Expected Shortfall Forecasts Research Articles

Forecasting volatility of tanker freight rates based on asymmetric regime-switching GARCH models

This paper investigates the performance of various conditional volatility models to forecast the second moment of tanker freight rates. Justified by existing theoretical and empirical evidence, we focus on asymmetric Markov regime-switching models to study the major global routes for long-haul trade of crude oil during the sample period from June 2000 to May 2015. Moreover, in contrast to a number of existing studies, we examine seasonally adjusted freight rates. We find that regime-switching GARCH models outperform their single-regime complements in terms of in-sample fit and out-of-sample forecasting accuracy. In particular, the asymmetric MRS-EGARCH and MRS-APARCH exhibit superior in- and out-of-sample performance. To additionally examine the applicability in freight risk management, we compare Value-at-Risk and Expected Shortfall forecasts. Our results show that accounting for volatility regimes and asymmetry does not enhance the performance of one-day-ahead forecasts of either risk measure for both long and short trading positions.

Multiple-Days-Ahead Value-At-Risk and Expected Shortfall Forecasting for Stock Indices, Commodities and Exchange Rates: Inter-Day Versus Intra-Day Data

In order to provide reliable Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts, this paper attempts to investigate whether an inter-day or an intra-day model provides accurate predictions. We investigate the performance of inter-day and intra-day volatility models by estimating the AR(1)-GARCH(1,1)-skT and the AR(1)-HAR-RV-skT frameworks, respectively. This paper is based on the recommendations of the Basel Committee on Banking Supervision. Regarding the forecasting performances, the exploitation of intra-day information does not appear to improve the accuracy of the and forecasts for the 10-steps-ahead and 20- steps-ahead for the 95%, 97.5% and 99% significance levels. On the contrary, the GARCH specification, based on the inter-day information set, is the superior model for forecasting the multiple-days-ahead and measurements. The intra-day volatility model is not as appropriate as it was expected to be for each of the different asset classes; stock indices, commodities and exchange rates. The multi-period and forecasts are estimated for a range of datasets (stock indices, commodities, foreign exchange rates) in order to provide risk managers and financial institutions with information relating the performance of the inter-day and intra-day volatility models across various markets. The inter-day specification predicts and measures adequately at a 95% confidence level. Regarding the 97.5% confidence level that has been recently proposed in the revised 2013 version of Basel III, the GARCH-skT specification provides accurate forecasts of the risk measures for stock indices and exchange rates, but not for commodities (i.e. Silver and Gold). In the case of the 99% confidence level, we do not achieve sufficiently accurate and forecasts for all the assets.

Previsão de value-at-risk e expected shortfall para mercados emergentes usando modelos FIGARCH

Este artigo compara os desempenhos dos modelos de memória longa (FIGARCH) e curta (GARCH) na previsão de volatilidade para cálculo de value at-risk (VaR) e expected shortfall (ES) para múltiplos períodos à frente para seis índices de ações de mercados emergentes Utilizou-se, para dados diários de 1999
 a 2014, uma adaptação da simulação de Monte Carlo para estimar previsões de VaR e ES para 1, 10 e 20 dias à frente, usando modelos FIGARCH e GARCH para quatro distribuições de erros. Os resultados sugerem que, em geral, os modelos FIGARCH melhoram a precisão das previsões para horizontes mais longos; que a distribuição dos erros pode influenciar a decisão de escolha do
 melhor modelo; e que apenas para os modelos FIGARCH houve redução do número de subestimações do VaR verdadeiro com o aumento do horizonte de previsão. Entretanto, os resultados apontam para uma maior variação das estimativas dos parâmetros para os modelos FIGARCH.

Tail risk in emerging markets of Southeastern Europe

ABSTRACTThis article examines the left-tail behaviour of returns on stocks in Southeastern Europe (SEE). We apply conditional extreme value theory (EVT) approach on daily returns of six stock market indices from SEE between 2004 and 2013. Predictive performance of value-at-risk (VaR) and expected shortfall (ES) based on EVT is compared against several alternatives, such as historical simulation and analytical approach based on GARCH with a single conditional distribution. Model backtesting with daily returns shows that EVT-based models provide more reliable VaR and ES forecasts than the alternative models in all six markets. Unlike the alternatives, the EVT-based models cannot be rejected as VaR confidence level is increased. This emphasizes the importance of extreme events in SEE markets and indicates that the ability of a model to capture volatility clustering accurately is not sufficient for a correct assessment of risk in these markets.

Backtesting Expected Shortfall: Accounting for Tail Risk

The Basel Committee on Banking Supervision (BIS) has recently sanctioned expected shortfall (ES) as the market risk measure to be used for banking regulatory purposes, replacing the well-known value at risk (VaR). This change is motivated by the appealing theoretical properties of ES as a measure of risk and the poor properties of VaR. In particular, VaR fails to control for “tail risk.” In this transition, the major challenge faced by financial institutions is the unavailability of simple tools for evaluation of ES forecasts (i.e., backtesting ES). The main purpose of this paper is to propose such tools. Specifically, we propose backtests for ES based on cumulative violations, which are the natural analogue of the commonly used backtests for VaR. We establish the asymptotic properties of the tests, and investigate their finite sample performance through some Monte Carlo simulations. An empirical application to three major stock indexes shows that VaR is generally unresponsive to extreme events such as those experienced during the recent financial crisis, whereas ES provides a more accurate description of the risk involved. This paper was accepted by Neng Wang, finance.

Backtesting Expected Shortfall: Accounting for Tail Risk

The Basel Committee on Banking Supervision (BIS) has recently sanctioned Expected Shortfall (ES) as the market risk measure to be used for banking regulatory purposes, replacing the well-known Value-at-Risk (VaR). This change is motivated by the appealing theoretical properties of ES as a measure of risk and the poor properties of VaR. In particular, VaR fails to control for tail risk. In this transition, the major challenge faced by financial institutions is the unavailability of simple tools for evaluation of ES forecasts (i.e. backtesting ES). The main purpose of this article is to propose such tools. Specifically, we propose backtests for ES based on cumulative violations, which are the natural analogue of the commonly used backtests for VaR. We establish the asymptotic properties of the tests, and investigate their finite sample performance through some Monte Carlo simulations. An empirical application to three major stock indexes shows that VaR is generally unresponsive to extreme events such as those experienced during the recent financial crisis, while ES provides a more accurate description of the risk involved.

Empirical analysis of long memory, leverage, and distribution effects for stock market risk estimates

In this study, eight generalized autoregressive conditional heteroskedasticity (GARCH) types of variance specifications and two return distribution settings, the normal and skewed generalized Student's t (SGT) of Theodossiou (1998), totaling nine GARCH-based models, are utilized to forecast the volatility of six stock indices, and then both the out-of-sample-period value-at-risk (VaR) and the expected shortfall (ES) are estimated following the rolling window approach. Moreover, the in-sample VaR is estimated for both the global financial crisis (GFC) period and the non-GFC period. Subsequently, through several accuracy measures, nine models are evaluated in order to explore the influence of long memory, leverage, and distribution effects on the performance of VaR and ES forecasts. As shown by the empirical results of the nine models, the long memory, leverage, and distribution effects subsist in the stock markets. Moreover, regarding the out-of-sample VaR forecasts, long memory is the most important effect, followed by the leverage effect for the low level, whereas the distribution effect is crucial for the high level. As for the three VaR approaches, weighted historical simulation achieves the best VaR forecasting performance, followed by filtered historical simulation, whereas the parametric approach has the worst VaR forecasting performance for all the levels. Furthermore, VaR models underestimate the true risk, whereas ES models overestimate the true risk, indicating that the ES risk measure is more conservative than the VaR risk measure. Additionally, based on back-testing, the VaR provides a better risk forecast than the ES since the ES highly overestimates the true risk. Notably, long memory is important for the ES estimate, whereas both the long memory and the leverage effect are crucial for the VaR estimate. Finally, via in-sample VaR forecasts in regard to the low level, it is found that long memory is important for the non-GFC period, whereas the distribution effect is crucial for the GFC period. On the other hand, with regard to the high level, the distribution effect is crucial for both the non-GFC and the GFC period. These results seem to be consistent with those found in the out-of-sample VaR forecasts. In accordance with these results, several important policy implications are proposed in this study.

Bayesian Expected Shortfall Forecasting Incorporating the Intraday Range

Intraday sources of data have proved to be effective for dynamic volatility and tail risk estimation. Expected shortfall (ES) is a tail risk measure, which is now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to implicitly model ES, is generalized to incorporate information on the intraday range. An asymmetric Gaussian density model error formulation allows a likelihood to be developed that leads to direct estimation and one-step-ahead forecasts of expectiles and, subsequently, of ES. Adaptive Markov chain Monte Carlo sampling schemes are employed for estimation, while their performance is assessed via a simulation study. The proposed models compare favorably with a large range of competitors in an empirical study forecasting seven financial return series over a 10-year period.

Modelling and forecasting value at risk and expected shortfall for GCC stock markets: Do long memory, structural breaks, asymmetry, and fat-tails matter?

This paper addresses the question whether dual long memory (LM), asymmetry and structural breaks in stock market returns matter when forecasting the value at risk (VaR) and expected shortfall (ES) for short and long trading positions. We answer this question for the Gulf Cooperation Council (GCC) stock markets. Empirically, we test the occurrence of structural breaks in the GCC return data using the Inclan and Tiao (1994)’s algorithm and we check the relevance of LM using Shimotsu (2006) procedure before estimating the ARFIMA-FIGARCH and ARFIMA-FIAPARCH models with different innovations’ distributions and computing VaR and ES. Our results show that all the GCC market's volatilities exhibit significant structural breaks matching mainly with the 2008–2009 global financial crises and the Arab spring. Also, they are governed by LM process either in the mean or in the conditional variance which cannot be due to the occurrence of structural breaks. Furthermore, the forecasting ability analysis shows that the FIAPARCH model under skewed Student-t distribution turn out to improve substantially the VaR and the ES forecasts.

GARCH models for daily stock returns: Impact of estimation frequency on Value-at-Risk and Expected Shortfall forecasts

We analyze the impact of the estimation frequency–updating parameter estimates on a daily, weekly, monthly or quarterly basis–for commonly used GARCH models in a large-scale study, using more than twelve years (2000–2012) of daily returns for constituents of the S&P 500 index. We assess the implication for one-day ahead 95% and 99% Value-at-Risk (VaR) forecasts with the test for correct conditional coverage of Christoffersen (1998) and for Expected Shortfall (ES) forecasts with the block-bootstrap test of ES violations of Jalal and Rockinger (2008). Using the false discovery rate methodology of Storey (2002) to estimate the percentage of stocks for which the model yields correct VaR and ES forecasts, we conclude that there is no difference in performance between updating the parameter estimates of the GARCH equation at a daily or weekly frequency, whereas monthly or even quarterly updates are only marginally outperformed.

A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification

In financial literature, Value-at-Risk (VaR) and Expected Shortfall (ES) modelling is focused on producing 1-step ahead conditional variance forecasts. The present paper provides a methodological contribution to the multi-step VaR and ES forecasting through a new adaptation of the Monte Carlo simulation approach for forecasting multi-period volatility to a fractionally integrated GARCH framework for leptokurtic and asymmetrically distributed portfolio returns. Accounting for long memory within the conditional variance process with skewed Student-t (skT) conditionally distributed innovations, accurate 95% and 99% VaR and ES forecasts are calculated for multi-period time horizons. The results show that the FIGARCH-skT model has a superior multi-period VaR and ES forecasting performance.

Forecasting the Risk of Speculative Assets by Means of Copula Distributions

The GARCH(1,1) model and its extensions have become a standard econometric tool for modeling volatility dynamics of financial returns and portfolio risk. In this paper, we propose an adjustment of GARCH implied conditional value-at-risk and expected shortfall forecasts that exploits the predictive content of uncorrelated, yet dependent model innovations. The adjustment is motivated by non-Gaussian characteristics of model residuals, and is implemented in a semiparametric fashion by means of conditional moments of simulated bivariate standardized copula distributions. We conduct in-sample forecasting comparisons for a set of 18 stock market indices. In total, four competing copula-GARCH models are contrasted against each other on the basis of their one-step ahead forecasting performance. With regard to forecast unbiasedness and precision, especially the Frank-GARCH models provide most conservative risk forecasts and out-perform all rival models.

GARCH Models for Daily Stock Returns: Impact of Estimation Frequency on Value-at-Risk and Expected Shortfall Forecasts

GARCH Models for Daily Stock Returns: Impact of Estimation Frequency on Value-at-Risk and Expected Shortfall Forecasts

GARCH Models for Daily Stock Returns: Impact of Estimation Frequency on Value-at-Risk and Expected Shortfall Forecasts

This discussion paper led to a publication in 'Economics Letters' , 2014, 123(2), 187-190. We analyze the impact of the estimation frequency - updating parameter estimates on a daily, weekly, monthly or quarterly basis - for commonly used GARCH models in a large-scale study, using more than twelve years (2000-2012) of daily returns for constituents of the SP it yields correct VaR and ES forecasts for an estimated 90% to 95% of the S&P 500 constituents. Third, specifying a Student- t (or Gaussian) innovations' density yields substantially and significantly worse forecasts, especially for ES. In sum, the somewhat more advanced model with infrequently updated parameter estimates yields much better VaR and ES forecasts than simpler models with daily updated parameter estimates.

A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification

The paper provides a methodological contribution to the multi-step Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting through a new adaptation of the Monte Carlo simulation approach for forecasting multi-period volatility to a Fractionally Integrated Generalized Autoregressive Conditional Heteroscedasticity (FIGARCH) framework for leptokurtic and asymmetrically distributed portfolio returns. Accounting for long memory within the conditional variance process with skewed Student-t (skT) conditionally distributed innovations, accurate 95 per cent and 99 per cent VaR and ES forecasts are calculated for multi-period time horizons. The results show that the FIGARCH-skT model has a superior multi-period VaR and ES forecasting performance.

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk (VaR) and expected shortfall (ES) across 20 stock indices worldwide. The dataset is composed of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.

Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution

A parametric approach to estimating and forecasting Value-at-Risk (VaR) and expected shortfall (ES) for a heteroscedastic financial return series is proposed. The well-known GJR–GARCH form models the volatility process, capturing the leverage effect. To capture potential skewness and heavy tails, the model assumes an asymmetric Laplace form as the conditional distribution of the series. Furthermore, dynamics in higher moments are modeled by allowing the shape parameter in this distribution to be time-varying. Estimation is via an adaptive Markov chain Monte Carlo (MCMC) sampling scheme, employing the Metropolis–Hastings (MH) algorithm with a mixture of Gaussian proposal distributions. A simulation study highlights accurate estimation and improved inference compared to a single-Gaussian-proposal MH method. The model is illustrated by applying it to four international stock market indices and two exchange rates, generating one-step-ahead forecasts of VaR and ES. Standard and non-standard tests are applied to these forecasts, and the finding is that the proposed model performs favourably compared to some popular competitors: in particular it is the only conservative model of risk over the period studied, which includes the recent global financial crisis.

Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall

Abstract We estimate several GARCH- and Extreme Value Theory (EVT)-based models to forecast intraday Value-at-Risk (VaR) and Expected Shortfall (ES) for S&P 500 stock index futures returns for both long and short positions. Among the GARCH-based models we consider is the so-called Autoregressive Conditional Density (ARCD) model, which allows time-variation in higher-order conditional moments. ARCD model with time-varying conditional skewness parameter has the best in-sample fit among the GARCH-based models. The EVT-based model and the GARCH-based models which take conditional skewness and kurtosis (time-varying or otherwise) into account provide accurate VaR forecasts. ARCD model with time-varying conditional skewness parameter seems to provide the most accurate ES forecasts.

Analyzing the Extreme Risk of a U.S Corporate Bond Portfolio, November 2009

We use the Barra Extreme Risk (BxR) model to analyze a US dollar-denominated corporate bond portfolio consisting of 2142 distinct issues. As in the case of equities, we find that the BxR proprietary extreme risk forecasts, xShortfall and xVaR, are higher than value-at-risk and expected-shortfall forecasts generated by a conditionally normal model. Further, the impact on xShortfall of tilting the portfolio toward high-yield bonds is materially greater than the impact on volatility, and the discrepancy increases as quality declines. As a result, increasing the weight on investment-grade bonds while lowering the weight on high-yield bonds mitigates tail risk more than it mitigates volatility. This intuitive result reflects the high degree of sensitivity of high-yield bonds to extreme events.

Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight from emerging markets) prior to and during the 2008 financial crisis. In addition to widely used VaR and ES models, we also study the behavior of conditional and unconditional extreme value (EV) models to generate 99 percent confidence level estimates as well as developing a new loss function that relates tail losses to ES forecasts. Backtesting results show that only our proposed new hybrid and Extreme Value (EV)-based VaR models provide adequate protection in both developed and emerging markets, but that the hybrid approach does this at a significantly lower cost in capital reserves. In ES estimation the hybrid model yields the smallest error statistics surpassing even the EV models, especially in the developed markets.