Can Robust Optimization Offer Improved Portfolio Performance? An Empirical Study of Indian market
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Can Robust Optimization Offer Improved Portfolio Performance? An Empirical Study of Indian market Shashank Oberoi1 · Mohammed Bilal Girach1 · Siddhartha P. Chakrabarty1
© The Indian Econometric Society 2020
Abstract The emergence of robust optimization has been driven primarily by the necessity to address the demerits of the Markowitz model. There has been a noteworthy debate regarding consideration of robust approaches as superior or at par with the Markowitz model, in terms of portfolio performance. In order to address this skepticism, we perform empirical analysis of three robust optimization models, namely the ones based on box, ellipsoidal and separable uncertainty sets. We conclude that robust approaches can be considered as a viable alternative to the Markowitz model, not only in simulated data but also in a real market setup, involving the Indian indices of S&P BSE 30 and S&P BSE 100. Finally, we offer qualitative and quantitative justification regarding the practical usefulness of robust optimization approaches from the point of view of number of stocks, sample size and types of data. Keywords Robust portfolio optimization · Worst case scenario · Uncertainty sets · S&P BSE 30 · S&P BSE 100 JEL Classification G11
Introduction The risk associated with individual assets can be reduced through investment in a diversified portfolio comprising of several assets. For optimal allocation of weights in a diversified portfolio, one of the well established methods is the * Siddhartha P. Chakrabarty [email protected] Shashank Oberoi [email protected] Mohammed Bilal Girach [email protected] 1
Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India
13
Vol.:(0123456789)
Journal of Quantitative Economics
classical mean-variance portfolio optimization introduced by Markowitz (1952, 1959). Despite being considered as the basic theoretical framework in the field of portfolio optimization, the Markowitz model is not widely accepted among investment practitioners. One of the most major limitations of the mean-variance model is the sensitivity of the optimal portfolios to the errors in the estimation of return and risk parameters. These parameters are estimated using sample mean and sample covariance matrix, which are maximum likelihood estimates (MLEs) (calculated using historical data) under the assumption that the asset returns are normally distributed. According to DeMiguel and Nogale (2009), since the efficiency of MLEs is extremely sensitive to deviations of the distribution of asset returns from the assumed normal distribution, it results in the optimal portfolios being vulnerable to the errors in estimation of input parameters. While referring to the Markowitz model as “estimation-error maximizers”, Michaud (1989) argues that it often overweights those assets having higher estimated expected return, lower estimated variance of returns and negative correlation between their returns (and vice versa). Best and Grauer (1991) study the sensitivity of
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