Mean–variance portfolio selection with ‘at-risk’ constraints and discrete distributions

Alexander, Gordon J.; Baptista, Alexandre M.; Yan, Shu

doi:10.1016/j.jbankfin.2007.01.019

Cited by 34 publications

(23 citation statements)

References 25 publications

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“…Similar results are obtained by Vorst (2001), who uses options to manipulate the VaR. Alexander, Baptista, and Yan (2007) show that the Conditional VaR (CVaR) constraint is more effective than the VaR constraint in curtailing large losses in the M-V framework (see also , Emmer, Klüppelberg, and Korn 2001;Yiu 2004;Pirvu 2007;Lejeune 2011).…”

Section: Literature Reviewsupporting

confidence: 69%

Value-at-risk capital requirement regulation, risk taking and asset allocation: a mean–variance analysis

Kaplanski

Levy

2013

The European Journal of Finance

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In this study, the mean-variance framework is employed to analyze the impact of the Basel value-at-risk (VaR) market risk regulation on the institution's optimal investment policy, the stockholders' welfare, as well as the tendency of the institution to change the risk profile of the held portfolio. It is shown that with the VaR regulation, the institution faces a new regulated capital market line, which induces resource allocation distortion in the economy. Surprisingly, only when a riskless asset is available does VaR regulation induce the institution to reduce risk. Otherwise, the regulation may induce higher risk, accompanied by asset allocation distortion. On the positive side, the regulation implies an upper bound on the risk the institution takes and it never induces the firm to select an inefficient portfolio. Moreover, when the riskless asset is available, tightening the regulation always increases the amount of maintained eligible capital and decreases risk.

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Section: Literature Reviewsupporting

confidence: 69%

Value-at-risk capital requirement regulation, risk taking and asset allocation: a mean–variance analysis

Kaplanski

Levy

2013

The European Journal of Finance

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“…Konno and Suzuki (1995) show an effi cient algorithm to optimize a mean-variance-skewness model. Alexander et al (2007) obtain effi cient portfolios under mean-variance model when VaR or CVaR are used as constraints. A pure multiobjective proposal can be found in Roman et al (2007) where a mean-variance-CVaR model is proposed and an optimization approach is given.…”

Section: Portfolio Selection Under Several Risk Measuresmentioning

confidence: 99%

“…Although variance is still the most widely used measure of risk in the practice of portfolio selection, VaR and CVaR are used as risk limit and to control risk by the fund management industry. This has motivated the inclusion of VaR and CVaR as constraints in the classical mean-variance problem (Alexander et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

Several risk measures in portfolio selection: Is it worthwhile?

Baixauli‐Soler

Alfaro-Cid

Fernández-Blanco

2010

Spanish Journal of Finance and Accounting / Revista Española de

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This paper is concerned with asset allocation using a set of three widely used risk measures, which are the variance or deviation, Value at Risk and the Conditional Value at Risk. Our purpose is to evaluate whether solving the asset allocation problem under several risk measures is worthwhile or not, given the added computational complexity. The main contribution of the paper is the solution of two models that consider several risk measures: the mean-variance-VaR model and the meanVaR-CVaR model. The inclusion of VaR as one of the objectives to minimize leads to nonconvex problems, therefore the approach we propose is based on a heuristic: multi-objective genetic algorithms. Our results show the adequacy of the multi-objective approach for the portfolio optimization problem and emphasize the importance of dealing with mean-σ-VaR or mean-VaR-CVaR models as opposed to mean-σ-CVaR, where both risk measures are redundant.RESUMEN Este articulo aborda el problema de selección de carteras empleando tres medidas de riesgo ampliamente utilizadas: varianza o desviación típica, Valor en Riesgo (VaR) y Valor en Riesgo Condicional (CVaR). Nuestro principal objetivo es evaluar la relevancia de incluir simultáneamente varias medidas del riesgo, dada la complejidad computacional que supone. La principal contribución de este artículo es la propuesta de solución de dos modelos que consideran simultáneamente dos medidas del riesgo muy utilizadas: el modelo de media-varianza-VaR y el modelo media-VaR-CVaR. La inclusión del VaR como uno de los objetivos a minimizar convierte el problema de optimización en no convexo, por lo que el método de resolución propuesto está basado en una heurística muy actual: algoritmo genético multiobjetivo. Nuestros resultados muestran la adecuación del enfoque multiobjetivo para resolver el problema de optimización de carteras y justifi ca y enfatiza la importancia de emplear los modelos media-varianza-VaR o media-VaR-CVaR en lugar del modelo media-varianza-CVaR, en el que las dos medidas de riesgo simultáneas resultan redundantes. PALABRAS CLAVE Selección de carteras; Valor en riesgo; Valor en riesgo condicional; Toma de decisiones multiobjetivo.

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“…Both conditions can be interpreted as a constraint on the minimum return that the bank must obtain, which technically corresponds to a bound on the admissible value at risk (VaR). Sentana (2003), Alexander and Baptista (2006) and Alexander et al (2007) have previously considered mean-variance analysis with a VaR constraint when returns are elliptical. However, the negative skewness of loan portfolios can cause large biases in the elliptical estimates of the VaR.…”

Section: Introductionmentioning

confidence: 99%

Assessing the risk-return trade-off in loan portfolios

Mencía

2012

Journal of Banking & Finance

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Mean–variance portfolio selection with ‘at-risk’ constraints and discrete distributions

Cited by 34 publications

References 25 publications

Value-at-risk capital requirement regulation, risk taking and asset allocation: a mean–variance analysis

Value-at-risk capital requirement regulation, risk taking and asset allocation: a mean–variance analysis

Several risk measures in portfolio selection: Is it worthwhile?

Assessing the risk-return trade-off in loan portfolios

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