Measuring and testing for the systemically important financial institutions

This paper analyzes ΔCoVaR proposed by Adrian and Brunnermeier (2011) as a tool for identifying/ranking systemically important institutions. We develop a test of significance of ΔCoVaR that allows determining whether or not a financial institution can be classified as being systemically important on the basis of the estimated systemic risk contribution, as well as a test of dominance aimed at testing whether or not, according to ΔCoVaR, one financial institution is more systemically important than another. We provide an empirical application on a sample of 26 large European banks to show the importance of statistical testing when using ΔCoVaR, and more generally also other market-based systemic risk measures, in this context.     

Assessing the contribution of banks,insurance and other financial services to systemic risk

The aim of this paper is to contribute to the debate on systemic risk by assessing the extent to which distress within the main different financial sectors, namely, the banking, insurance and other financial services industries contribute to systemic risk. To this end, we rely on the $\mathrm{\Delta }\mathit{CoVaR}$ systemic risk measure introduced by Adrian and Brunnermeier (2011). In order to provide a formal ranking of the financial sectors with respect to their contribution to systemic risk, the original $\mathrm{\Delta }\mathit{CoVaR}$ approach is extended here to include the Kolmogorov–Smirnov test developed by Abadie (2002), based on bootstrapping. Our empirical results reveal that in the Eurozone, for the period ranging from 2004 to 2012, the other financial services sector contributes relatively the most to systemic risk at times of distress affecting this sector. In turn, the banking sector appears to contribute more to systemic risk than the insurance sector. By contrast, the insurance industry is the systemically riskiest financial sector in the United States for the same period, while the banking sector contributes the least to systemic risk in this area. Beyond this ranking, the three financial sectors of interest are found to contribute significantly to systemic risk, both in the Eurozone and in the United States.     

What’s the contingency? A proposal for bank contingent capital triggered by systemic risk

Contingent capital (coco) automatically recapitalizes the banking system during financial crises if the trigger mechanism is properly designed. We propose a dual trigger mechanism based on: (1) aggregate systemic risk in the banking system, measured using CATFIN, and (2) the individual bank’s contribution to overall systemic risk, measured using delta CoVaR. The dual trigger is highly correlated with system-wide insolvency risk and prices systemic risk. We set different triggers for banks, insurance companies and broker-dealers. Using the 99% cut-off, systemic coco issued by Lehman and Bear Stearns would have been triggered in November 2007, months prior to their actual demise.     

Systemic risk in the Chinese financial system: A panel Granger causality analysis

In this paper, we investigate China’s changing financial interconnectedness via the presence of Granger-causality between firm level factors (Leverage, Market To Book Value and Returns) and systemic risk measures ($\Delta$CoVaR, MES, and SRISK ). The analysis is based on 161 Chinese financial intermediaries (14 Traditional Banks, 16 Finance Services, 131 Real Estate Finance Developers) continuously listed over the period 2007:1–2021:1. We find that, in addition to traditional banks, finance companies and real estate finance developers pose systemic threats to the Chinese financial system, in particular during the Global Financial Crisis and the 2015 Chinese stock crash. Finally, the outbreak of COVID-19 pandemic has put under strain the Chinese financial system, in particular the finance services.     

Score-driven copula models for portfolios of two risky assets

ABSTRACT

The precise measurement of the association between asset returns is important for financial investors and risk managers. In this paper, we focus on a recent class of association models: Dynamic Conditional Score (DCS) copula models. Our contributions are the following: (i) We compare the statistical performance of several DCS copulas for several portfolios. We study the Clayton, rotated Clayton, Frank, Gaussian, Gumbel, rotated Gumbel, Plackett and Student's t copulas. We find that the DCS model with the Student's t copula is the most parsimonious model. (ii) We demonstrate that the copula score function discounts extreme observations. (iii) We jointly estimate the marginal distributions and the copula, by using the Maximum Likelihood method. We use DCS models for mean, volatility and association of asset returns. (iv) We estimate robust DCS copula models, for which the probability of a zero return observation is not necessarily zero. (v) We compare different patterns of association in different regions of the distribution for different DCS copulas, by using density contour plots and Monte Carlo (MC) experiments. (vi) We undertake a portfolio performance study with the estimation and backtesting of MC Value-at-Risk for the DCS model with the Student's t copula.     

Measuring systemic importance of financial institutions: An extreme value theory approach

This paper proposes a set of market-based measures on the systemic importance of a financial institution or a group of financial institutions, each designed to capture different aspects of systemic importance of financial institutions. Multivariate extreme value theory approach is used to estimate these measures. Using six big Canadian banks as the proxy for Canadian banking sector, we apply these measures to identify systemically important banks in Canadian banking sector and major risk contributors from international financial institutions to Canadian banking sector. The empirical evidence reveals that (i) the top three banks, RBC Financial Group, TD Bank Financial Group, and Scotiabank, are more systemically important than other banks, while we also find that the size of a financial institution should not be considered as a proxy of systemic importance; (ii) compared to the European and Asian banks, the crashes of the U.S. banks, on average, are the most damaging to Canadian banking sector, while the risk contribution to the Canadian banking sector from Asian banks is quite lower than that from banks in the U.S. and euro area; (iii) the risk contribution to Canadian banking sector exhibits “home bias”, that is, cross-country risk contribution tends to be smaller than domestic risk contribution.     

How useful is the Marginal Expected Shortfall for the measurement of systemic exposure? A practical assessment

We explore the practical relevance from a supervisor’s perspective of a popular market-based indicator of the exposure of a financial institution to systemic risk, the Marginal Expected Shortfall (MES). The MES of an institution can be defined as its expected equity loss when the market itself is in its left tail. We estimate the dynamic MES recently proposed by Brownlees and Engle (2012) for a panel of 68 large US banks over the last decade and a half. Running panel regressions of the MES on bank characteristics, we first find that the MES can be roughly rationalized in terms of standard balance-sheet indicators of bank financial soundness and systemic importance. We then ask whether the cross section of the MES can help to identify ex ante, i.e. before a crisis unfolds, which institutions are more likely to suffer the most severe losses ex post, i.e. once it has unfolded. Unfortunately, using the 2007–2009 crisis as a natural experiment, we find that some standard balance-sheet ratios are better able than the MES to predict large equity losses conditionally to a true crisis.     

Systemic risk measurement: Multivariate GARCH estimation of CoVaR

We modify Adrian and Brunnermeier’s (2011) CoVaR, the VaR of the financial system conditional on an institution being in financial distress. We change the definition of financial distress from an institution being exactly at its VaR to being at most at its VaR. This change allows us to consider more severe distress events, to backtest CoVaR, and to improve its consistency (monotonicity) with respect to the dependence parameter. We define the systemic risk contribution of an institution as the change from its CoVaR in its benchmark state (defined as a one-standard deviation event) to its CoVaR under financial distress. We estimate the systemic risk contributions of four financial industry groups consisting of a large number of institutions for the sample period June 2000 to February 2008 and the 12 months prior to the beginning of the crisis. We also investigate the link between institutions’ contributions to systemic risk and their characteristics.     

Fund Management and Systemic Risk – Lessons from the Global Financial Crisis

Fund managers play an important role in increasing efficiency and stability in financial markets. But research also indicates that fund management in certain circumstances may contribute to the buildup of systemic risk and severity of financial crises. The global financial crisis provided a number of new experiences on the contribution of fund managers to systemic risk. In this article, we focus on these lessons from the crisis. We distinguish between three sources of systemic risk in the financial system that may arise from fund management: insufficient credit risk transfer to fund managers; runs on funds that cause sudden reductions in funding to banks and other financial entities; and contagion through business ties between fund managers and their sponsors. Our discussion relates to the current intense debate on the role the so‐called shadow banking system played in the global financial crisis. Several regulatory initiatives have been launched or suggested to reduce the systemic risk arising from non‐bank financial entities, and we briefly discuss the likely impact of these on the sources of systemic risk outlined in the article.     

Selecting copulas for risk management

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper, we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student’s t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student’s t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.     

Multiple-days-ahead value-at-risk and expected shortfall forecasting for stock indices,commodities and exchange rates: Inter-day versus intra-day data

In order to provide reliable Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts, this paper attempts to investigate whether an inter-day or an intra-day model provides accurate predictions. We investigate the performance of inter-day and intra-day volatility models by estimating the AR(1)-GARCH(1,1)-skT and the AR(1)-HAR-RV-skT frameworks, respectively. This paper is based on the recommendations of the Basel Committee on Banking Supervision. Regarding the forecasting performances, the exploitation of intra-day information does not appear to improve the accuracy of the VaR and ES forecasts for the 10-steps-ahead and 20-steps-ahead for the 95%, 97.5% and 99% significance levels. On the contrary, the GARCH specification, based on the inter-day information set, is the superior model for forecasting the multiple-days-ahead VaR and ES measurements. The intra-day volatility model is not as appropriate as it was expected to be for each of the different asset classes; stock indices, commodities and exchange rates.The multi-period VaR and ES forecasts are estimated for a range of datasets (stock indices, commodities, foreign exchange rates) in order to provide risk managers and financial institutions with information relating the performance of the inter-day and intra-day volatility models across various markets. The inter-day specification predicts VaR and ES measures adequately at a 95% confidence level. Regarding the 97.5% confidence level that has been recently proposed in the revised 2013 version of Basel III, the GARCH-skT specification provides accurate forecasts of the risk measures for stock indices and exchange rates, but not for commodities (that is Silver and Gold). In the case of the 99% confidence level, we do not achieve sufficiently accurate VaR and ES forecasts for all the assets.     

The t copula with multiple parameters of degrees of freedom: bivariate characteristics and application to risk management

The t copula is often used in risk management as it allows for modeling the tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, the grouped t copula was proposed recently, where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a generalized grouped t copula, where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied. We explain simulation and calibration procedures, including a simulation study on the finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula is significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall.     

Spillovers in risk of financial institutions

ABSTRACT

We analyse the total and directional spillovers across a set of financial institution systemic risk state variables: credit risk, real estate market risk, interest rate risk, interbank liquidity risk and overall market risk. We examine the response of the spillover levels, within the set of systemic risk state variables, to a number of events in the financial markets and to initiatives undertaken by the European Central Bank and the Bank of England. The relationship between the time-varying spillovers and policy-related events is analysed using a multiple structural break estimation procedure and looking at the temporary increases in the spillover indices. Our sample includes five European Union countries: core countries France and Germany, periphery countries Spain and Italy, and a reference country, the UK. We show that national stock markets and real estate markets have a leading role in shock transmission across selected state variables. However, the role of the other variables reverses over the course of the crisis. We document that the total and net spillover indices react strongly to the events relating to financial assistance packages in Europe.     

Good for one,bad for all: Determinants of individual versus systemic risk

We analyze a sample of large international banks in major advanced economies and examine the impact that bank-specific factors have on an institution's solvency risk and its contribution to systemic risk. We focus on the five categories that the Basel Committee on Banking Supervision has recently proposed as indicators of systemic importance. Our findings suggest that unstable funding is the main factor driving systemic risk. Furthermore, the combination of significant trading activities with global presence appears to exacerbate spillover risks to the global financial system. Interestingly, whereas trading activities contribute to the build-up of correlated or ‘wrong-way’ risk they help to mitigate individual solvency risk. Conversely, a decentralized approach to liquidity management seems to alleviate individual solvency risk but amplifies the transmission of financial distress across the financial system. This suggests that a macro-prudential approach to financial regulation should focus not only on scaling up micro-prudential measures but also on enabling the efficient transfer of risk between financial institutions.     

What is the systemic risk exposure of financial institutions?

I compare the performance of three measures of institution-level systemic risk exposure — Exposure CoVaR (Adrian and Brunnermeier, 2016), systemic expected shortfall (Acharya et al., 2016), and Granger causality (Billio et al., 2012). I modify Exposure CoVaR to allow for forecasting, and estimate the ability of each measure to forecast the performance of financial institutions during systemic crisis periods in 1998 (LTCM) and 2008 (Lehman Brothers). I find that Exposure CoVaR forecasts the within-crisis performance of financial institutions, and provides useful forecasts of future systemic risk exposures. Systemic expected shortfall and Granger causality do not forecast the performance of financial institutions reliably during crises. I also find, using cross-sectional regressions, that foreign equity exposure and securitization income determine systemic risk exposure during the 1998 and 2008 crises, respectively; financial institution size determines systemic risk exposure during both crisis periods; and executive compensation does not determine systemic risk exposure.     

An analysis of the literature on systemic financial risk: A survey

This article presents an analysis of the literature on systemic financial risk. To that end, we analyze and classify 266 articles that were published no later than September 2016 in the databases Scopus and Web of Knowledge; these articles were identified using the keywords “systemic risk”, “financial stability”, “financial”, “measure”, “indicator”, and “index”. They were evaluated based on 10 categories, namely, type of study, type of approach, object of study, method, spatial scope, temporal scope, context, focus, type of data used, and results. The analysis and classification of this literature made it possible to identify the remaining gaps in the literature on systemic risk; this contributes to a future research agenda on the topic. Moreover, the most influential articles in this field of research and the articles that compose the mainstream research on systemic financial risk were identified.     

Variance of the CTE Estimator

Abstract

The Conditional Tail Expectation (CTE), also called Expected Shortfall or Tail-VaR, is a robust, convenient, practical, and coherent measure for quantifying financial risk exposure. The CTE is quickly becoming the preferred measure for statutory balance sheet valuation whenever real-world stochastic methods are used to set liability provisions. We look at some statistical properties of the methods that are commonly used to estimate the CTE and develop a simple formula for the variance of the CTE estimator that is valid in the large sample limit. We also show that the formula works well for finite sample sizes. Formula results are compared with sample values from realworld Monte Carlo simulations for some common loss distributions, including equity-linked annuities with investment guarantees, whole life insurance and operational risks. We develop the CTE variance formula in the general case using a system of biased weights and explore importance sampling, a form of variance reduction, as a way to improve the quality of the estimators for a given sample size. The paper closes with a discussion of practical applications.     

Optimal reinsurance arrangements in the presence of two reinsurers

In this paper, we investigate the optimal form of reinsurance from the perspective of an insurer when he decides to cede part of the loss to two reinsurers, where the first reinsurer calculates the premium by expected value principle while the premium principle adopted by the second reinsurer satisfies three axioms: distribution invariance, risk loading, and preserving stop-loss order. In order to exclude the moral hazard, a typical reinsurance treaty assumes that both the insurer and reinsurers are obligated to pay more for the larger loss. Under the criterion of minimizing value at risk (VaR) or conditional value at risk (CVaR) of the insurer's total risk exposure, we show that an optimal reinsurance policy is to cede two adjacent layers, where the upper layer is distributed to the first reinsurer. To further illustrate the applicability of our results, we derive explicitly the optimal layer reinsurance by assuming a generalized Wang's premium principle to the second reinsurer.     

Change analysis of a dynamic copula for measuring dependence in multivariate financial data

This paper proposes a new approach to measure dependencies in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes within the dependence structure. Recently, two methods have been proposed using copulas to analyse such changes. The first approach investigates changes within the parameters of the copula. The second determines the sequence of copulas using moving windows. In this paper we take into account the non-stationarity of the data and analyse the impact of (1) time-varying parameters for a copula family, and (2) the sequence of copulas, on the computations of the VaR and ES measures. We propose tests based on conditional copulas and the goodness-of-fit to decide the type of change, and further give the corresponding change analysis. We illustrate our approach using the Standard & Poor 500 and Nasdaq indices in order to compute risk measures using the two previous methods.     

Multilayer networks in the frequency domain: Measuring extreme risk connectedness of Chinese financial institutions

We propose multilayer networks in the frequency domain, including the short-term, medium-term, and long-term layers, to investigate the extreme risk connectedness among financial institutions. Using the conditional autoregressive value at risk (CAViaR) tool to measure the extreme risk of financial institutions, we construct extreme risk networks and inter-sector extreme risk networks of 36 Chinese financial institutions through the proposed approach. We observe that the extreme risk connectedness across financial institutions is heterogeneous in the short-, medium-, and long-term. In general, the long-term connectedness among financial institutions rises sharply during times of financial stress, such as the 2015 Chinese stock market turbulence and the 2020 COVID-19 pandemic. Moreover, we note that the insurers are key players in driving the inter-sector extreme risk networks, because the inter-sector systemic importance of insurance institutions is dominant. Finally, our conclusions provide valuable information for regulators to prevent systemic risk.