Enhanced indexing using weighted conditional value at risk

Performance analysis is a key process in finance to evaluate or compare investment opportunities, allocations, or management. The classical method is to compute the market or sub-market returns and volatilities, and then calculate the standard performance measure, namely, the Sharpe ratio. This measure is based on the first two moments of a return distribution. Therefore, a significant weakness of this method is that it implicitly assumes that the distribution is Gaussian (if it is not Gaussian, the approach may lead to a bad fit). In fact, risk comes from not only volatility, but also from higher moments of distribution such as skewness and kurtosis. The standard method to resolve this issue is to use the modified Sharpe ratio; this method replaces the classical Sharpe ratio volatility with the value at risk. The latter is computed using the Cornish Fisher expansion, a tool based on the first four moments of return distribution. This methodology, however, may present a major pitfall: in some cases, quantile functions do not stay monotone. In this paper, we show how this tool can be used effectively through a specific procedure, rearrangement. We compare various metrics using rank correlation, and demonstrate how and in which cases the proposed procedure delivers ranking different from the standard Sharpe ratio ranking. Furthermore, we show how our technique offers

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“…Several ways have been proposed to solve these issues. See for instance Schyns et al (2010), Ameur et al (2018) or Sehgal & Mehra (2019).…”

Section: Literature Reviewmentioning

confidence: 99%

Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion

Amédée‐Manesme

Barthélémy

2020

Ann Oper Res

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“…Furthermore, as pointed out by Yoshimoto (1996) and Najafi and Mushakhian (2015), transaction costs (including fixed and variable components) are one of the main concerns of today's portfolio managers, and ignoring them may result in unsatisfactory outcomes. Another main extension of the Markowitz model is the risk controlling by other measures except for the variance such as worst‐case (Chen and Korn, 2019; Korn and Leoff, 2019), Omega‐ratio (Sehgal and Mehra, 2021; Yu et al., 2023), Sharp‐ratio (Jing et al., 2022), value‐at‐risk (VaR) (Wozabal, 2012), conditional VaR (CVaR) (Sehgal and Mehra, 2019; Filippi et al., 2020), multivariate CVaR (Noyan and Rudolf, 2013), mean‐reversion (Mousavi and Shen, 2022), as well as the idea of index‐tracking (Wu et al., 2017; Hooshmand and MirHassani, 2022; Soares Silva et al., 2022).…”

Section: Introductionmentioning

confidence: 99%

Model and efficient algorithm for the portfolio selection problem with real‐world constraints under value‐at‐risk measure

Hooshmand

Anoushirvani

MirHassani

2023

Int Trans Operational Res

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Value‐at‐risk (VaR) is a widely acceptable risk measure in finance and particularly, in the portfolio selection problem (PSP). However, due to the non‐convexity, its incorporation into an optimization model makes it challenging and difficult to solve. Hence, the development of iterative‐based heuristic algorithms (IBHAs) utilizing the problem structure would be valuable. The existing IBHAs are either inefficient in terms of solution quality and running time or are just applicable to solve simple PSPs without any real‐world constraint (i.e., cardinality, position size, and transaction cost constraints). To overcome these shortcomings, in this paper, we present a novel IBHA to efficiently solve the PSP with real‐world constraints under VaR measure. Our method is based on iterative resolution of two restricted versions of the original model in which some of the binary variables utilized in the formulation of VaR measure are fixed at specific values. Computational experiments over real‐world instances indicate that not only the running time of our algorithm is short, but also its solution quality is much better than the existing IBHAs in 97% of instances with an average improvement of about 10%.

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“…Many scholars use quantitative analysis methods to study modern investment portfolio theory on this basis. Sehgal et al [1] proposed an enhanced indexed portfolio optimization model, in order to seek to maximize the excess returns beyond the benchmark index. Huang Dongbin et al [2] used the entropy-TOPSIS method to calculate the comprehensive preference strength of effective factors based on the Shanghai and Shenzhen 300 constituent stocks, and proposed a comprehensive preference strength-mean-CVaR portfolio optimization model for effective factors.…”

Section: Introductionmentioning

confidence: 99%

Research on intelligent algorithms for solving portfolio problems

2021

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Investment is a behavior of coexistence of the benefits and risks. In the context of rich asset types, an effective investment portfolio can help investors obtain stable returns and diversify risks. In reality, portfolio problems often contain multiple constraints and objectives that cannot be effectively solved by traditional mathematical optimization methods. This paper proposes a hybrid beetle antennae search sine cosine algorithm based on non-linear inertia weight. Experiments are performed on five portfolio problem datasets in the real stock market. The results show that the proposed algorithm is effective and has some performance advantages in solving portfolio problems.

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Enhanced indexing using weighted conditional value at risk

Cited by 12 publications

References 28 publications

Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion

Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion

Model and efficient algorithm for the portfolio selection problem with real‐world constraints under value‐at‐risk measure

Research on intelligent algorithms for solving portfolio problems

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