Portfolio optimization based on modified expected shortfall

Abstract

Purpose An investor is expected to analyze the market risk while investing in equity stocks. This is because the investor has to choose a portfolio which maximizes the return with a minimum risk. The mean-variance approach by Markowitz (1952) is a dominant method of portfolio optimization, which uses variance as a risk measure. The purpose of this paper is to replace this risk measure with modified expected shortfall, defined by Jadhav et al. (2013). Design/methodology/approach Modified expected shortfall introduced by Jadhav et al. (2013) is found to be a coherent risk measure under univariate and multivariate elliptical distributions. This paper presents an approach of portfolio optimization based on mean-modified expected shortfall for the elliptical family of distributions. Findings It is proved that the modified expected shortfall of a portfolio can be represented in the form of expected return and standard deviation of the portfolio return and modified expected shortfall of standard elliptical distribution. The authors also establish that the optimum portfolio through mean-modified expected shortfall approach exists and is located within the efficient frontier of the mean-variance portfolio. The results have been empirically illustrated using returns from stocks listed in National Stock Exchange of India, Shanghai Stock Exchange of China, London Stock Exchange of the UK and New York Stock Exchange of the USA for the period February 2005-June 2018. The results are found to be consistent across all the four stock markets. Originality/value The mean-modified expected shortfall portfolio approach presented in this paper is new and is a natural extension of the Markowitz’s mean-variance and mean-expected shortfall portfolio optimization discussed by Deng et al. (2009).

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“…Ongoing research has underlined the requirement of systems management, trust, and the creation of social capital among business visionaries as methods to encourage the improvement and growth of small businesses (Haque, 2019). Entrepreneurs must build trust among themselves, as this will offer an approach to the great correspondence and potential results of a large systems administration (Jadhav & Ramanathan, 2019). Making solid social capital can help entrepreneurs develop their businesses through contacts.…”

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“…The stock market, which is one of the most important markets used by investors, is a market that should be treated cautiously due to its variable structure. Market risk is one of the systematic risks that should be analyzed before making an investment decision (Jadhav and Ramanathan, 2018). Traditional Portfolio Theory claims that investors could maximize their expected return by investing in multiple securities rather than investing in a single asset in order to increase their wealth.…”