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

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.

Theoretical and practical research on mathematical modeling of economy and finance based on artificial intelligence

“…Using this criterion for portfolio selection, the final wealth has the maximum expected value after some time. If the expected returns of the regime obey a log-normal distribution, the geometric expected returns will yield an efficient set consistent with Markowitz's expectation variance model [17].…”

Sectoral portfolio optimization by judicious selection of financial ratios via PCA

“…The traditional mean-risk formulations are unable to extract much information from the return distribution, and thus some researchers recommended the incorporation of either more than one risk measures or moments ( Konno et al 1993;Konno and Suzuki 1995;Sharma and Mehra 2013;Sharma and Mehra 2015;Zhao et al 2015) or SD (Roman and Mitra 2009) in portfolio optimization framework. Apart from being theoretically sound, portfolio optimization models incorporating SSD criteria from the benchmark portfolio are computational efficient (Fabian et al 2011;Bruni et al 2012;Roman et al 2013;Goel and Sharma 2019;Sehgal and Mehra 2020). Dentcheva and Ruszczyński (2003; used the lower partial moment (LPM) characterization of SSD in the constraints from the benchmark portfolio.…”

“…Guran et al (2019) applied the mean-variance PO on the energy sector stocks by first eliminating inefficient stocks with the help of SSD efficiency test. Goel and Sharma (2019) introduced deviation measure in SSD and explored its application to enhanced indexing. Sehgal and Mehra (2020) proposed a robust portfolio model with SSD constraints.…”

Whale Optimization Algorithm for Multiconstraint Second-Order Stochastic Dominance Portfolio Optimization

“…Specifically speaking, the historical return rate of FTSE 100 index assets prior to December 2018 is collected to construct the portfolio strategy. Besides, a series of indicators are introduced to evaluate the performance of portfolios by Goel and Sharma [47], such as EMR, downside deviation (DD), and Sharpe ratio. Moreover, the algorithms are coded in MATLAB 2016a, and all tests are performed on a PC with a Windows 10 operating system and 8 GB of RAM.…”