JEL classification: G01 G18 G21Keywords: Extreme value dependence Systemic risk Systemically important financial institutions a b s t r a c tIn this study, we investigate the extreme loss tail dependence between stock returns of large US depository institutions. We find that stock returns exhibit strong loss dependence even in their limiting joint extremes. Motivated by this result, we derive extremal dependence-based systemic risk indicators. The proposed systemic risk indicators reflect downturns in the US financial industry very well. We also develop a set of firm-level average extremal dependence measures. We show that these firm-level measures could have been used to identify the firms that were more vulnerable to the 2007-2008 financial crisis. Additionally, we explore the performance of selected systemic risk indicators in predicting the crisis performance of large US depository institutions and find that the average stock return correlations are also good predictors of crisis period returns. Finally, we identify factors predictive of extremal dependence for the US depository institutions in a panel regression setting. Strength of extremal dependence increases with asset size and similarity of financial fundamentals. On the other hand, strength of extremal dependence decreases with capitalization, liquidity, funding stability and asset quality. We believe the proposed indicators have the potential to inform the prudential supervision of systemic risk.Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

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This article examines tail dependence, the benefits of diversification and the relation between the two for emerging stock markets. We find most emerging equity markets are independent in limiting joint extremes. However, the dependence in finite levels of extremes is still much stronger than the dependence implied by multivariate normality. Therefore, simple correlation analysis can lead to gross underestimation of the chances of joint crashes in multiple markets. Assuming risk-averse investors guarding against extreme losses, diversification benefits are measured for each two-country optimal portfolio by the reduction in quantile risk measures such as value-at-risk and expected shortfall relative to an undiversified portfolio. It is shown that tail dependence measures developed from multivariate extreme value theory are negatively related to diversification benefits and more importantly can explain diversification benefits better than the correlation coefficient at the most extreme quantiles.

The 2004 Basel II accord requires internationally active banks to hold regulatory capital for operational risk, and the Federal Reserve's Comprehensive Capital Analysis and Review (CCAR) requires banks to project operational risk losses under stressed scenarios. As a result, banks subject to these rules have measured and managed operational risk more rigorously. But some types of operational riskparticularly legal risk -are challenging to model because such exposures tend to be fat-tailed. Tail operational risk losses have significantly impacted banks' balance sheets and income statements, even post crisis. So, operational risk practitioners, bank analysts, and regulators must develop reasonable methods to assess the efficacy of operational risk models and associated equity financing. We believe benchmarks should be used extensively to justify model outputs, improve model stability, and maintain capital reasonableness. Since any individual benchmark can be misleading, we outline a set of principles for using benchmarks effectively and describe how these principles can be applied to operational risk models. Also, we provide some examples of the benchmarks that have been used by US regulators in assessing Advanced Measurement Approach (AMA) capital reasonableness and that can be used in CCAR to assess the reasonableness of operational risk loss projections. We believe no single model's output and no single benchmark offers a comprehensive view, but that practitioners, analysts, and regulators must use models combined with rigorous benchmarks to determine operational risk capital and assess its adequacy.

Using supervisory operational loss data of the US banking industry, we analyze dependence among operational losses within banks and across banks. We find evidence of relatively strong dependence among tail losses of different operational loss types within banks. Applying a copula framework, we estimate that the median correlation parameter for the key operational loss types is around 30% and exceeds 50% for some banks in our sample. Our results contrast with the previous literature that documents that correlation parameter estimates are in the range of 5–10% and typically do not exceed 20%. Further, we demonstrate significant model risk from not accounting for dependence among tail losses, resulting in material underestimation of operational risk. In addition, we investigate dependence of operational losses across banks. Using a copula framework, we estimate correlation parameters between losses of large banks in our sample to be 42% on average. This result suggests the presence of systemic risk from the simultaneous occurrence of operational tail losses in different large banks.

The 2004 Basel II accord requires internationally active banks to hold regulatory capital for operational risk, and the Federal Reserve's Comprehensive Capital Analysis and Review (CCAR) requires banks to project operational risk losses under stressed scenarios. As a result, banks subject to these rules have measured and managed operational risk more rigorously. But some types of operational riskparticularly legal risk -are challenging to model because such exposures tend to be fat-tailed. Tail operational risk losses have significantly impacted banks' balance sheets and income statements, even post crisis. So, operational risk practitioners, bank analysts, and regulators must develop reasonable methods to assess the efficacy of operational risk models and associated equity financing. We believe benchmarks should be used extensively to justify model outputs, improve model stability, and maintain capital reasonableness. Since any individual benchmark can be misleading, we outline a set of principles for using benchmarks effectively and describe how these principles can be applied to operational risk models. Also, we provide some examples of the benchmarks that have been used by US regulators in assessing Advanced Measurement Approach (AMA) capital reasonableness and that can be used in CCAR to assess the reasonableness of operational risk loss projections. We believe no single model's output and no single benchmark offers a comprehensive view, but that practitioners, analysts, and regulators must use models combined with rigorous benchmarks to determine operational risk capital and assess its adequacy. JEL Classification: G21, G28

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