Wong wk 2010 backtesting value at risk based on tail losses. However, if the es captures risks more efficiently than the var, it also has one main downside which is its difficulty to be backtested. Backtesting bootstrap valueatrisk and expected shortfall. Adopting expected shortfall to measure risk, but continuing to use value at risk for backtesting 6. It outlines the models i underlying math, ii daily operation, and iii implementation, while stripping away statistical overhead to keep the concepts accessible. Es n es 0, where es 0 denotes theoretical expected shortfall under the null hypothesis. A simple traffic light approach to backtesting expected.
Pdf individual and flexible expected shortfall backtesting. Given a certain confidence level, this measure represents the expected loss when it is greater than the value of the var calculated with that confidence level. Put it simply, a statistics y of a random variable yis said to be elicitable if it minimizes the expected value of a scoring function s. Backtesting in value at risk is used to compare the predicted losses from the. Backtesting value at risk and expected shortfall books pics. Section 6 presents empirical analyses to examine whether past financial crisis have resulted in the tail risk of var and expected shortfall. Dynamic semiparametric models for expected shortfall and valueatrisk, papers 1707. Backtesting valueatrisk models pdf book manual free download. Hence, banks now face the paradox of using the es for the computation of their market risk capital requirements and the value at risk for the backtesting. Accounting for tail risk article pdf available in management science 634 march 2016 with 1,702 reads how we measure reads. This change is motivated by the appealing theoretical properties of es as a measure of risk and the poor properties of var. Backtesting value at risk and expected shortfall simona roccioletti auth.
In its consultative document on the third basel accord, dated may 3, 2012, the basel committee explicitly. Es, on the other hand, represents the expected value of losses given that losses have exceeded var, and it has been proven to be a coherent risk measure artzner et al. In particular, we propose the use of dieboldmariano 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. However, as the backtesting of the latter is harder than that of the former, valueatrisk remains as the benchmark for regulatory purposes. One of the main requirements and evolutions of the frtb is the switch from a value at risk var to an expected shortfall risk measurement approach. Section 5 adopts simulations with multivariate extreme value distributions7 to examine how tail dependence results in the tail risk of var and expected shortfall. Backtesting, valueatrisk, expected shortfall, volatility forecasting, arch models. They can be impacted by trades that take place during the value at risk horizontrades the value at risk measure. Backtesting trading risk of commercial banks using expected. Forecast combinations for value at risk and expected.
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 wellknown value atrisk var. For risk forecasts like value at risk var and expected shortfall es1, the forecasting process often involves sophisticated models. Backtesting value at risk and expected shortfall series. It uses the expected value of the quantiles of f tx t, transformed through the spectral risk measure for expected shortfall to form an analytical, normally distributed zscore for the average shortfall over tobservations. Using historical data, this example estimates var and es over a test window, using historical and parametric var approaches. You can find a backtest for expected shortfall detailed in the paper below. Backtesting marginal expected shortfall and related systemic. Accounting for tail risk, forthcoming in management science. What is the difference between var and expected shortfall. Expected shortfall is also known as conditional var, or expected tail loss. In recent years, the question of whether expected shortfall is possible to. Forecasting value at risk and expected shortfall with. Jan 14, 2015 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 wellknown value at risk var.
Expected shortfall estimation and backtesting matlab. In this section, some preliminary definitions of var and es are first provided, followed by the definition of the sample es statistic to be used in. Backtesting trading risk of commercial banks using. Recent results have shown backtests of expected shortfall es are necessarily approximated, in the sense that they are unavoidably sensitive to possible errors in the prediction of value at risk. Expectedshortfall,backtests, value at risk,elicitability. Wong wk 2008 backtesting trading risk of commercial banks using expected shortfall. For risk forecasts like value at risk var and expected shortfall es 1, the forecasting process often involves sophisticated models. Backtesting marginal expected shortfall and related systemic risk measures denisa banulescuy, christophe hurlin z, joromy leymarie x, olivier scaillet january 9, 2018 abstract this paper proposes two backtesting tests to assess the validity of the systemic risk measure forecasts.
Risk measures are used for internal control as well as in the supervision of banks by the basel committee of banking supervision. Denisa banulescu, christophe hurlin, joromy leymarie, olivier scaillet house of finance days backtesting marginal expected shortfall. A simple traffic light approach to backtesting expected shortfall. Martin auer, springer, 2018 this book describes a maximally simple market risk model that is still practical, and main risk measures like the valueatrisk and the expected shortfall. The standard var is interpreted as the worst possible loss under normal conditions over a specified period for a given confidence level.
Var is, however, still needed to estimate the tail conditional expectation the es. Backtesting, value atrisk, expected shortfall, volatility forecasting, arch models. Value at risk var is a widely used measure of downside investment risk for a single investment or a portfolio of investments. The valueatrisk var and more generally the distortion risk measures expected shortfall, etc. Currently, portfolio risk is measured in terms of its \ value at risk. If the var is 10 million and the es is 12 million, we know the expected loss tomorrow. Oct 15, 2018 backtesting is a technique for simulating a model or strategy on past data to gauge its accuracy and effectiveness. Carlo acerbi and balazs szekely introduce a backtest for es that minimises such sensitivity.
Expected shortfall is jointly elicitable with value at. Through the transition from value at risk var to expected shortfall es as the primary market risk. However, as the backtesting of the latter is harder than that of the former, value at risk remains as the benchmark for regulatory purposes. 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 wellknown value at risk var. In this paper it is argued that backtesting of expected shortfall or the trading book model from which it is calculated can be based on a simultaneous multinomial test of value at risk var exceptions at di erent. This example shows how to perform estimation and backtesting of expected shortfall models. One of the main requirements and evolutions of the frtb is the switch from a value atrisk var to an expected shortfall risk measurement approach. In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. Section 6 briefly illustrates how the proposed es backtesting could help risk management to be more responsive. Backtesting value at risk and expected shortfall request pdf. Regression based expected shortfall backtesting arxiv. More important, she investigates the issue related to the backtesting of expected shortfall. Backtesting value at risk and expected shortfall simona. Handson valueatrisk and expected shortfall springerlink.
Later, acerbi and tasche 2002 introduced expected shortfall, es, a risk measure that unlike the former is coherent. The model itself is a source of risk in getting inadequate risk estimates, so assessing the model risk of risk measures becomes vital as the pitfalls of inadequate modelling were revealed during the global. Expected shortfall is jointly elicitable with valueatrisk. A multivariate approach cristina danciulescu indiana university bloomington this draft, april 3rd, 2010 abstract the purpose of this paper is to develop a new and simple backtesting procedure that extends the previous work into the multivariate framework. Backtesting value at risk and expected shortfall springerlink. It is for this reason that cvar and expected shortfall are used. When riskmetrics announced valueatrisk var as its stated measure of risk in 1996, it initiated an industry standard for institutional risk management which.
Value at risk var and expected shortfall es must be estimated together because the es estimate depends on the var estimate. Backtesting, value at risk, expected shortfall, volatility forecasting, arch models. But the backtesting procedure also helps the bank to know whether the var or es allocated enough. This measure is used to answer the following question. As a risk measure, value at risk var is neither subadditive nor coherent. Risk measures are used to determine regulatory capital requirements. But no general backtest method for expected shortfall had ever been discovered moreover, many financial experts concluded that expected shortfall cant be backtested because of this debate, the basel committee suggested. Var gives the maximumdollar loss on a portfolio over a specific. This change is motivated by the appealing theoretical properties of es as a measure of risk and the poor ones of var. The null and alternative hypotheses can be written as h 0. The basel rules allow banks to useinternal valueatrisk varmodels to measure market risks in the trading book. Wu wb 2007 mestimation of linear models with dependent errors.
Jp morgans risk metrics, and afterwards by imposition of the basel ii accords. In this paper we propose an expected shortfall es backtesting approach that uses the dispersion of a truncated distribution by the estimated value atrisk var upper limit, does not limit the. This book describes a maximally simple market risk model that is still practical and main risk measures like the value at risk and the expected shortfall. About the application of value at risk var and expected shortfall es as portfolio risk measures. The expected shortfall es or conditional var cvar is a statistic used to quantify the risk of a portfolio. In this paper we propose an expected shortfall es backtesting approach that uses the dispersion of a truncated distribution by the estimated value at risk. Backtesting valueatrisk and expected shortfall in the. Value at risk tells us the minimum loss to expect, but it cannot quantify extreme values passed the threshold. The new standards for the minimum capital requirements for market risk, adopted in 2016 and revised in 2019, introduce a shift from a value at risk var measure to an expected shortfall es measure. We develop a new backtesting framework for expected shortfall by building on the standard value at risk procedure.
Conditional var cvar helps estimate the value of the loss when the loss exceeds the statistical threshold. Risk professionals had never heard of elicitability until 2011, when proved that expected shortfall es is not elicitable as opposed to value at risk var. The model itself is a source of risk in getting inadequate risk estimates, so assessing the model risk of risk measures becomes vital as could be seen during the global financial crisis when the pitfalls of inadequate modelling were. Backtesting expected shortfall via multiquantile regression, working papers halshs01909375, hal. Expected shortfall is jointly elicitable with value at risk. The main contribution of the work is the application of test 1 and test 2 developed by acerbi and szekely 2014 on different models and for five global market indexes. Abstract in recent years, the question of whether expected shortfall is possible to backtesthasbeenahottopicafterthe. The basel committees frtb proposes to replace value at risk var at 99% by expected shortfall es at 97. Firstly, a great deal of literature has focused on tail risk based on value at risk var estimates, although this measure fails to meet the requirements of a coherent risk metric as defined by artzner, delbaen, eber, and heath 1999. The value at risk var and more generally the distortion risk measures expected shortfall, etc.
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