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Optimum Risk Portfolio and Eigen Portfolio: A Comparative Analysis Using Selected Stocks from the Indian Stock Market

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  • Jaydip Sen
  • Sidra Mehtab

Abstract

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.

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  • Jaydip Sen & Sidra Mehtab, 2021. "Optimum Risk Portfolio and Eigen Portfolio: A Comparative Analysis Using Selected Stocks from the Indian Stock Market," Papers 2107.11371, arXiv.org.
    • Handle: RePEc:arx:papers:2107.11371
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    References listed on IDEAS

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    1. Ananda Chatterjee & Hrisav Bhowmick & Jaydip Sen, 2021. "Stock Price Prediction Using Time Series, Econometric, Machine Learning, and Deep Learning Models," Papers 2111.01137, arXiv.org.
    2. Jacobs, Heiko & Müller, Sebastian & Weber, Martin, 2014. "How should individual investors diversify? An empirical evaluation of alternative asset allocation policies," Journal of Financial Markets, Elsevier, vol. 19(C), pages 62-85.
    3. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    4. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    5. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    6. Hwang, Inchang & Xu, Simon & In, Francis, 2018. "Naive versus optimal diversification: Tail risk and performance," European Journal of Operational Research, Elsevier, vol. 265(1), pages 372-388.
    7. Jaydip Sen & Tamal Datta Chaudhuri, 2016. "Decomposition of Time Series Data of Stock Markets and its Implications for Prediction: An Application for the Indian Auto Sector," Papers 1601.02407, arXiv.org.
    8. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    9. Jaydip Sen & Sidra Mehtab, 2021. "Design and Analysis of Robust Deep Learning Models for Stock Price Prediction," Papers 2106.09664, arXiv.org.
    10. Carolina Fugazza & Massimo Guidolin & Giovanna Nicodano, 2015. "Equally Weighted vs. Long†Run Optimal Portfolios," European Financial Management, European Financial Management Association, vol. 21(4), pages 742-789, September.
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    Cited by:

    1. Jaydip Sen & Saikat Mondal & Sidra Mehtab, 2022. "Portfolio Optimization on NIFTY Thematic Sector Stocks Using an LSTM Model," Papers 2202.02723, arXiv.org.
    2. Jaydip Sen & Saikat Mondal & Gourab Nath, 2022. "Robust Portfolio Design and Stock Price Prediction Using an Optimized LSTM Model," Papers 2204.01850, arXiv.org.

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