On the coherence of expected shortfall

Expected shortfall (ES) in several variants has been proposed as remedy for the deficiencies of value-at-risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case even the coherence property of ES can get lost unless one took care of the details in its definition. We compare some of the definitions of ES, pointing out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions. Moreover, this ES can be estimated effectively even in cases where the usual estimators for VaR fail.     

Estimation of multiple period expected shortfall and median shortfall for risk management

With the regulatory requirements for risk management, Value at Risk (VaR) has become an essential tool in determining capital reserves to protect the risk induced by adverse market movements. The fact that VaR is not coherent has motivated the industry to explore alternative risk measures such as expected shortfall. The first objective of this paper is to propose statistical methods for estimating multiple-period expected shortfall under GARCH models. In addition to the expected shortfall, we investigate a new tool called median shortfall to measure risk. The second objective of this paper is to develop backtesting methods for assessing the performance of expected shortfall and median shortfall estimators from statistical and financial perspectives. By applying our expected shortfall estimators and other existing approaches to seven international markets, we demonstrate the superiority of our methods with respect to statistical and practical evaluations. Our expected shortfall estimators likely provide an unbiased reference for setting the minimum capital required for safeguarding against expected loss.     

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.     

Backtesting extreme value theory models of expected shortfall

We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts.     

Risk quantification for commodity ETFs: Backtesting value-at-risk and expected shortfall

This paper calibrates risk assessment of alternative methods for modeling commodity ETFs. We implement recently proposed backtesting techniques for both value-at-risk (VaR) and expected shortfall (ES) under parametric and semi-nonparametric techniques. Our results indicate that skewed-t and Gram-Charlier distributional assumptions present the best relative performance for individual Commodity ETFs for those confidence levels recommended by Basel Accords. In view of these results, we recommend the application of leptokurtic distributions and semi-nonparametric techniques to mitigate regulation concerns about global financial stability of commodity business.     

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 VaR and ES 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 VaR and ES 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 VaR and ES 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 VaR and ES 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 (that is Silver and Gold). In the case of the 99% confidence level, we do not achieve sufficiently accurate VaR and ES forecasts for all the assets.     

Backtesting trading risk of commercial banks using expected shortfall

This paper uses saddlepoint technique to backtest the trading risk of commercial banks using expected shortfall. It is found that four out of six US commercial banks have excessive trading risks. Monte Carlo simulation studies show that the proposed backtest is very accurate and powerful even for small test samples. More importantly, risk managers can carry out the proposed backtest based on any number of exceptions, so that incorrect risk models can be promptly detected before any further huge losses are realized.     

Multiday expected shortfall under generalized t distributions: evidence from global stock market

Review of Quantitative Finance and Accounting - Earnings management research often uses discretionary accruals from Jones-type models. These models assume a linear relation between sales changes...     

On the significance of expected shortfall as a coherent risk measure

This article shows that any coherent risk measure is given by a convex combination of expected shortfalls, and an expected shortfall (ES) is optimal in the sense that it gives the minimum value among the class of plausible coherent risk measures. Hence, it is of great practical interest to estimate the ES with given confidence level from the market data in a stable fashion. In this article, we propose an extrapolation method to estimate the ES of interest. Some numerical results are given to show the efficiency of our method.     

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.     

On the role of the estimation error in prediction of expected shortfall

In the estimation of risk measures such as Value at Risk and Expected shortfall relatively short estimation windows are typically used rendering the estimation error a possibly non-negligible component. In this paper we build upon previous results for the Value at Risk and discuss how the estimation error comes into play for the Expected Shortfall. We identify two important aspects where it may be of importance. On the one hand there is in the evaluation of predictors of the measure. On the other there is in the interpretation and communication of it. We illustrate magnitudes numerically and emphasize the practical importance of the latter aspect in an empirical application with stock market index data.     

Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions

Financial returns typically display heavy tails and some degree of skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be especially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using recent generalizations of the asymmetric Student-t and exponential power distributions to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial return volatility and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distributions are used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide evidence for the usefulness of the general distributions in improving fit and prediction of downside market risk of financial assets. Constrained versions, corresponding with distributions used in the previous literature, are also estimated in order to provide a comparison of the performance of different conditional distributions.     

Corporate social responsibility versus corporate shareholder responsibility: A family firm perspective

Recent literature suggests that some socially responsible corporate actions benefit shareholders while others do not. We study differences in policy toward corporate social responsibility (CSR) between family and non-family firms, using environmental performance as the proxy for CSR. We show that family firms are more responsible to shareholders than non-family firms in making environmental investments. When shareholder interests and societal interests coincide, i.e., when it comes to alleviating environmental concerns that have potential to harm society and elevate the firm's risk exposure, family firms do at least as well as non-family firms in protecting shareholder interests. However, when shareholder and societal interests diverge, i.e., when it comes to making environmental investments that might benefit society but do not benefit shareholders, family firms protect shareholder interests by undertaking a significantly lower level of such investments than non-family firms. Our findings suggest that lack of diversification by controlling families creates strong incentives for them to act in the financial interest of all shareholders, which more than overcomes any noneconomic benefits families may derive from engaging in social causes that do not benefit non-controlling shareholders.     

Banks' interest rate risk: the net interest income perspective versus the market value perspective

We use portfolios of passive investment strategies to replicate the interest risk of banks' banking books. The following empirical statements are derived. (i) Changes in banks' market value and in their net interest income are highly correlated, irrespective of the banks' portfolio composition. (ii) However, banks' portfolio composition has a huge impact on the ratio of changes in net interest income relative to changes in market value. These results are important for the design and interpretation of interest rate stress tests for banks.     

Linear versus process tracing approaches to judgment modelling: A new perspective on cue importance

For a bankruptcy prediction problem, the judgment formation process is studied using linear models and process tracing models. The linear models are constructed using traditional linear discriminant analysis techniques. The process tracing models are constructed using computer-generated algorithmically-based decision nets. All the models presented show good predictive accuracy. However, the linear models and process tracing models diverge widely on several measures of cue importance. This divergence, for a fairly straightforward problem, is intriguing since virtually all the evidence in the accounting literature about cue importance is based on linear models research. The importance of different information cues to decision-makers is clearly a critical issue in the design of effective accounting information systems. Thus, this study suggests the need for much more careful attention to the complex question of assessing cue importance.     

Bank business models,failure risk and earnings opacity: A short- versus long-term perspective

Despite the ongoing bank regulatory reforms, relatively little research attention has been given to the effects of bank business models and opacity of bank balance sheet structure which may hinder regulation and market discipline. In this study, we explore the effects of business model strategies on banks' earnings opacity in the UK banking sector. Distinguishing between the short-term (within) and long-term (between) effects, our findings suggest that retail-oriented business models reduce the likelihood of earnings management practices in the short term but not over the long term. In contrast, wholesale-oriented business models increase the probability of earnings manipulation both in the short and long term. While bank business models characterised by a greater degree of functional diversification tend to lower earnings manipulation in the short term, the long-term incentives cannot be mitigated. Our findings also demonstrate that low failure risk (or greater solvency) represents an important channel in mitigating the effects of business models on earnings management practices both in the short and long term. Our results are robust to alternative proxies for earnings management and failure risk, and the use of alternative methods.     

Economy-wide bond default rates: A maximum expected utility approach

We consider the 12-month moving average aggregate default rate of S&P-rated US-bonds. We estimate the conditional probability distribution of this default rate as a function of a weighted average bond rating, a lagged default rate and a preliminary predictor that is based on lagged new issuance. Our modeling approach is asymptotically optimal for an expected utility maximizing investor. The resulting conditional probability density is consistent with our intuition. We measure the model’s performance by the out-of-sample expected utility. According to this measure, our model clearly outperforms a simple regression model, a regression model with ARMA error terms and a Poisson model.     

Proportional consolidation versus the equity method: A risk measurement perspective on reporting interests in joint ventures

Under Canadian generally accepted accounting principles (GAAP), firms are required to proportionally consolidate joint venture investments, as opposed to the United States where the equity method is used. Using a sample of Canadian firms, this study investigates the relative information content of equity method and proportionally consolidated financial statement amounts for explaining market risk. This is possible for Canadian firms where detailed footnote disclosures permit the calculation of pro forma equity method amounts. The findings are surprising in that whereas proportionally consolidated financial statements are more risk relevant than equity method statements for explaining price volatility, equity method statements are more risk relevant than proportionally consolidated ones for explaining bond ratings. The findings suggest that different market participants use financial statement information differently. The study also finds that failure to disclose disaggregated joint venture accounting amounts, as is the case under US GAAP, masks information that could help market participants assess risk.     

Value-at-risk: Applying the extreme value approach to Asian markets in the recent financial turmoil

Value-at-risk (VaR) measures are generated using extreme value theory by modelling the tails of the return distributions of six Asian financial markets during the recent volatile market conditions. The maxima and minima of these return series were found to be satisfactorily modelled within an extreme value framework and the value at risk measures generated within this structure were found to be different to those generated by variance–covariance and historical methods, particularly for markets characterised by high degrees of leptokurtosis such as Malaysia and Indonesia.