We assess the quantitative effects of the recent proposal for more robust bank capital adequacy. Our theoretical proof and evidence accord with the core thesis that banks become more stable by increasing their equity capital cushion to absorb extreme losses in times of severe financial stress. This analysis contributes to the ongoing policy debate on total capital adequacy. Our Monte Carlo simulation helps develop an analytical solution for the default probability adjustment through the macroeconomic cycle. This study poses a conceptual challenge to the normative view that banks should maintain high leverage over time.
{"title":"Bank leverage and capital bias adjustment through the macroeconomic cycle","authors":"Andy Jia-Yuh Yeh","doi":"10.21314/jor.2020.442","DOIUrl":"https://doi.org/10.21314/jor.2020.442","url":null,"abstract":"We assess the quantitative effects of the recent proposal for more robust bank capital adequacy. Our theoretical proof and evidence accord with the core thesis that banks become more stable by increasing their equity capital cushion to absorb extreme losses in times of severe financial stress. This analysis contributes to the ongoing policy debate on total capital adequacy. Our Monte Carlo simulation helps develop an analytical solution for the default probability adjustment through the macroeconomic cycle. This study poses a conceptual challenge to the normative view that banks should maintain high leverage over time.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"6 15","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494965","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":"Bias-corrected estimators for the Vasicek model: an application in risk measure estimation","authors":"Zi‐Yi Guo","doi":"10.21314/JOR.2020.445","DOIUrl":"https://doi.org/10.21314/JOR.2020.445","url":null,"abstract":"","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"1 1","pages":"71-104"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67718328","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}
M. A. Arias-Serna, F. Caro-Lopera, Jean-Michel Loubes
This paper develops a method for estimating value-at-risk and conditional value-at-risk when the underlying risk factors follow a beta distribution in a univariate and a matrix-variate setting. For this purpose, we connect the theory of the Gaussian hypergeometric function of matrix argument and integration over positive definite matrixes. For certain choices of the shape parameters, a and b, analytical expressions of the risk measures are developed. More generally, a numerical solution for the risk measures for any parameterization of beta-distributed loss variables is presented. The proposed risk measures are finally used for quantifying the potential risk of economic loss in credit risk.
{"title":"Risk Measures: A Generalization from the Univariate to the Matrix-variate","authors":"M. A. Arias-Serna, F. Caro-Lopera, Jean-Michel Loubes","doi":"10.21314/JOR.2021.003","DOIUrl":"https://doi.org/10.21314/JOR.2021.003","url":null,"abstract":"This paper develops a method for estimating value-at-risk and conditional value-at-risk when the underlying risk factors follow a beta distribution in a univariate and a matrix-variate setting. For this purpose, we connect the theory of the Gaussian hypergeometric function of matrix argument and integration over positive definite matrixes. For certain choices of the shape parameters, a and b, analytical expressions of the risk measures are developed. More generally, a numerical solution for the risk measures for any parameterization of beta-distributed loss variables is presented. The proposed risk measures are finally used for quantifying the potential risk of economic loss in credit risk.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46399054","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}
Understanding the maturity profiles of nonmaturing deposits is vital to assess a bank’s funding liquidity risk and interest rate risk. Estimating these maturity profiles is, however, difficult because banks experience regular cash inflows and outflows on nonmaturing deposit accounts. As a result, it is hard to ascertain the time origin of each dollar deposit constituting the total outstanding balance of a portfolio of non-maturing deposit accounts. To overcome this challenge, we propose a new method to convert account balance data into deposit lifetime data amenable to survival analysis. This provides a way to infer a nonmaturing product’s maturity profile from a survival model. We demonstrate how the estimated maturity profile can be employed to project the runoff of outstanding balances on nonmaturing deposits. The model is illustrated with a case study on a retail bank savings product in a South African bank in the 1999–2016 period. Our case study results suggest that the proposed model is well suited to estimating the maturity profile of nonmaturing deposits.
{"title":"Estimating Maturity Profiles of Nonmaturing Deposits","authors":"Fidelis Musakwa Musakwa, E. Schaling","doi":"10.21314/JOR.2019.414","DOIUrl":"https://doi.org/10.21314/JOR.2019.414","url":null,"abstract":"Understanding the maturity profiles of nonmaturing deposits is vital to assess a bank’s funding liquidity risk and interest rate risk. Estimating these maturity profiles is, however, difficult because banks experience regular cash inflows and outflows on nonmaturing deposit accounts. As a result, it is hard to ascertain the time origin of each dollar deposit constituting the total outstanding balance of a portfolio of non-maturing deposit accounts. To overcome this challenge, we propose a new method to convert account balance data into deposit lifetime data amenable to survival analysis. This provides a way to infer a nonmaturing product’s maturity profile from a survival model. We demonstrate how the estimated maturity profile can be employed to project the runoff of outstanding balances on nonmaturing deposits. The model is illustrated with a case study on a retail bank savings product in a South African bank in the 1999–2016 period. Our case study results suggest that the proposed model is well suited to estimating the maturity profile of nonmaturing deposits.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42121436","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}
The third installment of the Basel Accords advocates a capital charge against credit valuation adjustment (CVA) variability. We propose an efficient numerical approach that allows us to compute risk measures for the CVA process by assessing the distribution of the CVA at a given horizon. This approach relies on a recursive formulation of the CVA, yielding the adjustment as a function of both the time to maturity and the value of the risk factors. Numerical experiments are presented to illustrate the impact of various parameters and assumptions on the CVA distribution. More specifically, we investigate the impact of the constant exposure approximation and show that this assumption significantly affects the tail of the distribution of CVA movements. We also find that distortions between physical and risk-neutral probability measures have practically no impact on the dispersion of the CVA distribution. Finally, we analyze the effect of wrong-way risk and of early exercise opportunities on the evaluation of risk measures.
{"title":"Counterparty Risk: Credit Valuation Adjustment Variability and Value-At-Risk","authors":"M. Breton, Oussama Marzouk","doi":"10.21314/JOR.2019.411","DOIUrl":"https://doi.org/10.21314/JOR.2019.411","url":null,"abstract":"The third installment of the Basel Accords advocates a capital charge against credit valuation adjustment (CVA) variability. We propose an efficient numerical approach that allows us to compute risk measures for the CVA process by assessing the distribution of the CVA at a given horizon. This approach relies on a recursive formulation of the CVA, yielding the adjustment as a function of both the time to maturity and the value of the risk factors. Numerical experiments are presented to illustrate the impact of various parameters and assumptions on the CVA distribution. More specifically, we investigate the impact of the constant exposure approximation and show that this assumption significantly affects the tail of the distribution of CVA movements. We also find that distortions between physical and risk-neutral probability measures have practically no impact on the dispersion of the CVA distribution. Finally, we analyze the effect of wrong-way risk and of early exercise opportunities on the evaluation of risk measures.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44490238","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}
Christoph J. Borner, Ingo Hoffmann, Fabian Poetter, Tim Schmitz
Attempts to allocate capital across a selection of different investments are often hampered by the fact that investors' decisions are made under limited information (no historical return data) and during an extremely limited timeframe. Nevertheless, in some cases, rational investors with a certain level of experience are able to ordinally rank investment alternatives through relative assessments of the probabilities that investments will be successful. However, to apply traditional portfolio optimization models, analysts must use historical (or simulated/expected) return data as the basis for their calculations. This paper develops an alternative portfolio optimization framework that is able to handle this kind of information (given by an ordinal ranking of investment alternatives) and to calculate an optimal capital allocation based on a Cobb-Douglas function, which we call the Sorted Weighted Portfolio (SWP). Considering risk-neutral investors, we show that the results of this portfolio optimization model usually outperform the output generated by the (intuitive) Equally Weighted Portfolio (EWP) of different investment alternatives, which is the result of optimization when one is unable to incorporate additional data (the ordinal ranking of the alternatives). To further extend this work, we show that our model can also address risk-averse investors to capture correlation effects.
{"title":"On capital allocation under information constraints","authors":"Christoph J. Borner, Ingo Hoffmann, Fabian Poetter, Tim Schmitz","doi":"10.21314/jor.2022.057","DOIUrl":"https://doi.org/10.21314/jor.2022.057","url":null,"abstract":"Attempts to allocate capital across a selection of different investments are often hampered by the fact that investors' decisions are made under limited information (no historical return data) and during an extremely limited timeframe. Nevertheless, in some cases, rational investors with a certain level of experience are able to ordinally rank investment alternatives through relative assessments of the probabilities that investments will be successful. However, to apply traditional portfolio optimization models, analysts must use historical (or simulated/expected) return data as the basis for their calculations. This paper develops an alternative portfolio optimization framework that is able to handle this kind of information (given by an ordinal ranking of investment alternatives) and to calculate an optimal capital allocation based on a Cobb-Douglas function, which we call the Sorted Weighted Portfolio (SWP). Considering risk-neutral investors, we show that the results of this portfolio optimization model usually outperform the output generated by the (intuitive) Equally Weighted Portfolio (EWP) of different investment alternatives, which is the result of optimization when one is unable to incorporate additional data (the ordinal ranking of the alternatives). To further extend this work, we show that our model can also address risk-averse investors to capture correlation effects.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43404083","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 develop an optimal currency hedging strategy that allows fund managers who own foreign assets to choose the hedge tenors that will maximize their foreign exchange (FX) carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged with FX forwards. The chosen liquidity risk metric is cashflow at risk (CFaR). The strategy involves time-dispersing the total nominal hedge value into future time buckets to maximize (minimize) the expected FX carry benefit (cost), given the constraint that the CFaRs in all the future time buckets are well managed within a liquidity budget. We show by Monte Carlo simulation and by backtesting that our hedging strategy successfully delivers good carry trade returns with little liquidity risk. We also provide practical insights on when and why fund managers should choose short-dated or long-dated tenors.
{"title":"Optimal Foreign Exchange Hedge Tenor with Liquidity Risk","authors":"Rongju Zhang, Mark Aarons, G. Loeper","doi":"10.21314/JOR.2021.002","DOIUrl":"https://doi.org/10.21314/JOR.2021.002","url":null,"abstract":"We develop an optimal currency hedging strategy that allows fund managers who own foreign assets to choose the hedge tenors that will maximize their foreign exchange (FX) carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged with FX forwards. The chosen liquidity risk metric is cashflow at risk (CFaR). The strategy involves time-dispersing the total nominal hedge value into future time buckets to maximize (minimize) the expected FX carry benefit (cost), given the constraint that the CFaRs in all the future time buckets are well managed within a liquidity budget. We show by Monte Carlo simulation and by backtesting that our hedging strategy successfully delivers good carry trade returns with little liquidity risk. We also provide practical insights on when and why fund managers should choose short-dated or long-dated tenors.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48590283","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 propose a vine copula model based on a bivariate extended skew-t distribution and derive its corresponding multivariate tail dependence function. Our simulations demonstrate that the proposed estimator dominates the conventional vine copula approach in the estimation of multivariate tail dependence. We apply our model to a safe haven analysis of US dollars (US$) and gold prices against stocks. The estimated multivariate lower tail dependence coefficients suggest that even though either US$ or gold can be safe haven assets against stocks, combining US$ and gold in a portfolio does not provide a safe haven property against stocks. Therefore, incorporating multiple safe haven assets in a portfolio may end in heavier losses in the event of a market downturn. Our results highlight the importance of simultaneously investigating multiple safe haven assets in financial risk analysis.
{"title":"Could Holding Multiple Safe Havens Improve Diversification in a Portfolio? The Extended Skew-T Vine Copula Approach","authors":"Meng-Shiuh Chang, Jing Yuan, Jing Xu","doi":"10.21314/JOR.2019.407","DOIUrl":"https://doi.org/10.21314/JOR.2019.407","url":null,"abstract":"We propose a vine copula model based on a bivariate extended skew-t distribution and derive its corresponding multivariate tail dependence function. Our simulations demonstrate that the proposed estimator dominates the conventional vine copula approach in the estimation of multivariate tail dependence. We apply our model to a safe haven analysis of US dollars (US$) and gold prices against stocks. The estimated multivariate lower tail dependence coefficients suggest that even though either US$ or gold can be safe haven assets against stocks, combining US$ and gold in a portfolio does not provide a safe haven property against stocks. Therefore, incorporating multiple safe haven assets in a portfolio may end in heavier losses in the event of a market downturn. Our results highlight the importance of simultaneously investigating multiple safe haven assets in financial risk analysis.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43403587","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}
This work presents a theoretical and empirical evaluation of the Anderson–Darling test when the sample size is limited. The test can be used to backtest risk factor dynamics in the context of counterparty credit risk modeling. We show the limits of the test when backtesting the distributions of an interest rate model over long time horizons, and we propose a modified version of it that can more efficiently detect the underestimation of a model’s volatility. Finally, we provide an empirical application.
{"title":"The efficiency of the Anderson–Darling test with a limited sample size: an application to backtesting counterparty credit risk internal models","authors":"Matteo Formenti, Luca Spadafora, Marcello Terraneo, Fabio Ramponi","doi":"10.21314/jor.2019.415","DOIUrl":"https://doi.org/10.21314/jor.2019.415","url":null,"abstract":"This work presents a theoretical and empirical evaluation of the Anderson–Darling test when the sample size is limited. The test can be used to backtest risk factor dynamics in the context of counterparty credit risk modeling. We show the limits of the test when backtesting the distributions of an interest rate model over long time horizons, and we propose a modified version of it that can more efficiently detect the underestimation of a model’s volatility. Finally, we provide an empirical application.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"6 23","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494963","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}
The concept of second-order risk operationalizes the estimation risk induced by model uncertainty in portfolio construction. We study its contribution to the realized volatility of recently developed alternative risk parity strategies that invest in an uncorrelated decomposition of the asset universe. For each strategy, we derive closed-form solutions for the second-order risk, subsequently illustrated in empirical analysis based on real market data. Our results suggest a relation between the contribution of second-order risk and the sensitivity of a portfolio to single eigenvectors of the covariance matrix of assets’ returns. Among the strategies considered, we find the principal risk parity strategy that invests equally in each eigenvector underlying the variance–covariance matrix to be immune to second-order risk. For the other strategies, second-order risk can be partially mitigated by means of statistical methods. In particular, we provide evidence for the eigenvalue adjustment being the most effective method for correcting the second-order risk bias.
{"title":"Second-order risk of alternative risk parity strategies","authors":"Simone Bernardi, Markus Leippold, Harald Lohre","doi":"10.21314/jor.2018.401","DOIUrl":"https://doi.org/10.21314/jor.2018.401","url":null,"abstract":"The concept of second-order risk operationalizes the estimation risk induced by model uncertainty in portfolio construction. We study its contribution to the realized volatility of recently developed alternative risk parity strategies that invest in an uncorrelated decomposition of the asset universe. For each strategy, we derive closed-form solutions for the second-order risk, subsequently illustrated in empirical analysis based on real market data. Our results suggest a relation between the contribution of second-order risk and the sensitivity of a portfolio to single eigenvectors of the covariance matrix of assets’ returns. Among the strategies considered, we find the principal risk parity strategy that invests equally in each eigenvector underlying the variance–covariance matrix to be immune to second-order risk. For the other strategies, second-order risk can be partially mitigated by means of statistical methods. In particular, we provide evidence for the eigenvalue adjustment being the most effective method for correcting the second-order risk bias.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"6 24","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494962","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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