Coherent Measures of Risk

Artzner, Philippe; Delbaen, Freddy; Eber, Jean-Marc; Heath, David

doi:10.1017/cbo9780511615337.007

Cited by 948 publications

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“…Bawa (1978) and Fishburn (1977) introduced the lower partial moment (LPM) as an alternative risk measure to variance. Using insights from Kahneman and Tversky (1979) 2 , we show 1 We can extend this argument to some non-Gaussian distributions. In general, as long as the downside risk measure, defined over the portfolio's return distribution, is increasing in variance for all expected return levels, M-V portfolios are also optimal for downside loss averse preferences.…”

Section: Introductionmentioning

confidence: 79%

“…This is because for a fixed expected return, LPM is strictly increasing in variance, and therefore M-V and M-LPM optimal portfolios are similar. 1 This appears to be the case for the traditional equity portfolio analysis (see Grootveld and Hallerbach (1999)). However, for portfolios that consist of fixed income securities, derivatives, or stocks with event risks, the M-V optimal portfolio can differ significantly from the M-LPM optimal portfolio.…”

Section: Introductionmentioning

confidence: 92%

“…Downside risk measures such as the Value at Risk (VaR) are crucial to this debate (see also the literature related to coherent risk measures, for example, Artzner et al (1999) and Jarrow (2002)). Two, foreign currency and equity derivatives are becoming more popular in managing equity portfolios.…”

Section: Introductionmentioning

confidence: 99%

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Downside Loss Aversion and Portfolio Management

Jarrow

Zhao

2005

SSRN Journal

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Downside loss averse preferences have seen a resurgence in the portfolio management literature. This is due to the increasing usage of derivatives in managing equity portfolios, and the increased usage of quantitative techniques for bond portfolio management. We employ the lower partial moment as a risk measure for downside loss aversion, and compare mean-variance (M-V) and mean-lower partial moment (M-LPM) optimal portfolios under non-normal asset return distributions. When asset returns are nearly normally distributed, there is little difference between the optimal M-V and M-LPM portfolios. When asset returns are non-normal with large left tails, we document significant differences in M-V and M-LPM optimal portfolios. This observation is consistent with industry usage of M-V theory for equity portfolios, but not for fixed income portfolios.

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Section: Introductionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 92%

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Downside Loss Aversion and Portfolio Management

Jarrow

Zhao

2005

SSRN Journal

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“…Artzner, Delbaen, Eber e Heath (1997,1999, adicionalmente, propõem um conjunto de axiomas que constituem propriedades para que uma medida de risco seja considerada coerente. Os axiomas são: monotocidade, subaditividade, homogeneidade positiva e invariância à translação (Acerbi & Tasche, 2002).…”

Section: Value-at-risk E Conditional Value-at-riskunclassified

Análise comparativa de distintas métricas de risco na composição de um fundo de fundos de investimento imobiliário

Lovatto¹,

Henrique

Lima

2017

Rev. contab. organ.

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O propósito central deste estudo é analisar a complementaridade dos resultados de diferentes métricas de risco na composição de um Fundo de FIIs. A partir da revisão de literatura, optou-se pela adoção das métricas de risco variância e Conditional Value-at-Risk, desenvolvidas nos estudos de Markowitz (1952) e Rockafellar e Uryasev (2000, 2002), respectivamente. O estudo abrangeu uma amostra de 30 FIIs listados em bolsa de valores no âmbito da BMF&BOVESPA com retornos diários entre Julho de 2013 e Julho de 2015. Como metodologia, empregou-se modelagem e simulação computacional de carteiras teóricas para minimização do risco não-sistemático, submetendo-as a restrições de acordo com perfis de risco e instruções regulatórias. A principal constatação é de que as diferentes métricas produziram diferentes resultados nos portfólios de menor nível de risco. Observou-se, adicionalmente, que a métrica variância subestimou a probabilidade de perdas extremas.

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“…Most of the distortion functions g are concave, which makes the corresponding distortion premiums Ψ[F, g] coherent (Artzner et al, 1999 andWirch andHardy, 1999). In this paper, we are motivated by the risk losses for heavy-tailed distribution.…”

Section: Introductionmentioning

confidence: 99%

Bias-corrected estimation in distortion risk premiums for heavy-tailed losses

Brahimi¹,

Meddi²,

Necir³

2012

afst

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Abstract. Recently Necir and Meraghni (2009) proposed an asymptotically normal estimator for distortion risk premiums when losses follow heavy-tailed distributions. In this paper, we propose a bias-corrected estimator of this class of risk premiums and establish its asymptotic normality. Our considerations are based on the high quantile estimator given by Matthys and Beirlant (2003).Résumé. Récemment Necir and Meraghni (2009) ont proposé un estimateur asymptotiquement normal pour les primes de risque de distorsion lorsque les pertes suivent des distributionsà queues lourdes. Dans cet article, nous proposons un estimateurà biais réduit, pour cette classe de primes de risque et nousétablissons sa normalité asymptotique. Nos considérations sont basées sur l'estimateur des quantile extrêmes intoduit par Matthys and Beirlant (2003).

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Coherent Measures of Risk

Cited by 948 publications

References 0 publications

Downside Loss Aversion and Portfolio Management

Downside Loss Aversion and Portfolio Management

Análise comparativa de distintas métricas de risco na composição de um fundo de fundos de investimento imobiliário

Bias-corrected estimation in distortion risk premiums for heavy-tailed losses

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