Strong regulatory actions are needed to combat climate change, but climate policy uncertainty makes it difficult for investors to quantify the impact of future climate regulation. We show that such uncertainty is priced in the option market. The cost of option protection against downside tail risks is larger for firms with more carbon-intense business models. For carbon-intense firms, the cost of protection against downside tail risk is magnified at times when the public’s attention to climate change spikes, and it decreased after the election of climate change skeptic President Trump.
{"title":"Carbon Tail Risk","authors":"Emirhan Ilhan, Z. Sautner, G. Vilkov","doi":"10.2139/ssrn.3204420","DOIUrl":"https://doi.org/10.2139/ssrn.3204420","url":null,"abstract":"\u0000 Strong regulatory actions are needed to combat climate change, but climate policy uncertainty makes it difficult for investors to quantify the impact of future climate regulation. We show that such uncertainty is priced in the option market. The cost of option protection against downside tail risks is larger for firms with more carbon-intense business models. For carbon-intense firms, the cost of protection against downside tail risk is magnified at times when the public’s attention to climate change spikes, and it decreased after the election of climate change skeptic President Trump.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134268654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We employ the R-vine copula approach to study the dependence structures among non-ferrous metal commodity futures on the London Metal Exchange, focusing on the comparison before and after the 2008 financial crisis. We document that the center of dependence structure among non-ferrous metal futures has changed from copper to zinc after the crisis. We find that the risk diversification benefit among non-ferrous metals diminishes after the crisis, and there is a significantly increase in their tail dependence. We further develop a R-vine copula-based method for forecasting Value-at-Risk, and the back-testing results show superior forecast accuracy over benchmark methods. Our study is useful for market participants to enhance their risk management for non-ferrous metals.
{"title":"A R-Vine Copula Analysis of Non-ferrous Metal Futures with Application in Forecasting Value-at-Risk","authors":"Xuyuan Han, Zhenya Liu, Shixuan Wang","doi":"10.2139/ssrn.3619728","DOIUrl":"https://doi.org/10.2139/ssrn.3619728","url":null,"abstract":"We employ the R-vine copula approach to study the dependence structures among non-ferrous metal commodity futures on the London Metal Exchange, focusing on the comparison before and after the 2008 financial crisis. We document that the center of dependence structure among non-ferrous metal futures has changed from copper to zinc after the crisis. We find that the risk diversification benefit among non-ferrous metals diminishes after the crisis, and there is a significantly increase in their tail dependence. We further develop a R-vine copula-based method for forecasting Value-at-Risk, and the back-testing results show superior forecast accuracy over benchmark methods. Our study is useful for market participants to enhance their risk management for non-ferrous metals.<br>","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122167885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper we introduce a new distortion risk measure that is motivated by the equivalence made by the regulator between the using the CVaR of 97.5 percent instead of VaR of 99 percent. We introduce a distortion function that matches the value of the normal quantiles with the same for CVaR. We also study this distortion and show it's convex and that it is more risk averse than Wang's distortion.
{"title":"Regulatory Distortions and Alternatives","authors":"H. Assa","doi":"10.2139/ssrn.3611878","DOIUrl":"https://doi.org/10.2139/ssrn.3611878","url":null,"abstract":"Abstract In this paper we introduce a new distortion risk measure that is motivated by the equivalence made by the regulator between the using the CVaR of 97.5 percent instead of VaR of 99 percent. We introduce a distortion function that matches the value of the normal quantiles with the same for CVaR. We also study this distortion and show it's convex and that it is more risk averse than Wang's distortion.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127921390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In competitive capital markets, portfolios of risky debt claims have high systematic risk exposure in bad times if they offer a high "yield" in good times. We apply this idea to measurement of bank risk. Rather than trying to directly measure asset risks on the balance sheet — the typical (manipulation-prone) approach in model-based regulation — we explore high rates of profit in good times as an indicator of systematic tail risk exposure. We show empirically, for cross-sections of banks in the financial crisis of 2007–2008 as well as the savings and loan crisis of the 1980s, that high accounting profitability prior to the crisis predicts high systematic tail risk of equity market values during the crisis, and most strongly so if pre-crisis profits arise from non-interest income or are paid out as dividends and managerial compensation. Pre-crisis profit measures do a better job in predicting systematic tail risk than conventional measures based on risk-weighted assets.
{"title":"Judging Banks' Risk by the Profits They Report","authors":"Ben S. Meiselman, S. Nagel, A. Purnanandam","doi":"10.2139/ssrn.3169730","DOIUrl":"https://doi.org/10.2139/ssrn.3169730","url":null,"abstract":"In competitive capital markets, portfolios of risky debt claims have high systematic risk exposure in bad times if they offer a high \"yield\" in good times. We apply this idea to measurement of bank risk. Rather than trying to directly measure asset risks on the balance sheet — the typical (manipulation-prone) approach in model-based regulation — we explore high rates of profit in good times as an indicator of systematic tail risk exposure. We show empirically, for cross-sections of banks in the financial crisis of 2007–2008 as well as the savings and loan crisis of the 1980s, that high accounting profitability prior to the crisis predicts high systematic tail risk of equity market values during the crisis, and most strongly so if pre-crisis profits arise from non-interest income or are paid out as dividends and managerial compensation. Pre-crisis profit measures do a better job in predicting systematic tail risk than conventional measures based on risk-weighted assets.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114035331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we refer to the axiomatic theory of risk and investigate the problem of formal verification of the expected shortfall (ES) model based on a sample ES. Recognizing the infeasibility of parametric methods, we explore the bootstrap technique, which, unlike the current value-at-risk model-based (VaR model-based) Basel III testing framework, permits the creation of more powerful sample ES-based procedures. Our contribution to the debate on the possibilities of sample ES-based testing is twofold. First, we introduce a bootstrap test based on the idea of ES prediction corrected variables. In this way, we obtain a procedure that makes no distributional assumptions about the underlying returns process, and whose p-value computation does not assume any asymptotic convergence. Second, we provide a unifying framework for ES value verification, in which we compare alternative sample ES-based approaches: the residual-based procedures versus the ES prediction corrected tests as well as the VaR model-dependent approach versus the fixed failure rate tests. By examining its statistical properties and practical applicability, we find evidence that the proposed bootstrap procedure, based on ES prediction corrected variables, is superior to other methods. This provides important guidance for developing international standards of market risk management.
{"title":"Extremal Risk Management: Expected Shortfall Value Verification Using the Bootstrap Method","authors":"Marta Małecka","doi":"10.21314/jcf.2020.380","DOIUrl":"https://doi.org/10.21314/jcf.2020.380","url":null,"abstract":"In this paper, we refer to the axiomatic theory of risk and investigate the problem of formal verification of the expected shortfall (ES) model based on a sample ES. Recognizing the infeasibility of parametric methods, we explore the bootstrap technique, which, unlike the current value-at-risk model-based (VaR model-based) Basel III testing framework, permits the creation of more powerful sample ES-based procedures. Our contribution to the debate on the possibilities of sample ES-based testing is twofold. First, we introduce a bootstrap test based on the idea of ES prediction corrected variables. In this way, we obtain a procedure that makes no distributional assumptions about the underlying returns process, and whose p-value computation does not assume any asymptotic convergence. Second, we provide a unifying framework for ES value verification, in which we compare alternative sample ES-based approaches: the residual-based procedures versus the ES prediction corrected tests as well as the VaR model-dependent approach versus the fixed failure rate tests. By examining its statistical properties and practical applicability, we find evidence that the proposed bootstrap procedure, based on ES prediction corrected variables, is superior to other methods. This provides important guidance for developing international standards of market risk management.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116301365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Insolvency often precedes default for nonpayment of debt. A firm is instantaneously insolvent whenever the market value of its assets is below the face value of its debt. Default occurs when the firm is instantaneously insolvent when the firm's debt matures. The natural log of the ratio of the market value of assets to face value of debt measures distance to insolvency (or degree of insolvency) in the Black-Scholes formula and Merton distance to default. The measure is useful outside of the restrictive conditions of option pricing theory. It is negative for instantaneously insolvent firms, zero for firms at the border of solvency and insolvency, and positive for an instantaneously solvent firm.
{"title":"Distance to Insolvency","authors":"J. B. Heaton","doi":"10.2139/ssrn.3485325","DOIUrl":"https://doi.org/10.2139/ssrn.3485325","url":null,"abstract":"Insolvency often precedes default for nonpayment of debt. A firm is instantaneously insolvent whenever the market value of its assets is below the face value of its debt. Default occurs when the firm is instantaneously insolvent when the firm's debt matures. The natural log of the ratio of the market value of assets to face value of debt measures distance to insolvency (or degree of insolvency) in the Black-Scholes formula and Merton distance to default. The measure is useful outside of the restrictive conditions of option pricing theory. It is negative for instantaneously insolvent firms, zero for firms at the border of solvency and insolvency, and positive for an instantaneously solvent firm.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124010455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the recent Fundamental Review of the Trading Book (FRTB), the Basel Committee on Banking Supervision proposed the shift from the 99% Value-at-Risk (VaR) to the 97.5% Expected Shortfall (ES) for internal models in market risk assessment. Inspired by the above transition, we introduce a new distributional index, the probability equivalence level of VaR and ES (PELVE), which identifies the balancing point for the equivalence between VaR and ES. PELVE enjoys many desirable theoretical properties and it distinguishes empirically heavy-tailed distributions from light-tailed ones via a threshold of 2.72. Convergence properties and asymptotic normality of the empirical PELVE estimators are established. Applying PELVE to financial asset and portfolio data leads to interesting observations that are not captured by VaR or ES alone. We find that, in general, the transition from VaR to ES in the FRTB yields an increase in risk capital for single-asset portfolios, but for well-diversified portfolios, the capital requirement remains almost unchanged. This leads to both a theoretical justification and an empirical evidence for the conclusion that the use of ES rewards portfolio diversification more than the use of VaR.
{"title":"PELVE: Probability Equivalent Level of VaR and ES","authors":"Hanson Li, Ruodu Wang","doi":"10.2139/ssrn.3489566","DOIUrl":"https://doi.org/10.2139/ssrn.3489566","url":null,"abstract":"In the recent Fundamental Review of the Trading Book (FRTB), the Basel Committee on Banking Supervision proposed the shift from the 99% Value-at-Risk (VaR) to the 97.5% Expected Shortfall (ES) for internal models in market risk assessment. Inspired by the above transition, we introduce a new distributional index, the probability equivalence level of VaR and ES (PELVE), which identifies the balancing point for the equivalence between VaR and ES. PELVE enjoys many desirable theoretical properties and it distinguishes empirically heavy-tailed distributions from light-tailed ones via a threshold of 2.72. Convergence properties and asymptotic normality of the empirical PELVE estimators are established. Applying PELVE to financial asset and portfolio data leads to interesting observations that are not captured by VaR or ES alone. We find that, in general, the transition from VaR to ES in the FRTB yields an increase in risk capital for single-asset portfolios, but for well-diversified portfolios, the capital requirement remains almost unchanged. This leads to both a theoretical justification and an empirical evidence for the conclusion that the use of ES rewards portfolio diversification more than the use of VaR.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127253175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Value at risk (VaR) and expected shortfall (ES) are two of the most widely used risk measures in economics and finance. In this paper, we use a semiparametric method, together with realized variance measures, to jointly estimate structural models for the two risk measures. The semiparametric estimations rely on using a class of consistent loss functions recently proposed by Fissler and Ziegel (2016). We develop an efficient and stable two-stage method to implement the estimations. We then compare out-of-sample forecast performances from the estimated structural models with other existing methods. Through comprehensive evaluations with different performance measures, we find the proposed models featuring with the realized variance measures as exogenous variables can deliver comparable or even better performances on forecasting VaR and ES of major stock indices around the world than the existing methods.
{"title":"Forecasting Expected Shortfall and Value-at-Risk with the FZ Loss and Realized Variance Measures","authors":"R. Chou, T. Yen, Yu-Min Yen","doi":"10.2139/ssrn.3448882","DOIUrl":"https://doi.org/10.2139/ssrn.3448882","url":null,"abstract":"Value at risk (VaR) and expected shortfall (ES) are two of the most widely used risk measures in economics and finance. In this paper, we use a semiparametric method, together with realized variance measures, to jointly estimate structural models for the two risk measures. The semiparametric estimations rely on using a class of consistent loss functions recently proposed by Fissler and Ziegel (2016). We develop an efficient and stable two-stage method to implement the estimations. We then compare out-of-sample forecast performances from the estimated structural models with other existing methods. Through comprehensive evaluations with different performance measures, we find the proposed models featuring with the realized variance measures as exogenous variables can deliver comparable or even better performances on forecasting VaR and ES of major stock indices around the world than the existing methods.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"58-60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123124751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose forecast encompassing tests for the Expected Shortfall (ES) jointly with the Value at Risk (VaR) based on flexible link (or combination) functions. Our setup allows testing encompassing for convex forecast combinations and for link functions which preclude crossings of the combined VaR and ES forecasts. As the tests based on these link functions involve parameters which are on the boundary of the parameter space under the null hypothesis, we derive and base our tests on nonstandard asymptotic theory on the boundary. Our simulation study shows that the encompassing tests based on our new link functions outperform tests based on unrestricted linear link functions for one-step and multi-step forecasts. We further illustrate the potential of the proposed tests in a real data analysis for forecasting VaR and ES of the S&P 500 index.
{"title":"Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary [Previous title: \"A Regression-based Joint Encompassing Test for Value-at-Risk and Expected Shortfall Forecasts\"]","authors":"Timo Dimitriadis, Xiaochun Liu, Julie Schnaitmann","doi":"10.2139/ssrn.3497321","DOIUrl":"https://doi.org/10.2139/ssrn.3497321","url":null,"abstract":"We propose forecast encompassing tests for the Expected Shortfall (ES) jointly with the Value at Risk (VaR) based on flexible link (or combination) functions. Our setup allows testing encompassing for convex forecast combinations and for link functions which preclude crossings of the combined VaR and ES forecasts. As the tests based on these link functions involve parameters which are on the boundary of the parameter space under the null hypothesis, we derive and base our tests on nonstandard asymptotic theory on the boundary. Our simulation study shows that the encompassing tests based on our new link functions outperform tests based on unrestricted linear link functions for one-step and multi-step forecasts. We further illustrate the potential of the proposed tests in a real data analysis for forecasting VaR and ES of the S&P 500 index.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117204213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The challenge of using small sample sizes for operational risk capital models fitted via maximum likelihood estimation is well recognized, yet the literature generally provides warning examples rather than a systematic approach. We present a general framework for analyzing maximum likelihood estimation error on operational value-at-risk as a function of sample size for five severity distributions commonly used in operational risk capital models. More specifically, we study the estimation error along three dimensions: the choice of severity distribution, the sample size and the heaviness of the underlying losses. We apply these results to model selection and explore implications for operational risk modeling.
{"title":"Maximum Likelihood Estimation Error and Operational Value-at-Risk Stability","authors":"Paul L. Larsen","doi":"10.21314/JOP.2018.217","DOIUrl":"https://doi.org/10.21314/JOP.2018.217","url":null,"abstract":"The challenge of using small sample sizes for operational risk capital models fitted via maximum likelihood estimation is well recognized, yet the literature generally provides warning examples rather than a systematic approach. We present a general framework for analyzing maximum likelihood estimation error on operational value-at-risk as a function of sample size for five severity distributions commonly used in operational risk capital models. More specifically, we study the estimation error along three dimensions: the choice of severity distribution, the sample size and the heaviness of the underlying losses. We apply these results to model selection and explore implications for operational risk modeling.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134501168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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