We propose a new backtesting framework for expected shortfall (ES) that can be used by regulators. Instead of looking at estimated capital reserve and realized cashflow separately, one can bind them into a secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of ES with respect to its target confidence level, we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realizations for the secured position that adds up to a negative total. Surprisingly, this simple quantity can be used to construct an efficient backtesting framework for unconditional coverage of ES in a natural extension of the regulatory traffic-light approach for value-at-risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures.
{"title":"Backtesting expected shortfall: a simple recipe?","authors":"Felix Moldenhauer, Marcin Pitera","doi":"10.21314/jor.2019.418","DOIUrl":"https://doi.org/10.21314/jor.2019.418","url":null,"abstract":"We propose a new backtesting framework for expected shortfall (ES) that can be used by regulators. Instead of looking at estimated capital reserve and realized cashflow separately, one can bind them into a secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of ES with respect to its target confidence level, we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realizations for the secured position that adds up to a negative total. Surprisingly, this simple quantity can be used to construct an efficient backtesting framework for unconditional coverage of ES in a natural extension of the regulatory traffic-light approach for value-at-risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"6 21","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric versus parametric expected shortfall","authors":"R. Douglas Martin,Shengyu Zhang","doi":"10.21314/jor.2019.416","DOIUrl":"https://doi.org/10.21314/jor.2019.416","url":null,"abstract":"","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"24 1","pages":"1-41"},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138517037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rating migrations of US financial institutions: are different outcomes equivalent?","authors":"Huong Dieu Dang","doi":"10.21314/jor.2019.421","DOIUrl":"https://doi.org/10.21314/jor.2019.421","url":null,"abstract":"","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67718288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the new class of Performance measures Adjusted for the Risk Situation (PARS), which incorporate individual risk characteristics in the financial performance measure. The (risk) situation of an individual or company is represented by all of its future cash flows including (financial) consumption preferences; due to the effected risk transformation, PARS have zero volatility under the investment strategy replicating these future cash flows. We give several examples of cash flow structures for individuals and companies, showing how their PARS could be defined. In the context of a debt manager, we demonstrate how the PARS can be applied to the dynamic control of bond portfolios via sensitivities.
{"title":"Performance Measures Adjusted for the Risk Situation (PARS)","authors":"Christoph Peters, R. Seydel","doi":"10.2139/ssrn.3277693","DOIUrl":"https://doi.org/10.2139/ssrn.3277693","url":null,"abstract":"We introduce the new class of Performance measures Adjusted for the Risk Situation (PARS), which incorporate individual risk characteristics in the financial performance measure. The (risk) situation of an individual or company is represented by all of its future cash flows including (financial) consumption preferences; due to the effected risk transformation, PARS have zero volatility under the investment strategy replicating these future cash flows. \u0000We give several examples of cash flow structures for individuals and companies, showing how their PARS could be defined. In the context of a debt manager, we demonstrate how the PARS can be applied to the dynamic control of bond portfolios via sensitivities.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44576634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a new interest rate risk measure that is a product of two factors: one related to the distance between assets and liabilities in the Lp -space of financial instruments, and the other linked to the performance of the financial market. We prove a corresponding immunization inequality, showing that the expected deficit of assets, when compared with liabilities, is bounded from below by a linear function of this measure. We provide comparisons with other interest rate risk measures, such as duration gap and M2 , and give examples of applications to some models of interest rates.
{"title":"Balance-Sheet Interest Rate Risk: A Weighted Lp Approach","authors":"L. Gajek, Elżbieta Krajewska","doi":"10.21314/JOR.2018.395","DOIUrl":"https://doi.org/10.21314/JOR.2018.395","url":null,"abstract":"We introduce a new interest rate risk measure that is a product of two factors: one related to the distance between assets and liabilities in the Lp -space of financial instruments, and the other linked to the performance of the financial market. We prove a corresponding immunization inequality, showing that the expected deficit of assets, when compared with liabilities, is bounded from below by a linear function of this measure. We provide comparisons with other interest rate risk measures, such as duration gap and M2 , and give examples of applications to some models of interest rates.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48580753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
While value-at-risk has been the standard risk measure for a long time, expected shortfall (ES) has become more and more popular in recent times, as it provides important information about tail risk. We present a new backtest for the unconditional coverage property of the ES. The test is based on the so-called cumulative violation process, and its main advantage is that the distribution is known for finite out-of-sample size. This leads to better size and power properties compared with existing tests. Moreover, we extend the test principle to a multivariate test and analyze its behavior via simulations and an application to bank returns.
{"title":"New Backtests for Unconditional Coverage of Expected Shortfall","authors":"Robert Löser, Dominik Wied, D. Ziggel","doi":"10.17877/DE290R-17329","DOIUrl":"https://doi.org/10.17877/DE290R-17329","url":null,"abstract":"While value-at-risk has been the standard risk measure for a long time, expected shortfall (ES) has become more and more popular in recent times, as it provides important information about tail risk. We present a new backtest for the unconditional coverage property of the ES. The test is based on the so-called cumulative violation process, and its main advantage is that the distribution is known for finite out-of-sample size. This leads to better size and power properties compared with existing tests. Moreover, we extend the test principle to a multivariate test and analyze its behavior via simulations and an application to bank returns.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48620978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation for resulting risk measures from the properties of both alternative functionals and combination functions. To that, we build on the development of a representation for arbitrary mixture of convex risk measures. In this case, we obtain a penalty that recalls the notion of inf-convolution under theoretical measure integration. As an application, we address the context of probability-based risk measurements for functionals on the set of distribution functions. We develop results related to this specific context. We also explore features of individual interest generated by our framework, such as the preservation of continuity properties, the representation of worst-case risk measures, stochastic dominance and elicitability. We also address model uncertainty measurement under our framework and propose a new class of measures for this task.
{"title":"A theory for combinations of risk measures","authors":"M. Righi","doi":"10.21314/JOR.2022.054","DOIUrl":"https://doi.org/10.21314/JOR.2022.054","url":null,"abstract":"We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation for resulting risk measures from the properties of both alternative functionals and combination functions. To that, we build on the development of a representation for arbitrary mixture of convex risk measures. In this case, we obtain a penalty that recalls the notion of inf-convolution under theoretical measure integration. As an application, we address the context of probability-based risk measurements for functionals on the set of distribution functions. We develop results related to this specific context. We also explore features of individual interest generated by our framework, such as the preservation of continuity properties, the representation of worst-case risk measures, stochastic dominance and elicitability. We also address model uncertainty measurement under our framework and propose a new class of measures for this task.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44566720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Order flow toxicity is a measure of a trader's exposure to the risk that counter-parties possess private information or other informational advantages. High levels of order flow toxicity can culminate in market makers providing liquidity at a loss or in suboptimal execution of trades. From a regulatory perspective, high levels of toxicity can be harmful to overall market liquidity and precede precipitous drops in asset prices. Bulk Volume VPIN (BV-VPIN) is one way of measuring the "toxicity" component of order flow that has been successfully applied in High Frequency Trading (HFT) environments. We apply the BV-VPIN to daily data for a range of international indices to extend previous analysis of its properties. We find that a rise in BV-VPIN effectively foreshadows high-levels of volatility in the equities indices of several countries. If a BV-VPIN futures contract exists, we show that it would exhibit safe haven characteristics during market downturns. In particular, a simple active portfolio management strategy that times investments in equities (risk-free asset) when BV-VPIN levels are low (high) outperforms a buy-and-hold strategy. Thus, we find support for the application of BV-VPIN in international equities.
{"title":"BV–VPIN: Measuring the Impact of Order Flow Toxicity and Liquidity on International Equity Markets","authors":"R. Low, Te Li, Terry A. Marsh","doi":"10.21314/JOR.2018.399","DOIUrl":"https://doi.org/10.21314/JOR.2018.399","url":null,"abstract":"Order flow toxicity is a measure of a trader's exposure to the risk that counter-parties possess private information or other informational advantages. High levels of order flow toxicity can culminate in market makers providing liquidity at a loss or in suboptimal execution of trades. From a regulatory perspective, high levels of toxicity can be harmful to overall market liquidity and precede precipitous drops in asset prices. Bulk Volume VPIN (BV-VPIN) is one way of measuring the \"toxicity\" component of order flow that has been successfully applied in High Frequency Trading (HFT) environments. We apply the BV-VPIN to daily data for a range of international indices to extend previous analysis of its properties. We find that a rise in BV-VPIN effectively foreshadows high-levels of volatility in the equities indices of several countries. If a BV-VPIN futures contract exists, we show that it would exhibit safe haven characteristics during market downturns. In particular, a simple active portfolio management strategy that times investments in equities (risk-free asset) when BV-VPIN levels are low (high) outperforms a buy-and-hold strategy. Thus, we find support for the application of BV-VPIN in international equities.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47362503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Catalina Bolancé, Ramon Alemany, Alemar E. Padilla Barreto
In this paper, a sensitivity analysis using pair–copula decomposition of multivariate dependency models is performed on estimates of value-at-risk (VaR) and conditional value-at-risk (CVaR). To illustrate the results, we use four financial share portfolios selected to exemplify this purpose. For each share, we calculate filtered log returns using autoregressive moving average–generalized autoregressive conditional heteroscedasticity models and study their dependence. We analyze how selecting pairs of assets to define vines prior to pair–copula decomposition affects the estimated VaR and CVaR. Further, using bootstrap confidence intervals, we compare the results of different risk measures obtained by employing alternative measures of dependence to select the order in which the drawable vine (D-vine) is defined in different portfolios. Moreover, we carry out a simulation study to analyze the finite sample properties of the different criteria for selecting the pair–copula decomposition associated with the D-vine. We find some differences between the results obtained for VaR and CVaR.
{"title":"Impact of D-Vine Structure on Risk Estimation","authors":"Catalina Bolancé, Ramon Alemany, Alemar E. Padilla Barreto","doi":"10.21314/JOR.2018.384","DOIUrl":"https://doi.org/10.21314/JOR.2018.384","url":null,"abstract":"In this paper, a sensitivity analysis using pair–copula decomposition of multivariate dependency models is performed on estimates of value-at-risk (VaR) and conditional value-at-risk (CVaR). To illustrate the results, we use four financial share portfolios selected to exemplify this purpose. For each share, we calculate filtered log returns using autoregressive moving average–generalized autoregressive conditional heteroscedasticity models and study their dependence. We analyze how selecting pairs of assets to define vines prior to pair–copula decomposition affects the estimated VaR and CVaR. Further, using bootstrap confidence intervals, we compare the results of different risk measures obtained by employing alternative measures of dependence to select the order in which the drawable vine (D-vine) is defined in different portfolios. Moreover, we carry out a simulation study to analyze the finite sample properties of the different criteria for selecting the pair–copula decomposition associated with the D-vine. We find some differences between the results obtained for VaR and CVaR.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46566817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Systemic risk is the risk that the defaults of one or more institutions trigger a collapse of the entire financial system. In this paper, we propose a measure for systemic risk, CoCVaR, the conditional value-at-risk (CVaR) of the financial system conditional on an institution being in financial distress. This measure is similar to Adrian and Brunnermeier’s CoVaR from 2008, but we change the systemic risk from VaR to CVaR. This measure considers severe losses of the financial system beyond VaR. CoCVaR is estimated using CVaR (superquantile) regression. We define the systemic risk contribution of an institution as the difference between CoCVaR conditional on the institution being under distress and the CoCVaR in the median state of the institution. We estimate the systemic risk contributions of the ten largest publicly traded banks in the United States for a sample period February 2000 to January 2015 and compare CoCVaR and CoVaR risk contributions for this period. We find that the new CoCVaR provides a unique perspective on the systemic risk contribution.
{"title":"The CoCVaR Approach: Systemic Risk Contribution Measurement","authors":"Wei-Qiang Huang, S. Uryasev","doi":"10.21314/JOR.2018.383","DOIUrl":"https://doi.org/10.21314/JOR.2018.383","url":null,"abstract":"Systemic risk is the risk that the defaults of one or more institutions trigger a collapse of the entire financial system. In this paper, we propose a measure for systemic risk, CoCVaR, the conditional value-at-risk (CVaR) of the financial system conditional on an institution being in financial distress. This measure is similar to Adrian and Brunnermeier’s CoVaR from 2008, but we change the systemic risk from VaR to CVaR. This measure considers severe losses of the financial system beyond VaR. CoCVaR is estimated using CVaR (superquantile) regression. We define the systemic risk contribution of an institution as the difference between CoCVaR conditional on the institution being under distress and the CoCVaR in the median state of the institution. We estimate the systemic risk contributions of the ten largest publicly traded banks in the United States for a sample period February 2000 to January 2015 and compare CoCVaR and CoVaR risk contributions for this period. We find that the new CoCVaR provides a unique perspective on the systemic risk contribution.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43383989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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