Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis

Alexander, Gordon J.; Baptista, Alexandre M.

doi:10.1016/s0165-1889(01)00041-0

Cited by 279 publications

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“…It may happen that high returns increase the variance. (Alexander and Baptista, 2002). It is shown that the minimum VaR portfolio is efficient by Markowitz.…”

Section: Brief Literature Reviewmentioning

confidence: 99%

“…It may happen that high returns increase the variance. The VaR framework for portfolio construction was considered in (Alexander and Baptista, 2002; Bodnar et al, 2002; Rockafellar et al, 2006a Rockafellar et al, , 2006bKilianova and Pflug, 2009). For example, a theoretical background for the portfolio VaR minimisation is presented in (Alexander and Baptista, 2002).…”

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confidence: 99%

“…The variance of the portfolio is equal to V w =Var(X w (t))=w'∑w. The VaR at the confidence level (VaR ) of the portfolio with the weight vector w is equal to the rate of return such that P{X w <-VaR }=1-.The optimisation problem of the portfolio VaR minimisation (Alexander and Baptista, 2002) is given by It should be noted that the short sales are allowed, i.e. we do not use the condition 0≤w i ≤1 in (1).…”

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Estimation of confidence level for Value-at-Risk: statistical analysis

Zabolotskyy¹

2016

EA-XXI

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Abstract. The paper investigates the problem of estimation of the confidence level for Value-at-Risk to get the minimum VaR portfolio with a predefined level of expected return. The equation which describes the relation between the confidence level and the rate of the expected return depends on the unknown parameters of distribution of asset returns which should be estimated. The classical sample estimators for unknown parameters are used. The author has examined the properties of the estimator for the confidence level in considerable detail. Under the assumption that the asset returns are multivariate, we find the asymptotic distribution of the estimator for the confidence level. Moreover, we extend this result to the case of elliptically contoured distributed asset returns. Based on the distributional properties, the confidence interval for the confidence level for VaR is constructed and the test procedure whether the resulting portfolio is statistically different from the global minimum variance portfolio is provided. Using a simulation study, we demonstrate that our results give a good approximation even in the case of moderate sample sizes n=250, n=500 not only in the case of normally distributed asset returns, but also when asset returns follow the elliptically countered distribution. We have concluded that investors can use the results of the paper with regard to all sectors of the economy. We used monthly asset returns of five stocks included into Dow Jones Index, namely: McDonald's, Johnson&Johnson, Procter&Gamble, AT&T, and Verizon Communications from 01 October 2010 to 01 September 2015 to give numerical illustration of our fundamental results. Keywords: Portfolio Selection Problem; Value-at-Risk; Variance; Expected Return; Sample Estimator; Risk Measure JEL Classification: G11; G17; C13 Acknowledgements. The author of the article is thankful to Professor Wolfgang Schmid for suggestions which have improved an earlier version of this paper. The author is thankful for the financial support to the European Commission via ERASMUS MUNDUS Action 2 HERMES project 2013-2596/001-001-EMA2 «Statistical analysis of optimal portfolios». DOI: http://dx.doi.org/10.21003/ea.V158-19Заболоцький Т. М. кандидат економічних наук, доцент кафедри інформаційних технологій, Львівський інститут Університету банківської справи, Львів, Україна Оцінка рівня довіри для Value-At-Risk: статистичний аналіз Анотація. У статті досліджено проблему оцінки рівня довіри для Value-at-Risk, щоб отримати портфель з мінімальним рівнем VaR із наперед заданим рівнем очікуваної дохідності. Рівність, що описує співвідношення між рівнем довіри та рівнем очікуваної дохідності, залежить від невідомих параметрів розподілу дохідності активів, які повинні бути оцінені на практиці. У роботі використано класичні вибіркові оцінки для невідомих параметрів. Детально досліджено властивості розподілу отриманої оцінки для рівня довіри. Використовуючи властивості розподілу, побудовано інтервал довіри для рівня довіри для VaR і статистичні тести для перевірки гіп...

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“…It may happen that high returns increase the variance. (Alexander and Baptista, 2002). It is shown that the minimum VaR portfolio is efficient by Markowitz.…”

Section: Brief Literature Reviewmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Estimation of confidence level for Value-at-Risk: statistical analysis

Zabolotskyy¹

2016

EA-XXI

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“…Traditionally, these probabilities and risk measures have been computed based on the assumption that asset returns have a multivariate normal distribution. Indeed, if asset returns are assumed to be multivariate normal then closed form solutions can be used for multi-asset portfolio VaR and the calculation of constrained portfolio weights; see for instance Alexander and Baptista (2002) and Alexander and Baptista (2008). However, risk management with VaR constraints (VaR-RM) leads one to select positions with higher variance.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric estimation of multi-asset portfolio tail risk

Dias

2014

Journal of Banking & Finance

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When correlations between assets turn positive, multi-asset portfolios can become riskier than single assets. This article presents the estimation of tail risk at very high quantiles using a semiparametric estimator which is particularly suitable for portfolios with a large number of assets. The estimator captures simultaneously the information contained in each individual asset return that composes the portfolio, and the interrelation between assets. Noticeably, the accuracy of the estimates does not deteriorate when the number of assets in the portfolio increases. The implementation is as easy for a large number of assets as it is for a small number. We estimate the probability distribution of large losses for the American stock market considering portfolios with ten, fifty and one hundred assets of stocks with different market capitalization. In either case, the approximation for the portfolio tail risk is very accurate. We compare our results with well known benchmark models.JEL classification: C51, G01, G11, G17.

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“…Several recent papers analyze the risk-return trade off from a VaR perspective, for ex-ample Duffie and Pan (1997), Lucas and Klaassen (1998), Gourieroux, Laurent, and Scaillet (2000), Campbell, Huisman, and Koedijk (2001) and Alexander and Baptista (2002).…”

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confidence: 99%

Evaluating portfolio Value-at-Risk using semi-parametric GARCH models

Rombouts

Verbeek²

2009

Quantitative Finance

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In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, we specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations. Finally, we examine the economic value of the multivariate GARCH models by determining optimal portfolios based on maximizing expected returns subject to a VaR constraint, over a period of 500 consecutive days. Again, the superiority and robustness of the semi-parametric model is confirmed.

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Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis

Cited by 279 publications

References 23 publications

Estimation of confidence level for Value-at-Risk: statistical analysis

Estimation of confidence level for Value-at-Risk: statistical analysis

Semiparametric estimation of multi-asset portfolio tail risk

Evaluating portfolio Value-at-Risk using semi-parametric GARCH models

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