Elicitability of range value at risk

The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring functions should be (strictly) consistent for the functional of interest, that is, the expected score should be minimised by the correctly specified functional value. A functional is elicitable if it possesses a strictly consistent scoring function. In quantitative risk management, the elicitability of a risk measure is closely related to comparative backtesting procedures. As such, it has gained considerable interest in the debate about which risk measure to choose in practice. While this discussion has mainly focused on the dichotomy between Value at Risk (VaR) - a quantile - and Expected Shortfall (ES) - a tail expectation, this paper is concerned with Range Value at Risk (RVaR). RVaR can be regarded as an interpolation of VaR and ES, which constitutes a tradeoff between the sensitivity of the latter and the robustness of the former. Recalling that RVaR is not elicitable, we show that a triplet of RVaR with two VaR components at different levels is elicitable. We characterise the class of strictly consistent scoring functions. Moreover, additional properties of these scoring functions are examined, including the diagnostic tool of Murphy diagrams. The results are illustrated with a simulation study, and we put our approach in perspective with respect to the classical approach of trimmed least squares in robust regression

Order-Sensitivity and Equivariance of Scoring Functions

The relative performance of competing point forecasts is usually measured in terms of loss or scoring functions. It is widely accepted that these scoring function should be strictly consistent in the sense that the expected score is minimized by the correctly specified forecast for a certain statistical functional such as the mean, median, or a certain risk measure. Thus, strict consistency opens the way to meaningful forecast comparison, but is also important in regression and M-estimation. Usually strictly consistent scoring functions for an elicitable functional are not unique. To give guidance on the choice of a scoring function, this paper introduces two additional quality criteria. Order-sensitivity opens the possibility to compare two deliberately misspecified forecasts given that the forecasts are ordered in a certain sense. On the other hand, equivariant scoring functions obey similar equivariance properties as the functional at hand - such as translation invariance or positive homogeneity. In our study, we consider scoring functions for popular functionals, putting special emphasis on vector-valued functionals, e.g. the pair (mean, variance) or (Value at Risk, Expected Shortfall)

Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting

In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. In particular, we propose the use of Diebold-Mariano tests, and show how they can be implemented for Expected Shortfall (ES), based on the recent result of Fissler and Ziegel (2015) that ES is jointly elicitable with Value at Risk

Risk Management

In a recent paper, Acerbi and Szekely (Risk Magazine, 76-81, 2014) presented three methods to test expected shortfall, and this is the first empirical application of that paper on emerging markets. We employ daily stock index returns from the Morgan Stanley Capital International Inc. Emerging Markets Index covering the 2000-2015 period, extending Acerbi and Szekely (Risk Magazine, 76-81, 2014) results to derive the significance thresholds for the Student's skewed-t distribution using two testing methods. We find that the thresholds for the Z(1) Test and Z(2) Test for skewed-t distribution are similar to the values obtained by Acerbi and Szekely for Student's t distribution. Therefore, the Z(1) and Z(2) thresholds are invariant to the skewed-t-shaped parameter values found in the emerging market stock indices. Empirical results show outperformance of Student's skewed-t and Student's t distributions over Gaussian distribution

The Legislative Response to the Shareholders V Stakeholders Debate: A Comparative Overview

The debate as to whose interests should be considered by directors in terms of their duty to act in the best interests of the corporation—shareholders or stakeholders—has been popular among corporate law scholars for a number of years. In some jurisdictions the judiciary indicated a willingness to depart from a strict shareholder-centric approach by recognising that the interests of creditors become paramount under certain circumstances. Until relatively recently the legislature remained silent on this topic. However, corporate law reform afforded the legislature an opportunity to revisit this debate in at least four common law jurisdictions—Australia, the UK, South Africa and Singapore. This article provides a comparative overview and analysis of relevant legislation in these jurisdictions to illustrate the extent to which, if at all, the legislatures in these jurisdictions have been persuaded to depart from the notion of shareholder supremacy and ultimately assesses the implications of a particular approach adopted by the respective legislatures.http://www.hartjournals.co.uk/jcls/hb201

Revisitando o desmame precoce através de recortes da história Revisando el destete precoz a través de recortes de la historia Revisiting early weaning through historical analysis

A ação básica de saúde requer estratégia direcionada quanto à tomada de consciência da importância do aleitamento materno, principalmente para redução da morbi-mortalidade infantil. A história da amamentação mostra um hiato sobre como os povos lidaram com o desmame precoce. Objetiva-se, neste estudo, revisitar o desmame precoce através de recortes históricos. A revisão bibliográfica foi a estratégia utilizada para este estudo. A amostra constou de livros, monografias, teses, dissertações, textos publicados em revistas científicas e artigos captados via Internet, no período de 1978 a 1998, os quais retratam histórias desde a época mitológica até os séculos atuais. A revisão apontou que o desmame é sócio-culturalmente construído e determinado e que a mulher, para manter o aleitamento materno, necessita não só de suporte/apoio familiar e social, mas também governamental.<br>La acción básica de salud requiere estrategias dirigidas hacia la toma de conciencia de la importancia del amamantamiento materno principalmente para la disminución de la morbi-mortalidad infantil. La historia del amamantamiento muestra un vacío acerca de cómo los pueblos lidiaron con el destete precoz. El presente estudio pretende revisar el destete precoz a través de recortes históricos. La revisión bibliográfica fue la estrategia utilizada para el estudio. La muestra estuvo compuesta por libros, monografías, tesis, disertaciones, textos publicados en las revistas científicas capturados a través de Internet en el periodo de 1978 a 1998, los cuales retratan la historia desde la época mitológica hasta los siglos más actuales. La revisión mostró que el destete es socialmente construido y determinado y que la mujer para mantener la lactancia materna necesita no solo de soporte familiar y social si no también del apoyo gubernamental.<br>Basic health actions require strategies towards awareness development concerning the importance of breastfeeding, particuarly aiming at the reduction of child morbi-mortality The history of breastfeeding presents a gap of information about how people have dealt with early weanin. This study aimed at revisiting early weaning the historical analysis of breastfeeding. The literture review methodology was used. The samples consisted of books, monographs, theses, dissertations, texts published in scientific journals and scientific articles obtained through the internet in the period of 1978 to 1998. These sources portray stories from mythological times up to this day. The review pointed out that weaning is socially and culturally constructed and determined and that, in order to maintain breastfeeding, women require not only social and family support, but also governmental support

Uso de métodos contraceptivos entre mulheres com vida sexual ativa em São Leopoldo, Rio Grande do Sul, Brasil Use of contraceptive methods by sexually active women in São Leopoldo, Rio Grande do Sul, Brazil

Foi realizado um estudo transversal de base populacional em São Leopoldo, Rio Grande do Sul, Brasil, com objetivo de analisar o uso de métodos contraceptivos. A amostra envolveu 867 mulheres de 20 a 60 anos com vida sexual ativa. Entre as mulheres que referiram atividade sexual, 627 (61,1%) referiram utilizar algum método contraceptivo. Entre as mulheres de 20 a 49 anos, 48,8% referiram utilizar anticoncepcionais orais; 18,7%, ligadura tubária; 17,3%, preservativos masculinos; e 7,3%, dispositivo intra-uterino. Entre as 186 mulheres de 50 a 60 anos que referiram vida sexual ativa, o método mais prevalente foi a ligadura tubária com 79,6%. Foi observada uma modificação de efeito em relação à prevalência de anticoncepcionais orais, idade e escolaridade, evidenciando uma menor prevalência nas mulheres de 20 a 29 anos e com baixa escolaridade. Assim, os achados da análise em São Leopoldo apontam para uma diversidade na prevalência do uso de métodos contraceptivos, inclusive não fazendo distinção na ocorrência de laqueadura tubária de acordo com variáveis sócio-econômicas, mas ainda revelam a necessidade de propiciar-se escolhas tecnicamente mais adequadas às mulheres mais jovens e com baixa escolaridade.<br>In 2003, a population-based cross-sectional study was conducted in the urban area of São Leopoldo, Rio Grande do Sul, Brazil. The sample included 867 sexually active women from 20 to 60 years of age. The objective was to describe the use of contraceptive methods. Data were collected using a standardized questionnaire. The study analyzed the prevalence of contraceptive use and socioeconomic variables in women reporting an active sex life (84.5%), stratified by age groups. Some 627 (61.1%) women reported use of contraceptive methods. In the 20-49-year old group, 48.8% reported using oral contraceptives, 18.7% tubal ligation, 17.3% condoms, and 7.3% IUDs. In the 50-60-year old group, the most widely used method was tubal ligation (79.6%). Regarding tubal ligation, the schooling variable showed a linear trend, that is, women with less schooling showed a higher prevalence. Prevalence of oral contraception was higher in low-income women