Expected Shortfall Measures Research Articles

Risk Measures for Investment Values and Returns Based on Skewed-Heavy Tailed Distributions: Analytical Derivations and Comparison

The skewed generalized t (SGT) displays an exceptional ability in modelling the tails of the empirical distributions of returns of financial and other assets. This feature makes it an appealing candidate for the computation of value at risk and expected shortfall measures, used by regulators, investors, portfolio managers and actuaries to measure and manage the risk exposure of their assets. This paper makes a specific contribution by deriving the analytical equations for the computation of value at risk, expected shortfall and downside risk measures for asset values and returns based on the SGT distribution. An assessment using simulations and estimation show that risk measures based on returns overestimate risk exposure.

Recovery of quantile and quantile density function using the frequency moments

The problem of recovering quantiles and quantile density functions of a positive random variable via the values of frequency moments is studied. The uniform upper bounds of the proposed approximations are derived. Several simple examples and corresponding plots illustrate the behavior of the recovered approximations. Some applications of the constructions are discussed as well. Namely, using the empirical counterparts of the constructions yield the estimates of the quantiles, and the quantile density functions. By means of simulations, the average errors in terms of L2-norm are evaluated to justify the consistency of the estimate of the quantile density function. As an application of the constructions, the question of estimating the so-called expected shortfall measure in risk models is also studied.

Volatility measures as predictors of extreme returns

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book-to-market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E-GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.

Time Series Simulation with Randomized Quasi-Monte Carlo Methods: An Application to Value at Risk and Expected Shortfall

Quasi-Monte Carlo methods are designed to produce efficient estimates of simulated values but the error statistics of these estimates are difficult to compute. Randomized quasi-Monte Carlo methods have been developed to address this shortcoming. In this paper we compare quasi-Monte Carlo and randomized quasi-Monte Carlo techniques for simulating time series. We use randomized quasi-Monte Carlo to compute value-at-risk and expected shortfall measures for a stock portfolio whose returns follow a highly nonlinear Markov switching stochastic volatility model which does not admit analytical solutions for the returns distribution. Quasi-Monte Carlo methods are more accurate but do not allow the computation of reliable confidence intervals about risk measures. We find that randomized quasi-Monte Carlo methods maintain many of the advantages of quasi-Monte Carlo while also providing the ability to produce reliable confidence intervals of the simulated risk measures. However, the advantages in speed of convergence of randomized quasi-Monte Carlo diminish as the forecast horizon increases.

Good deeds earn chits? Evidence from philanthropic family controlled firms

This study examines whether charitable family controlled firms have lower default risk. Using Taiwan data that provide clear information about firms’ benevolent intention and avoid endogeneity issue of risk and charitable activities, we show that charitable family controlled firms have lower default risk, which is proxied by value-at-risk and expected shortfall measures. Our finding shows that charitable activities bring benefits of lower risk to shareholders. This study also provides various channels that can lower default risk for the charitable firms. That is, these firms appear to have higher credit ratings, engage less in earnings management, and have higher worker productivity. This study argues that the benevolent mindset of decision makers at firms help lower default risk.

NetMES: a network based marginal expected shortfall measure

NetMES: a network based marginal expected shortfall measure

How do risk attitudes of clearing firms matter for managing default exposure in futures markets?

This article proposes a theoretical framework that is built upon extreme value theory to study three instruments (i.e. margin, capital requirement and price limits) for managing default risk in futures markets. Specifically, the exceedances over a price threshold are modeled using a generalized Pareto distribution, and the models are static (one-period). We incorporate the risk attitudes of clearing firms into the framework to investigate the efficacy of these instruments under several risk measures, including value-at-risk measures, expected-shortfall measures and spectral risk measures. An empirical study on the VIX futures (or VX) data shows that the effectiveness of these market instruments rests not only on clearing firms' risk attitudes, but also on the tail fatness of the futures price distribution. Moreover, the shift in the risk attitudes of clearing firms may cause interactions among these instruments, which casts new light on the economic rationale of price limits.

An Evaluation of Bank VaR Measures for Market Risk During and Before the Financial Crisis

We study the performance and behavior of Value at Risk (VaR) measures used by a number of large banks during and before the financial crisis. Alternative benchmark VaR measures, including GARCH-based measures, are also estimated directly from the banks' trading revenues and help to explain the bank VaR performance results. While highly conservative in the pre-crisis period, bank VaR exceedances were excessive and clustered in the crisis period. All benchmark VaRs were more accurate in the pre-crisis period with GARCH VaR measures the most accurate in the crisis period having lower exceedance rates with no exceedance clustering. Variance decompositions indicate a limited ability of the banks' VaR methodologies to adjust to the crisis-period market conditions. Despite their weaker performance, the bank VaRs exhibited greater predictive power for a measure of realized PnL volatility than benchmark VaR measures. Benchmark Expected Shortfall measures are also considered.

An Evaluation of Bank VaR Measures for Market Risk During and Before the Financial Crisis

We study the performance and behavior of Value at Risk (VaR) measures used by a number of large banks during and before the financial crisis. Alternative benchmark VaR measures, including GARCH-based measures, are also estimated directly from the banks' trading revenues and help to explain the bank VaR performance results. While highly conservative in the pre-crisis period, bank VaR exceedances were excessive and clustered in the crisis period. All benchmark VaRs were more accurate in the pre-crisis period with GARCH VaR measures the most accurate in the crisis period having lower exceedance rates with no exceedance clustering. Variance decompositions indicate a limited ability of the banks' VaR methodologies to adjust to the crisis-period market conditions. Despite their weaker performance, the bank VaRs exhibited greater predictive power for a measure of realized PnL volatility than benchmark VaR measures. Benchmark Expected Shortfall measures are also considered.

Risk management in the energy markets and Value-at-Risk modelling: a hybrid approach

This paper proposes a set of Value-at-Risk (VaR) models appropriate to capture the dynamics of energy prices and subsequently quantify energy price risk by calculating VaR and expected shortfall measures. Amongst the competing VaR methodologies evaluated in this paper, besides the commonly used benchmark models, a Monte Carlo (MC) simulation approach and a hybrid MC with historical simulation approach, both assuming various processes for the underlying spot prices, are also being employed. All VaR models are empirically tested on eight spot energy commodities that trade futures contracts on the New York Mercantile Exchange (NYMEX) and the constructed Spot Energy Index. A two-stage evaluation and selection process is applied, combining statistical and economic measures, to choose amongst the competing VaR models. Finally, both long and short trading positions are considered as it is of utmost importance for energy traders and risk managers to be able to capture efficiently the characteristics of both tails of the distributions.

Out of sample value-at-risk and backtesting with the standardized pearson type-IV skewed distribution

This paper studies the efficiency of an econometric model where the volatility is modeled by a GARCH (1,1) process, and the innovations follow a standardized form of the Pearson type-IV distribution. The performance of the model is examined by in sample and out of sample testing, and the accuracy is explored by a variety of Value-at-Risk methods, the success/failure ratio, the Kupiec-LR test, the independence and conditional coverage tests of Christoffersen, the expected shortfall measures, and the dynamic quantile test of Engle and Manganelli. Overall, the proposed model is a valid and accurate model performing better than the skewed Student-t distribution, providing the financial analyst with a good candidate as an alternative distributional scheme.

Operational risk: A Basel II11 step before Basel III

The Banking Committee on Banking Supervision recommended that operational risk should be quantified using the Basel matrix, which enables the sorting of risk incidents. This paper analyses these incidents in depth and suggests strategies for carrying out the supervisory guidelines proposed by the regulators, as follows. On the one hand, banks need to provide a univariate capital charge for each cell of the Basel matrix. That requires constructing loss distribution functions (LDFs), which implies estimating a frequency and a severity distribution. It is shown that the choice of the theoretical distributions to build the LDFs has a tremendous impact on the capital charges, especially if extreme losses are not taken into account. On the other hand, banks also need to provide a global capital charge corresponding to the whole matrix. The paper highlights that a lack of consideration or a poor appreciation of the dependence structure may lead to incorrect capital charges. Finally, the paper finds two crucial points that should be taken into account by regulators and risk managers: (1) The necessity of splitting information sets in two parts while adjusting the severity distribution: the first covering small and medium losses, and the latter containing extreme losses (this point implies problems of granularity as mentioned in the Basel II guidelines); (2) The choice of the risk measure, which provides the capital amount. The paper concludes that the expected shortfall measure enables a better anticipation of large operational risk incidents.

L'approche dare pour une mesure de risque diversifiée

Résumé Nous proposons dans cet article, à partir des approches de Taylor [2008] et de Gouriéroux et Jasiak [2008], d’agréger différents modèles de quantiles et d’expectiles afin d’obtenir une méthode plus robuste de calcul de la valeur-en-risque et de la perte conditionnelle maximale en diversifiant le risque de modèle. Cette nouvelle méthode exploite les techniques de régression sur quantiles afin d’obtenir une meilleure estimation des queues de distributions des rendements. Nous comparons notre mesure à la plupart des mesures de risques extrêmes disponibles, en utilisant les principaux tests de validation de la littérature. Cette comparaison menée sur données financières françaises, nous permet de confirmer les qualités de la méthode proposée.

VaR and expected shortfall: a non-normal regime switching framework

We have developed a regime switching framework to compute the Value at Risk and Expected Shortfall measures. Although Value at Risk as a risk measure has been criticized by some researchers for lack of subadditivity, it is still a central tool in banking regulations and internal risk management in the finance industry. In contrast, Expected Shortfall is coherent and convex, so it is a better measure of risk than Value at Risk. Expected Shortfall is widely used in the insurance industry and has the potential to replace Value at Risk as a standard risk measure in the near future. We have proposed regime switching models to measure value at risk and expected shortfall for a single financial asset as well as financial portfolios. Our models capture the volatility clustering phenomenon and variance-independent variation in the higher moments by assuming the returns follow Student-t distributions.

Energy Vulnerability and EU-Russia Energy Relations

The concept of energy vulnerability is reviewed and discussed with a focus on Russia’s foreign energy relations, in particular those with European countries. A definition and a conceptual framework for quantifying energy vulnerability are proposed in the context of a review of recent research on energy vulnerability indices. In particular it is suggested that source country diversification should be reflected using the expected shortfall measure used in financial economics, rather than the Herfindahl-Hirschman or Shannon-Wiener indices, and that the former should then enter a calibrated function in order to yield expected economic loss. The issues of asymmetric failure probabilities and accidental versus intentional supply disruptions are then discussed with examples of recent Russian actions. Energy vulnerability measurement and modelling should ultimately inform policy. In particular, member states should legislate that no energy infrastructure project by one or more member states may increase the energy vulnerability of another member state. Additionally, European environmental policies, notably the EU ETS, should be amended so as to account for induced changes in energy vulnerability. Finally, member states should increase the level of transparency and disclosure with respect to gas import statistics and gas supply contracts.

Extreme Risk Management

Quantitative risk management relies on a constellation of tools that are used to analyze portfolio risk. We develop the standard toolkit, which includes betas, risk budgets and correlations, in a general, coherent, mnemonic framework centered around marginal risk contributions. We apply these tools to generate side-by-side analyses of volatility and expected shortfall, which is a measure of average portfolio excess of value-at-risk. We focus on two examples whose importance is highlighted by the current economic crisis. By examining downside protection provided by an out-of-the-money put option we show that the diversification benefit of the option is greater for a risk measure that is more highly concentrated in the tail of the distribution. By comparing two-asset portfolios that are distinguished only by the likelihood of coincident extreme events, we show that expected shortfall measures market contagion in a way that volatility cannot.

Portfolio selection in an expected shortfall framework during the recent ‘credit crunch’ period

Portfolio selection models using variance, Value-at-Risk (VaR) and expected shortfall measures of risk are analysed, assuming differing underlying return distributions. The expected shortfall approach provides advantages relative to the VaR approach in terms of lower portfolio downside risks. Furthermore, using the extreme value distribution provides more insights for the investor relative to the empirical distribution. Analysing portfolio selection using these differing risk measures around the recent sub-prime mortgage problem period provides topical insights into the asset allocation process for the investor.

A conditional-SGT-VaR approach with alternative GARCH models

This paper proposes a conditional technique for the estimation of VaR and expected shortfall measures based on the skewed generalized t (SGT) distribution. The estimation of the conditional mean and conditional variance of returns is based on ten popular variations of the GARCH model. The results indicate that the TS-GARCH and EGARCH models have the best overall performance. The remaining GARCH specifications, except in a few cases, produce acceptable results. An unconditional SGT-VaR performs well on an in-sample evaluation and fails the tests on an out-of-sample evaluation. The latter indicates the need to incorporate time-varying mean and volatility estimates in the computation of VaR and expected shortfall measures.