Expected shortfall es is the expected loss on days when there is a value at risk var failure. Expected shortfall is also known as conditional var, or expected tail loss. Currently, portfolio risk is measured in terms of its \ value at risk. Backtesting, value atrisk, expected shortfall, volatility forecasting, arch models. Carlo acerbi and balazs szekely introduce a backtest for es that minimises such sensitivity.
Expected shortfall is jointly elicitable with value at risk. 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. 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. Through the transition from value at risk var to expected shortfall es as the primary market risk. Backtesting marginal expected shortfall and related systemic. 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. Wong wk 2008 backtesting trading risk of commercial banks using expected shortfall. A simple traffic light approach to backtesting expected. 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. This change is motivated by the appealing theoretical properties of es as a measure of risk and the poor ones of var. More important, she investigates the issue related to the backtesting of expected shortfall. 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.
For risk forecasts like value at risk var and expected shortfall es1, the forecasting process often involves sophisticated models. Forecast combinations for value at risk and expected. Expectedshortfall,backtests, value at risk,elicitability. Forecasting value at risk and expected shortfall with. 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. In its consultative document on the third basel accord, dated may 3, 2012, the basel committee explicitly. This example shows how to perform estimation and backtesting of expected shortfall models. About the application of value at risk var and expected shortfall es as portfolio risk measures. The valueatrisk var and more generally the distortion risk measures expected shortfall, etc. Wu wb 2007 mestimation of linear models with dependent errors. Accounting for tail risk, forthcoming in management science. Var is, however, still needed to estimate the tail conditional expectation the es. Expected shortfall is jointly elicitable with value at.
The basel committees frtb proposes to replace value at risk var at 99% by expected shortfall es at 97. Regression based expected shortfall backtesting arxiv. Backtesting, value at risk, expected shortfall, volatility forecasting, arch models. You can find a backtest for expected shortfall detailed in the paper below. Es n es 0, where es 0 denotes theoretical expected shortfall under the null hypothesis. 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. Denisa banulescu, christophe hurlin, joromy leymarie, olivier scaillet house of finance days backtesting marginal expected shortfall.
We develop a new backtesting framework for expected shortfall by building on the standard value at risk procedure. Backtesting expected shortfall via multiquantile regression, working papers halshs01909375, hal. Oct 15, 2018 backtesting is a technique for simulating a model or strategy on past data to gauge its accuracy and effectiveness. Hence, banks now face the paradox of using the es for the computation of their market risk capital requirements and the value atrisk for the backtesting. 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. 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. For risk forecasts like value at risk var and expected shortfall es 1, the forecasting process often involves sophisticated models. Wong wk 2010 backtesting value at risk based on tail losses. 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. They can be impacted by trades that take place during the value at risk horizontrades the value at risk measure. Value at risk tells us the minimum loss to expect, but it cannot quantify extreme values passed the threshold. However, as the backtesting of the latter is harder than that of the former, valueatrisk remains as the benchmark for regulatory purposes. However, as the backtesting of the latter is harder than that of the former, value at risk remains as the benchmark for regulatory purposes.
Backtesting value at risk and expected shortfall springerlink. If the var is 10 million and the es is 12 million, we know the expected loss tomorrow. When riskmetrics announced valueatrisk var as its stated measure of risk in 1996, it initiated an industry standard for institutional risk management which. It is for this reason that cvar and expected shortfall are used. Backtesting value at risk and expected shortfall series. Backtesting valueatrisk and expected shortfall in the. 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. Accounting for tail risk article pdf available in management science 634 march 2016 with 1,702 reads how we measure reads. 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. Var gives the maximumdollar loss on a portfolio over a specific. Backtesting value at risk and expected shortfall books pics. The null and alternative hypotheses can be written as h 0.
But the backtesting procedure also helps the bank to know whether the var or es allocated enough. 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. Backtesting value at risk and expected shortfall simona roccioletti auth. 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. Section 5 adopts simulations with multivariate extreme value distributions7 to examine how tail dependence results in the tail risk of var and expected shortfall. 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. Backtesting in value at risk is used to compare the predicted losses from the. Expected shortfall is jointly elicitable with value at risk implications for backtesting risk, 5 2016, pp. The basel rules allow banks to useinternal valueatrisk varmodels to measure market risks in the trading book. Backtesting value at risk and expected shortfall request pdf. Conditional var cvar helps estimate the value of the loss when the loss exceeds the statistical threshold. The standard var is interpreted as the worst possible loss under normal conditions over a specified period for a given confidence level. Adopting expected shortfall to measure risk, but continuing to use value at risk for backtesting 6. Backtesting value at risk and expected shortfall simona.
Backtesting trading risk of commercial banks using. 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. 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. 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. Risk measures are used to determine regulatory capital requirements. What is the difference between var and expected shortfall. 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 valueatrisk models pdf book manual free download. This measure is used to answer the following question. As a risk measure, value at risk var is neither subadditive nor coherent. 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.
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. 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. Backtesting trading risk of commercial banks using expected. In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. Backtesting bootstrap valueatrisk and expected shortfall. Abstract in recent years, the question of whether expected shortfall is possible to backtesthasbeenahottopicafterthe. 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. It outlines the models i underlying math, ii daily operation, and iii implementation, while stripping away statistical overhead to keep the concepts accessible. Backtesting, valueatrisk, expected shortfall, volatility forecasting, arch models. A simple traffic light approach to backtesting expected shortfall. Using historical data, this example estimates var and es over a test window, using historical and parametric var approaches. 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. In recent years, the question of whether expected shortfall is possible to. Risk measures are used for internal control as well as in the supervision of banks by the basel committee of banking supervision.
Handson valueatrisk and expected shortfall springerlink. The value at risk var and more generally the distortion risk measures expected shortfall, etc. Pdf individual and flexible expected shortfall backtesting. The expected shortfall es or conditional var cvar is a statistic used to quantify the risk of a portfolio. 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. This proposal has initiated a controversial debate in the academy and financial industry about the appropriateness of such measure, mainly due to its troublesome backtesting implementation. This change is motivated by the appealing theoretical properties of es as a measure of risk and the poor properties of var.
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. Value at risk var is a widely used measure of downside investment risk for a single investment or a portfolio of investments. 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. Expected shortfall is jointly elicitable with valueatrisk. Expected shortfall estimation and backtesting matlab. 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. Section 6 briefly illustrates how the proposed es backtesting could help risk management to be more responsive. Jp morgans risk metrics, and afterwards by imposition of the basel ii accords.
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