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Portfolio optimization based on modified expected shortfall

Deepak Jadhav (Department of Statistics, Savitribai Phule Pune University, Pune, India)
T.V. Ramanathan (Department of Statistics, Savitribai Phule Pune University, Pune, India)

Studies in Economics and Finance

ISSN: 1086-7376

Article publication date: 28 June 2019

Issue publication date: 8 August 2019




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).


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.


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.


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).



Jadhav, D. and Ramanathan, T.V. (2019), "Portfolio optimization based on modified expected shortfall", Studies in Economics and Finance, Vol. 36 No. 3, pp. 440-463.



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