Optimization and Engineering

, Volume 18, Issue 2, pp 407–442 | Cite as

Enhanced indexing for risk averse investors using relaxed second order stochastic dominance



The less efficient markets offer scope for enhanced indexing (EI), an investment strategy of portfolio selection which seeks to earn more return than the benchmark index. In this context, we examine the use of relaxed second order stochastic dominance (RSSD) by introducing underachievement and overachievement variables in the second order stochastic dominance (SSD), for EI. We propose a linear optimization model that maximizes the mean return subject to the constraints formed using RSSD. We impose bounds on the ratio of the total underachievement to the sum of total underachievement and total overachievement variables depicting the risk-return tradeoff in the model. The proposed model for EI is inspired from many applications of SSD and almost SSD (ASSD). We examine the performance of the proposed model with the SSD model, EI model of maximizing mean return and minimizing the underperformance (MM) from the benchmark index, \(\epsilon \)-almost second order stochastic dominance (\(\epsilon \)-ASSD) model, and the naïve 1/N portfolio, on two Indian stock indices, CNX 100 and CNX 200, through a rolling window strategy. To widen the empirical analysis, we also compare all models on the eight publicly available real financial data sets from Beasley OR library through a single window strategy. The portfolios from the proposed model are shown to produce statistically significant mean excess return and excess Sharpe ratio (both from the benchmark indices) more often than the MM and \(\epsilon \)-ASSD models. Also, the portfolios from the proposed model always have smaller violation area in SSD constraints from benchmark indices than the MM and \(\epsilon \)-ASSD models.


Enhanced indexing Stochastic dominance \( \epsilon \)-Almost stochastic dominance Second order stochastic dominance Relaxed stochastic dominance 



The first author is thankful to the Council of Scientific and Industrial Research (CSIR), India, for financial support. The authors are indebted to the referees and editors for their valuable suggestions.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology Delhi New DelhiIndia

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