An evaluation of the effectiveness of Value-at-Risk (VaR) models for Australian banks under Basel III

This study compares Value-at-Risk (VaR) measures for Australian banks over a period that includes the Global Financial Crisis (GFC) to determine whether the methodology and parameter selection are important for capital adequacy holdings that will ultimately support a bank in a crisis period. VaR methodology promoted under Basel II was largely criticised during the GFC for its failure to capture downside risk. However, results from this study indicate that 1-year parametric and historical models produce better measures of VaR than models with longer time frames. VaR estimates produced using Monte Carlo simulations show a high percentage of violations but with lower average magnitude of a violation when they occur. VaR estimates produced by the ARMA GARCH model also show a relatively high percentage of violations, however, the average magnitude of a violation is quite low. Our findings support the design of the revised Basel II VaR methodology which has also been adopted under Basel III.

O uso do value at risk (var) como medida de risco para fundos de pensão

Este estudo faz uma revisão das origens do VaR, bem como dos conceitos e teorias que o fundamentam, e sua aplicabilidade aos fundos de pensão. Descreve as principais metodologias de cálculo e as situações nas quais o uso de cada uma é mais adequado. Revisa a literatura internacional acerca do uso do VaR como medida de risco pelos fundos de pensão. A seguir faz a previsão do VaR para as carteiras reais de três fundos de pensão brasileiros com três metodologias distintas: paramétrica, simulação histórica e simulação de Monte Carlo, esta última com duas suposições distintas para a distribuição dos retornos dos fatores de risco (normal e histórica). A partir disso, realiza um teste qualitativo, através da comparação do número de perdas efetivas realizadas pelas carteiras dos três fundos de pensão com o número de perdas correspondente admitido para os diferentes níveis de confiança utilizados no cálculo do VaR. O trabalho não encontra evidências de superioridade de nenhuma das metodologias de cálculo, sendo que todas elas superestimaram as perdas verificadas na prática (o VaR foi excedido menos vezes do que o esperado).

Cálculo do Value at Risk (VaR) para o Ibovespa, pós crise de 2008, por meio dos modelos de heterocedasticidade condicional (GARCH) e de volatilidade estocástica (Local Scale Model - LSM)

O objetivo deste estudo é propor a implementação de um modelo estatístico para cálculo da volatilidade, não difundido na literatura brasileira, o modelo de escala local (LSM), apresentando suas vantagens e desvantagens em relação aos modelos habitualmente utilizados para mensuração de risco. Para estimação dos parâmetros serão usadas as cotações diárias do Ibovespa, no período de janeiro de 2009 a dezembro de 2014, e para a aferição da acurácia empírica dos modelos serão realizados testes fora da amostra, comparando os VaR obtidos para o período de janeiro a dezembro de 2014. Foram introduzidas variáveis explicativas na tentativa de aprimorar os modelos e optou-se pelo correspondente americano do Ibovespa, o índice Dow Jones, por ter apresentado propriedades como: alta correlação, causalidade no sentido de Granger, e razão de log-verossimilhança significativa. Uma das inovações do modelo de escala local é não utilizar diretamente a variância, mas sim a sua recíproca, chamada de “precisão” da série, que segue uma espécie de passeio aleatório multiplicativo. O LSM captou todos os fatos estilizados das séries financeiras, e os resultados foram favoráveis a sua utilização, logo, o modelo torna-se uma alternativa de especificação eficiente e parcimoniosa para estimar e prever volatilidade, na medida em que possui apenas um parâmetro a ser estimado, o que representa uma mudança de paradigma em relação aos modelos de heterocedasticidade condicional.

Dynamic D-Vine copula model with applications to Value-at-Risk (VaR)

Regular vine copulas are multivariate dependence models constructed from pair-copulas (bivariate copulas). In this paper, we allow the dependence parameters of the pair-copulas in a D-vine decomposition to be potentially time-varying, following a nonlinear restricted ARMA(1,m) process, in order to obtain a very flexible dependence model for applications to multivariate financial return data. We investigate the dependence among the broad stock market indexes from Germany (DAX), France (CAC 40), Britain (FTSE 100), the United States (S&P 500) and Brazil (IBOVESPA) both in a crisis and in a non-crisis period. We find evidence of stronger dependence among the indexes in bear markets. Surprisingly, though, the dynamic D-vine copula indicates the occurrence of a sharp decrease in dependence between the indexes FTSE and CAC in the beginning of 2011, and also between CAC and DAX during mid-2011 and in the beginning of 2008, suggesting the absence of contagion in these cases. We also evaluate the dynamic D-vine copula with respect to Value-at-Risk (VaR) forecasting accuracy in crisis periods. The dynamic D-vine outperforms the static D-vine in terms of predictive accuracy for our real data sets.

Value at Risk (VaR) en empresas del sector real en Colombia: caso, Bogotá ELEKTRIKA

La estimación y gestión del riesgo con la evolución del mercado ha tomado gran relevancia, principalmente en el sector financiero y de capitales, no obstante las variables macroeconómicas que afectan el riesgo en el tiempo son cada vez más volátiles y generan un mayor nivel de incertidumbre; se puede presentar en igual medida o con un mayor impacto en empresas del sector real, principalmente en aquellas cuyas condiciones de valoración causan un mayor impacto para los inversionistas, tal es el caso de las Asociaciones Público Privadas, mecanismos de contratación que vinculan al sector privado con el público en el desarrollo de proyectos de mayor nivel, donde se requiere establecer la valoración y cuantificación del riesgo que cada una de las partes está dispuesto a asumir -- Hoy por hoy existen métodos de medición sofisticados que permiten la estimación del Value at Risk (VaR), los cuales han sido desarrollados principalmente por el sistema financiero, sin contar con una aplicación en el sector real -- Es por eso que surge la necesidad de esta investigación para obtener una metodología que permita estimar el VaR bajo los conceptos teóricos de economía, estadística y simulación

Forecasting time-varying value-at-risk

In this thesis we are interested in financial risk and the instrument we want to use is Value-at-Risk (VaR). VaR is the maximum loss over a given period of time at a given confidence level. Many definitions of VaR exist and some will be introduced throughout this thesis. There two main ways to measure risk and VaR: through volatility and through percentiles. Large volatility in financial returns implies greater probability of large losses, but also larger probability of large profits. Percentiles describe tail behaviour. The estimation of VaR is a complex task. It is important to know the main characteristics of financial data to choose the best model. The existing literature is very wide, maybe controversial, but helpful in drawing a picture of the problem. It is commonly recognised that financial data are characterised by heavy tails, time-varying volatility, asymmetric response to bad and good news, and skewness. Ignoring any of these features can lead to underestimating VaR with a possible ultimate consequence being the default of the protagonist (firm, bank or investor). In recent years, skewness has attracted special attention. An open problem is the detection and modelling of time-varying skewness. Is skewness constant or there is some significant variability which in turn can affect the estimation of VaR? This thesis aims to answer this question and to open the way to a new approach to model simultaneously time-varying volatility (conditional variance) and skewness. The new tools are modifications of the Generalised Lambda Distributions (GLDs). They are four-parameter distributions, which allow the first four moments to be modelled nearly independently: in particular we are interested in what we will call para-moments, i.e., mean, variance, skewness and kurtosis. The GLDs will be used in two different ways. Firstly, semi-parametrically, we consider a moving window to estimate the parameters and calculate the percentiles of the GLDs. Secondly, parametrically, we attempt to extend the GLDs to include time-varying dependence in the parameters. We used the local linear regression to estimate semi-parametrically conditional mean and conditional variance. The method is not efficient enough to capture all the dependence structure in the three indices —ASX 200, S&P 500 and FT 30—, however it provides an idea of the DGP underlying the process and helps choosing a good technique to model the data. We find that GLDs suggest that moments up to the fourth order do not always exist, there existence appears to vary over time. This is a very important finding, considering that past papers (see for example Bali et al., 2008; Hashmi and Tay, 2007; Lanne and Pentti, 2007) modelled time-varying skewness, implicitly assuming the existence of the third moment. However, the GLDs suggest that mean, variance, skewness and in general the conditional distribution vary over time, as already suggested by the existing literature. The GLDs give good results in estimating VaR on three real indices, ASX 200, S&P 500 and FT 30, with results very similar to the results provided by historical simulation.

Diversification and value-at-risk

A pervasive and puzzling feature of banks’ Value-at-Risk (VaR) is its abnormally high level, which leads to excessive regulatory capital. A possible explanation for the tendency of commercial banks to overstate their VaR is that they incompletely account for the diversification effect among broad risk categories (e.g., equity, interest rate, commodity, credit spread, and foreign exchange). By underestimating the diversification effect, bank’s proprietary VaR models produce overly prudent market risk assessments. In this paper, we examine empirically the validity of this hypothesis using actual VaR data from major US commercial banks. In contrast to the VaR diversification hypothesis, we find that US banks show no sign of systematic underestimation of the diversification effect. In particular, diversification effects used by banks is very close to (and quite often larger than) our empirical diversification estimates. A direct implication of this finding is that individual VaRs for each broad risk category, just like aggregate VaRs, are biased risk assessments.

The level and quality of Value-at-Risk disclosure by commercial banks

In this paper we study both the level of Value-at-Risk (VaR) disclosure and the accuracy of the disclosed VaR figures for a sample of US and international commercial banks. To measure the level of VaR disclosures, we develop a VaR Disclosure Index that captures many different facets of market risk disclosure. Using panel data over the period 1996–2005, we find an overall upward trend in the quantity of information released to the public. We also find that Historical Simulation is by far the most popular VaR method. We assess the accuracy of VaR figures by studying the number of VaR exceedances and whether actual daily VaRs contain information about the volatility of subsequent trading revenues. Unlike the level of VaR disclosure, the quality of VaR disclosure shows no sign of improvement over time. We find that VaR computed using Historical Simulation contains very little information about future volatility.

Incorporating Higher Moments into Value at Risk Forecasting

Value-at-risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a simple approach to forecasting of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting the standard normal distribution with the first four moments, which are allowed to vary over time. In an extensive empirical study, we compare the GCE approach to other models of VaR forecasting and conclude that it provides accurate and robust estimates of the realized VaR. In spite of its simplicity, on our dataset GCE outperforms other estimates that are generated by both constant and time-varying higher-moments models.

A comparison of extreme value theory approaches for determining value at risk

This paper compares a number of different extreme value models for determining the value at risk (VaR) of three LIFFE futures contracts. A semi-nonparametric approach is also proposed, where the tail events are modeled using the generalised Pareto distribution, and normal market conditions are captured by the empirical distribution function. The value at risk estimates from this approach are compared with those of standard nonparametric extreme value tail estimation approaches, with a small sample bias-corrected extreme value approach, and with those calculated from bootstrapping the unconditional density and bootstrapping from a GARCH(1,1) model. The results indicate that, for a holdout sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate.

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models.

A survey of value-at-risk and its role in the banking industry

This paper discusses the various aspects of Value-at-Risk (VaR) and the VaR-based risk management process as it pertains to the banking industry. Since its inception in the 1990’s, VaR has become the industry standard by which market risk is both measured and managed by financial institutions today. However, there has been much debate regarding VaR’s validity and the extent of its role within the banking industry. Yet, now that it is an integral part of the regulatory framework, establishing VaR’s legitimacy is more important than ever. Therefore, this paper examines the recent literature on VaR’s use as a market risk management tool within the banking environment in an attempt to clarify some of the more contentious issues which have been raised by researchers. The discussion begins by highlighting the underlying theory on which VaR is based, specific aspects which have proven controversial and its use from a regulatory perspective. The focus then turns to what little literature exists on the subject of VaR and asset returns in an attempt to provide some direction for future research.

Avaliação do impacto da lei Sarbanes-Oxley no Value-at-Risk das empresas que operam na NYSE: uma abordagem de quebra estrutural em regressão quantílica

O objetivo do presente estudo é avaliar a existência de quebra estrutural no Value-at-Risk (VaR) das empresas que negociam suas ações na bolsa de valores de Nova Iorque (NYSE). O evento que justi ca a suspeita de mudança estrutural é a lei de governança corporativa conhecida como Sarbanes-Oxley Act (ou simplesmente SOX), a mais profunda reforma implementada no sistema de legislação nanceira dos Estados Unidos desde 1934. A metodologia empregada é baseada em um teste de quebra estrutural endógeno para modelos de regressão quantílica. A amostra foi composta de 176 companhias com registro ativo na NYSE e foi analisado o VaR de 1%, 5% e 10% de cada uma delas. Os resultados obtidos apontam uma ligação da SOX com o ponto de quebra estrutural mais notável nos VaRs de 10% e 5%, tomando-se como base a concentração das quebras no período de um ano após a implementação da SOX, a partir do teste de Qu(2007). Utilizando o mesmo critério para o VaR de 1%, a relação encontrada não foi tão forte quanto nos outros dois casos, possivelmente pelo fato de que para uma exposição ao risco tão extrema, fatores mais especí cos relacionados à companhia devem ter maior importância do que as informações gerais sobre o mercado e a economia, incluídas na especi cação do VaR. Encontrou-se ainda uma forte relação entre certas características como tamanho, liquidez e representação no grupo industrial e o impacto da SOX no VaR.

Value-at-risk : aplicação de cinco metodologias a carteiras teóricas compostas por ações e títulos de renda fixa no Brasil

Faz revisão teórica dos modelos de value-at-risk (VAR). Revisa principais estudos anteriores sobre VAR no Brasil e no exterior. Testa o desempenho de cinco metodologias de VAR, a saber: metodologia Paramétrica com uso da Volatilidade Histórica, Paramétrica com uso da Volatilidade EWMA, Paramétrica• com uso da Volatilidade GARCH(1,1), Simulação Histórica e uma Metodologia Híbrida proposta por BOUDOUKH e taI (1998). Aplica as metodologias a carteiras teóricas compostas por proporções diversas de ações e títulos de renda fixa de 30 dias no mercado financeiro brasileiro. O trabalho encontra evidências da superioridade da Metodologia Híbrida com fator de caimento de 0,99 e da Simulação Histórica, sendo esta apenas marginalmente inferior, Estes resultados se coadunam com evidências encontradas nas séries em estudo de nãonormalidade, heterocedasticidade e autocorrelação