARR ratios over almost all out-of-sample periods. This highlights the importance of value investment where ratios are carefully selected and embedded quantitatively in the portfolio selection process.

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Notes

  1. In financial markets, sectors are the groups of stocks classified according to their similar business functionality and operations.

  2. https://www.bseindia.com/downloads1/spbsesectordiversificationconsultation5222019.pdf

  3. https://www.thebalance.com/what-is-the-sector-weighting-of-the-s-and-p-500-4579847

  4. Loads gives the information of the amount of variance of the original variable (ratio), the principal component accounts for.

  5. https://prowessiq.cmie.com/.

  6. To trace the downside risk, we first sort the return series of portfolio z in ascending order as \(R_{z1}<R_{z2}< \cdots <R_{zM}\), where M denotes the number of rolling windows generated and then calculate the cumulative returns of the sorted return series. The sorted cumulative return series for each portfolio is then plotted in R software. Note that lower the graph, higher is the downside risk from the respective portfolio.

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Acknowledgements

The authors sincerely thank the Editor-in-chief and the referee for their valuable comments and suggestions, which have considerably improved the presentation and quality of the paper. The authors acknowledge the support of the Institute of Management Technology (IMT), Ghaziabad for the access to Prowess IQ Database for the collection of Indian data and the Department of Management Studies, IIT Roorkee for the access to Bloomberg database management for the collection of U.S. S &P 500 index data. The first author would also like to thank the Ministry of Human Resource and Development (MHRD), New Delhi, India for financial support.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Roorkee, 247667, India

    Vrinda Dhingra & Shiv K. Gupta

  2. Department of Mathematics, Netaji Subhas University of Technology, Delhi, 110078, India

    Amita Sharma

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  1. Vrinda Dhingra
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Correspondence to Shiv K. Gupta.

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Data declaration

The U.S. S &P 500 data for the current study has been fetched by the authors from the Bloomberg Database Management software, accessed through the Department of Management Sciences, IIT Roorkee, India and that of the the Indian S &P BSE 500 data has been fetched using Prowess IQ Database, accessed through IMT Ghaziabad, India. The data is privately fetched and hence not publicly available; however can be made available from the corresponding author on a reasonable request.

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Dhingra, V., Sharma, A. & Gupta, S.K. Sectoral portfolio optimization by judicious selection of financial ratios via PCA. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09849-1

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