An extension of Sharpe's single-index model: portfolio selection with expert betas

Bilbao, Amelia; Arenas, Mar; Jiménez, Mariano; Pérez-Gladish, Blanca; Rodriguez, Michael

doi:10.1057/palgrave.jors.2602133

Cited by 19 publications

(11 citation statements)

References 17 publications

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“…The security's Beta is usually calculated based on historical prices of the security and the obtained value may vary according to the selected frame of time. Bilbao et al () studied the impact of the time frame on the value of Beta. They added to the historical data series, the expert opinions (fuzzy number), and therefore they considered the security's Beta as fuzzy numbers.…”

Section: Random Betamentioning

confidence: 99%

A multiple objective stochastic portfolio selection problem with random Beta

Abdelaziz¹,

Masmoudi

2013

Int Trans Operational Res

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When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security's Beta has a deterministic value. Recently, many researchers argued that in selecting the optimal portfolio, securities’ Beta should be considered as an uncertain parameter. In this paper, we set up fundamentals to model the portfolio's Beta as a random variable and propose a multiple objective stochastic portfolio selection model with random Beta. To solve the proposed model, we apply a stochastic goal programming approach. A numerical example from the US stock exchange market is reported.

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Section: Random Betamentioning

confidence: 99%

A multiple objective stochastic portfolio selection problem with random Beta

Abdelaziz¹,

Masmoudi

2013

Int Trans Operational Res

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“…Multiple criteria approaches to portfolio selection and related approaches (from year 2000) are as follows: (i) portfolio choice with fuzzy information (Arenas et al , ; Pérez‐Gladish et al , ); (ii) approximating the optimum portfolio on the mean–variance efficient frontier by linkages between utility theory and compromise programming (Ballestero and Pla‐Santamaria, , , ); (iii) extending the classical (risk–return) approach to other different criteria (Steuer et al , ); (iv) novel approaches from multi‐objective programming (Steuer et al , ); (v) constructing equity mutual funds portfolios by goal programming (Pendaraki et al , ); (vi) mean–semivariance efficient frontier (Ballestero, ); (vii) hybrid models, neural networks and algorithms (Huang et al , ; Ong et al , ; Lin et al , ); (viii) satisfaction functions are proposed to integrate the decision maker's preferences into GP models under uncertainty (Aouni et al , ); (ix) fuzzy techniques are useful when probability distributions are unknown (Ben Abdelaziz and Masri, ); and (x) portfolio selection based on Sharpe's beta is developed with and without fuzzy techniques in the studies by Bilbao et al () and Ballestero et al ().…”

Section: Literaturementioning

confidence: 99%

“…About this issue, see Section 3. References to mean valuestochastic goal programming are, among others, those of Weihua et al (2001), Tozer and Stokes (2002), Bordley and Kirkwood (2004), Sahoo and Biswal (2005) multi-objective programming (Steuer et al, 2005); (v) constructing equity mutual funds portfolios by goal programming (Pendaraki et al, 2004); (vi) meansemivariance efficient frontier (Ballestero, 2005b); (vii) hybrid models, neural networks and algorithms Ong et al, 2005;Lin et al, 2006); (viii) satisfaction functions are proposed to integrate the decision maker's preferences into GP models under uncertainty (Aouni et al, 2005); (ix) fuzzy techniques are useful when probability distributions are unknown (Ben Abdelaziz and Masri, 2005); and (x) portfolio selection based on Sharpe's beta is developed with and without fuzzy techniques in the studies by Bilbao et al (2006) and Ballestero et al (2009).…”

Section: References To Pave the Way For Our Proposalmentioning

confidence: 99%

Portfolio Selection from Multiple Benchmarks: A Goal Programming Approach to an Actual Case

Bravo

Pla‐Santamaria

2010

Multi Criteria Decision Anal

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This paper deals with benchmark-based portfolio choice for buy-and-hold strategies of investing. Multiple benchmarks for returns are considered, which is more realistic than taking a unique benchmark -a unique aspiration difficult to select in practice among the various aspirations for returns that the investor has in mind. Portfolio selection with multiple benchmarks leads to a multi-objective problem, which is addressed by mean value -stochastic goal programming. In particular, two benchmarks are considered, which involves two goals. Weights for goals depend on investor's preferences and Arrow's absolute risk aversion coefficients. An efficient frontier of portfolios is obtained. Advantages of this stochastic method in our context are as follows: (i) Mean value-stochastic goal programming relies on classical utility theory under uncertainty and Arrow's absolute risk aversion, which ensures soundness and strictness, and (ii) the numerical model is easily solved by using available software such as mean-variance software. Numerical results are tabulated and discussed.

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“…(a) Efficient frontiers from linkages between utility theory and compromise programming to bound the optimum portfolio (Ballestero andPla-Santamaria 2004, 2005). (b) Efficient frontiers from beta parameters (Bilbao et al 2006;Ballestero et al 2009). (c) New approaches based on multi-objective programming (Steuer et al 2005;Steuer et al 2007;Ben Abdelaziz et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips

Pla‐Santamaria

Bravo

2012

Ann Oper Res

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To create efficient funds appealing to a sector of bank clients, the objective of minimizing downside risk is relevant to managers of funds offered by the banks. In this paper, a case focusing on this objective is developed. More precisely, the scope and purpose of the paper is to apply the mean-semivariance efficient frontier model, which is a recent approach to portfolio selection of stocks when the investor is especially interested in the constrained minimization of downside risk measured by the portfolio semivariance. Concerning the opportunity set and observation period, the mean-semivariance efficient frontier model is applied to an actual case of portfolio choice from Dow Jones stocks with daily prices observed over the period 2005-2009. From these daily prices, time series of returns (capital gains weekly computed) are obtained as a piece of basic information. Diversification constraints are established so that each portfolio weight cannot exceed 5 per cent. The results show significant differences between the portfolios obtained by mean-semivariance efficient frontier model and those portfolios of equal expected returns obtained by classical Markowitz mean-variance efficient frontier model. Precise comparisons between them are made, leading to the conclusion that the results are consistent with the objective of reflecting downside risk.

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An extension of Sharpe's single-index model: portfolio selection with expert betas

Cited by 19 publications

References 17 publications

A multiple objective stochastic portfolio selection problem with random Beta

A multiple objective stochastic portfolio selection problem with random Beta

Portfolio Selection from Multiple Benchmarks: A Goal Programming Approach to an Actual Case

Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips

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