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

Sharma, Amita; Agrawal, Shubhada; Mehra, Aparna

doi:10.1007/s11081-016-9329-y

Cited by 15 publications

(8 citation statements)

References 48 publications

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“…A significant reduction can specifically be seen in CVaR α values for datasets (DI) and (DIII). Figure 2 displays the out-of-sample downside risk [42] from (µGM D) and (RµM GM D) models and (M GM D) and (RM GM D) models on dataset (DIII) 2 . We obtained these graphs by arranging the out-of-sample returns in ascending order and plotting the sorted cumulative return.…”

Section: Window Analysismentioning

confidence: 99%

Worst-case analysis of Gini mean difference safety measure

Sehgal¹,

Mehra²

2021

JIMO

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The paper introduces the worst-case portfolio optimization models within the robust optimization framework for maximizing return through either the mean or median metrics. The risk in the portfolio is quantified by Gini mean difference. We put forward the worst-case models under the mixed and interval+polyhedral uncertainty sets. The proposed models turn out to be linear and mixed integer linear programs under the mixed uncertainty set, and semidefinite program under interval+polyhedral uncertainty set. The performance comparison of the proposed models on the listed stocks of Euro Stoxx 50, Dow Jones Global Titans 50, S&P Asia 50, consistently exhibit advantage over their conventional non-robust counterpart models on various risk parameters including the standard deviation, worst return, value at risk, conditional value at risk and maximum drawdown of the portfolio.2010 Mathematics Subject Classification. Primary: 91G10, 91B30, 62G35; Secondary: 90C90, 90C05, 90C11.

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Section: Window Analysismentioning

confidence: 99%

Worst-case analysis of Gini mean difference safety measure

Sehgal¹,

Mehra²

2021

JIMO

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“…For this reason, some forms of relaxation of the SD have been proposed. Sharma et al (2017) used underachievement (surplus) and overachievement (slack) variables and control the relaxed SSD condition by imposing bounds on the ratio of the total underachievement to the sum of total underachievement and overachievement variables. More recently, Bruni et al (2017) applied a Zero-order -SD rule and its cumulative version.…”

Section: Related Literaturementioning

confidence: 99%

Enhanced indexation via chance constraints

Beraldi

Bruni

2020

Oper Res Int J

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The enhanced index tracking (EIT) represents a popular investment strategy designed to create a portfolio of assets that outperforms a benchmark, while bearing a limited additional risk. This paper analyzes the EIT problem by the chance constraints (CC) paradigm and proposes a formulation where the return of the tracking portfolio is imposed to overcome the benchmark with a high probability value. Besides the CC-based formulation, where the eventual shortage is controlled in probabilistic terms, the paper introduces a model based on the Integrated version of the CC. Here the negative deviation of the portfolio performance from the benchmark is measured and the corresponding expected value is limited to be lower than a given threshold. Extensive computational experiments are carried out on different set of benchmark instances. Both the proposed formulations suggest investment strategies that track very closely the benchmark over the out-of-sample horizon and often achieve better performance. When compared with other existing strategies, the empirical analysis reveals that no optimization model clearly dominates the others, even though the formulation based on the traditional form of the CC seems to be very competitive.

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“…The formulation is solved using a separation procedure for the latter family of constraints. Along similar lines, Sharma et al (2017a) propose an LP model for the EITP that aims at maximizing the mean portfolio return subject to constraints that limit the violation of the second order stochastic dominance criterion. Roman et al (2013) devise two models for the EITP that aim at selecting a portfolio having a return distribution that dominates the distribution of the benchmark with respect to the second-order stochastic dominance relation.…”

Section: Introductionmentioning

confidence: 99%

Enhanced index tracking with CVaR-based ratio measures

et al. 2020

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The enhanced index tracking problem (EITP) calls for the determination of an optimal portfolio of assets with the bi-objective of maximizing the excess return of the portfolio above a benchmark and minimizing the tracking error. The EITP is capturing a growing attention among academics, both for its practical relevance and for the scientific challenges that its study, as a multi-objective problem, poses. Several optimization models have been proposed in the literature, where the tracking error is measured in terms of standard deviation or in linear form using, for instance, the mean absolute deviation. More recently, reward-risk optimization measures, like the Omega ratio, have been adopted for the EITP. On the other side, shortfall or quantile risk measures have nowadays gained an established popularity in a variety of financial applications. In this paper, we propose a class of bi-criteria optimization models for the EITP, where risk is measured using the weighted multiple conditional value-at-risk (WCVaR). The WCVaR is defined as a weighted combination of multiple CVaR measures, and thus allows a more detailed risk aversion modeling compared to the use of a single CVaR measure. The application of the WCVaR to the EITP is analyzed, both theoretically and empirically. Through extensive computational experiments, the performance of the optimal portfolios selected by means of the proposed optimization models is compared, both in-sample and, more importantly, out-of-sample, to the one of the portfolios obtained using another recent optimization model taken from the literature. KeywordsEnhanced index tracking · Quantile risk measures · Conditional value-at-risk · Mean-risk models · Risk-reward ratios · Risk-averse optimization · Stochastic dominance · Linear programming Annals of Operations ResearchSortino ratio (see Sortino and Price 1994) are widely used to evaluate, compare and rank different investment strategies. To the best of our knowledge, Meade and Beasley (2011) are the first ones attempting to use a reward-risk ratio in the context of enhanced indexation. The authors introduce a non-linear optimization model, based on the maximization of a modified Sortino ratio, and solve it by means of a genetic algorithm. However, the non-linearity of this model may represent an undesirable limitation to its use in financial practice, especially when portfolios have to meet several side constraints (such as cardinality constraints or buy-in thresholds) or when large-scale instances have to be solved since, in most cases, the inclusion of these features requires the introduction of binary and integer variables (see the survey by Mansini et al. 2014). Based on this observation, Guastaroba et al. (2016) introduce two mathematical formulations for the EITP based on the Omega ratio. The Omega ratio is a performance measure introduced by Keating and Shadwick (2002) which, broadly speaking, can be defined as the ratio between expected value of the profits, defined as the portfolio returns over a predetermined target τ , and e...

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

Cited by 15 publications

References 48 publications

Worst-case analysis of Gini mean difference safety measure

Worst-case analysis of Gini mean difference safety measure

Enhanced indexation via chance constraints

Enhanced index tracking with CVaR-based ratio measures

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