International Transactions in Operational Research

Deviation measure in second‐order stochastic dominance with an application to enhanced indexing

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Abstract Deviation measures form a separate class of functionals applied to the difference of a random variable to its mean value. In this paper, we aim to introduce a deviation measure in the second‐order stochastic dominance (SSD) criterion to select an optimal portfolio having a higher utility of deviation from its mean value than that of the benchmark portfolio. A new strategy, called deviation SSD (DSSD), is proposed in portfolio optimization. Performance of the proposed model in an application to enhanced indexing is evaluated and compared to other two standard portfolio optimization models that employ SSD criterion on lower partial moments of order one (LSSD) and tail risk measure (TSSD). We use historical data of 16 global indices to assess the performance of the proposed model. In addition to this, we solved the models on simulated data, capturing the joint dependence between indices using historical data of two data sets, each data set comprising six indices. The simulated data are generated by first fitting the autoregressive moving average–Glosten–Jagannathan–Runkle–generalized autoregressive conditional heteroscedastic model on historical data to determine marginal distributions, and thereafter capture the dependence structure using the best fitted regular vine copula. The portfolios from DSSD model achieve higher excess mean return than TSSD model and lower variance, downside deviation, and conditional value‐at‐risk than LSSD model. Also, portfolios from DSSD model demonstrate higher values of information ratio, stable tail‐adjusted return ratio and Sortino ratio than the other two models. Lastly, DSSD model is observed to produce well‐diversified portfolios compared to LSSD model.

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