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### I. Introduction
- Firms and financial institutions holding portfolios of diverse projects/assets face correlation risk arising from correlation of cash flows across projects/assets.
- Capital structures mix equity and debt, differentiated by seniority; equity is subordinated to debt.
- Correlation bias: different claim holders prefer different levels of asset correlation.
  - Junior claim holders (shareholders) prefer highly correlated assets.
  - Senior claim holders (debt holders) prefer less correlated (more diversified) assets.
- Managers typically act on behalf of the most junior claim holders (shareholders), biasing portfolio choice toward highly correlated assets.
- Bias toward highly correlated assets produces fat tails, increasing likelihood of extreme upside and downside outcomes and raising firm failure probability.
- Widespread dominance of the shareholders’ correlation bias plus herd behavior can cause financial systems to oscillate between tranquility and disruption; fat-tail events exemplified by the recent global financial crisis originating in U.S. subprime problems.
- The paper proposes a copula approach to capital structure (extending Black and Scholes (1973) and Merton (1974)) to analyze the correlation bias and its interaction with systemic risk and regulatory reform.

### II. Understanding the correlation bias
- Black and Scholes (1973) and Merton (1974) framework: payoffs to equity and debt equivalent to options on firm asset value; shareholders hold a long asset volatility position so increased asset volatility increases equity value.
- The basic model does not account for asset value being determined by a portfolio of projects whose mutual dependence (correlation) affects volatility.
- Shareholders can increase firm volatility by increasing correlation among projects in the portfolio.

Key illustrative facts and mechanics:
- Two two-project portfolios example (each project requires initial investment of 100):
  - Portfolio 1: projects A and B uncorrelated; each project success/failure probability = ½; three potential profit/loss outcomes: lose 100, break even at 0, or gain 100.
  - Both portfolios have expected value of 100.
  - If financed only with equity, shareholders prefer Portfolio 1: standard deviation smaller and probability of losing money is 25 percent.
  - With partial debt financing, shareholders prefer higher-correlation Portfolio 2 as debt share increases: for a 50-50 mix of debt and equity, Portfolio 1 yields shareholders an expected profit/loss of 25 while Portfolio 2 delivers 50.
  - Shareholders’ preference increases debtholders’ probability of total loss (50 percent in Portfolio 2 vs. 25 percent in Portfolio 1); bondholders prefer Portfolio 1.

Copula capital structure model and implications:
- Copula pricing model (Vasicek (1977) and Gaussian copula specialization by Li (2000)): asset/project value determined by common factor and idiosyncratic factor; asset correlation determined by correlation with the common factor; model extendable to multifactor copulas.
- Copula model extends Black-Scholes-Merton by accommodating portfolios of multiple projects and several claim types; equity value equates to a portfolio of options on several projects.
- Main insight: explicit correlation bias—shareholders prefer highly correlated assets, increasing idiosyncratic and systemic risk.
- Effects of changes in project riskiness:
  - Improvement in probability of project success benefits all claims if payoff of success is independent of project riskiness.
  - If payoff increases with project risk, equity benefits more (consistent with Black-Scholes-Merton convexity result).
  - Increase in correlation of cash flows benefits shareholders but not senior debt holders.
- Intuition: high correlation creates binary outcomes (majority succeed or fail); shareholders’ downside limited to equity stake while upside accrues to shareholders due to convexity of their payoff.
- Subordinated debt sensitivity to correlation is non-monotonic:
  - At very low correlation, losses small, absorbed by equity.
  - As correlation increases below a threshold, subordinated debt value declines due to partial losses after equity exhaustion.
  - Once correlation crosses the threshold, subordinated debt value starts increasing because high correlation increases likelihood of either few failures (protecting subordinated tranche) or fully catastrophic loss; above threshold subordinated holders prefer higher correlation.
- Relative size of equity and subordinated debt determines strength of junior claimants’ bias:
  - Smaller subordinated claims strengthen incentive to opt for high correlation.
  - In subordinated debt, smaller equity buffer lowers the threshold correlation.

### III. Correlation bias, systemic risk and prudential regulation
A. Systemic risk
- Correlation bias combined with corporate control can induce high portfolio correlation across institutions, raising failure likelihood.
- Excess portfolio correlation at firm level can translate into systemic risk; prudential regulation must consider claim holders’ correlation biases.
- Correlation bias induces upside and downside fat-tail risk, contributing to swings from tranquility to turmoil.
- Asset correlation is procyclical: correlation tends to increase during periods of turmoil.
- Financial system interconnectedness (direct cross-institution claims and indirect linkages from common exposures and similar accounting/risk management practices) means individual failures can create domino effects.
- Herding behavior increases the too-many-to-fail (TMTF) problem by concentrating similar portfolios across institutions; reputational factors and strategy convergence (overcrowding) can prompt herding.
  - Historical examples cited: losses by credit correlation traders in 2005 and quantitative alternative asset managers in 2007.
- Reducing systemic risk from correlation bias requires corporate governance and regulatory measures to reduce portfolio correlation across financial institutions.

B. Corporate governance
- Correlation bias risk arises when corporate control is exercised by shareholders (or management acting for shareholders).
- Banks typically have relatively small equity shares in capital structure; high leverage can be a market solution to governance problems in presence of asymmetric information (Kashyap, Rajan and Stein (2008)).
- Managers, as most junior claimants, can be even more biased than shareholders toward highly correlated projects/assets.
- Governance solution proposed:
  - Shift some corporate control to claim holders other than shareholders (debt holders).
  - Mechanism example: require debt holders to also hold some equity in the firm (observed in bank-based systems in Japan and continental Europe).
  - Caveat: Whether bank portfolios in bank-based systems are less correlated than in market-based systems (UK, USA) is an open empirical question.
- Practical constraints:
  - Debt holders often too diversified and lack expertise to monitor efficiently; deposits and explicit/implicit guarantees undermine monitoring incentives.
  - Absent substantial governance changes, prudential regulation must substitute for debt-holder monitoring.

Prudential reforms discussed and limitations:
- Post-2008-9 reforms mentioned:
  - Contingent capital / hybrid securities.
  - Increases in minimum capital requirements.
  - Systemic risk capital charges.
  - "Skin-in-the-game" requirements for originators of structured/securitized products.
- General conclusion:
  - These reforms, while addressing some aspects of TBTF and recapitalization, are largely ineffective at eliminating the correlation bias because they do not change the ownership-control structure that gives junior claimants incentives to increase asset correlation.

Contingent capital and hybrid securities
- Capital structure design proposed: two subordinated tranches—common equity (most junior) and subordinated debt that converts to equity once a pre-insolvency threshold is crossed (decline in common equity or regulatory capital to RWA ratio).
- Arguments for contingent capital:
  - Facilitates orderly recapitalization during distress when capital markets are impaired.
  - Risk of dilution in distress provides shareholders incentives to avoid excessive risk taking.
  - Converts ambiguity over bailouts into clearer incentives for subordinated debt holders to price risk.
- Limitations with respect to correlation bias:
  - Functionally, contingent capital and hybrid securities are subordinated debt; convertibility makes them resemble equity more closely.
  - Convertibility increases subordination of equity, strengthening incentives to "gamble" (increase volatility and asset correlation).
  - Therefore contingent capital may increase, not reduce, correlation bias.

Minimum capital requirements (Basel III) — specifics and loopholes
- Basel III reforms as stated:
  - Raise minimum common equity requirements to 4½ percent of risk-weighted assets (RWA) from 2 percent.
  - Add a conservation buffer of 2½ percent on top, raising total common equity ratio to 7 percent of RWA.
  - National authorities could impose a countercyclical macroprudential common equity overlay of up to 2 ½ percent of RWA.
  - Tier-1 capital requirements increased to 6 percent.
  - Minimum total capital requirement remains equal to 8 percent of RWA.
- Key limitation related to correlation bias:
  - The increase is relative to RWA rather than to total assets, creating a loophole: banks can concentrate portfolios on highly correlated low risk-weighted assets and satisfy capital ratios while increasing leverage and reducing common equity relative to total assets.
- Leverage ratio note:
  - Introduction of a non-risk based leverage ratio requiring Tier-1 assets to no less than 3 percent of non-weighted assets plus off-balance sheet structures could limit leverage build-up.
  - However, because Tier-1 assets include instruments other than common equity, the leverage ratio may not be sufficient to address shareholders' correlation preferences.

Table of specified Basel III values (as presented):
- Common Equity: 4.5 / 2.5 / 7.0
- Tier 1 capital: 6.0 / 8.0
- Total capital: 8.0 / 10.5 - 2.5

Systemic risk capital charges
- Intent:
  - Impose capital charges proportional to each bank’s contribution to systemic risk to incentivize reduced default and spillover risk and encourage relatively diversified bank and trading books.
- Practical difficulties:
  - Measurement challenges: reliance on market-based measures (mark-to-market firm value, equity/bond/CDS prices, distance-to-default, Moody’s KMV expected default frequencies, Altman Z-scores) that may misprice risk.
  - Correlation bias may induce upside fat-tail risk and long tranquil periods; if historical data used spans tranquil periods, systemic charge may understate spillover risks.
  - Harmonization across jurisdictions is difficult for global systemic institutions.
  - Evolving strategies and changing spillover channels mean a bank’s systemic contribution can change over time, undermining static charge calibrations.

"Skin-in-the-game" measures for securitizations
- Motivation:
  - Require originators of structured vehicles to retain relatively risky claims so they perform due diligence on collateral.
  - Regulatory expectation: total capital held against securitized claims should not be less than capital that would be held against collateral assets.
- Copula-model insight and limitations:
  - Originators holding junior/subordinated claims have strong incentives to include highly correlated assets (to benefit junior tranches), thus worsening correlation bias.
  - Standard practice—originator retention of equity tranche and payment waterfall structures—did not prevent origination incentives to increase collateral correlation in 2008-9.
  - Evidence: structured vehicle collateral correlation was much higher in crisis than used for pricing; parameter gaming (e.g., correlation) has occurred (U.S. SEC action referenced; settlement included a $550 million fine).
- Suggested stronger requirement:
  - Require originators to hold stakes in every single tranche of a securitized product ("skin, flesh, and bones") rather than only the equity/subordinated tranche.

### Measures that may work against correlation bias risk (policy recommendations)
- Increase common equity relative to non-weighted assets:
  - Require substantially higher levels of common equity relative to total (unweighted) assets rather than relative to RWA.
  - Note in-source calibration remark: Basel III requirements specify a maximum leverage ratio of 33 for Tier-1 capital; even if Tier-1 comprised only common equity, that recommended leverage ratio implies a very thin equity layer supporting the capital structure. Calibrating a maximum common equity leverage ratio requires assessing acceptable institution risk and the impact of correlation bias, potentially via simulation.
- Enforce the Volcker Rule and portfolio diversification requirements:
  - Ban proprietary trading for systemic financial institutions (Volcker rule) to reduce complex, highly correlated trading book activity.
  - Strengthen concentration and large position limits for banking portfolios and consider quantitative limits guided by regulator-performed risk factor analysis or validated internal models (bearing in mind model risk and gaming incentive concerns).
- Force originators to hold stakes across all securitization tranches:
  - Require originators to retain proportional stakes across every tranche ("skin, flesh, and bones") to align incentives across seniority classes and reduce tranche-driven correlation incentives.
- Enhance corporate control by debt holders:
  - Increase the share of long-term debt in bank liabilities and ensure long-term creditors are represented on boards.
  - Increase long-term debt to strengthen asset-liability management and create stronger creditor monitoring incentives.
  - Careful design required to balance power between directors representing shareholders and those representing debt holders; the copula model could inform design choices.
- Other recommendations noted:
  - Ban proprietary trading in systemic institutions.
  - Enforce diversification requirements in both banking and trading books.

### Conclusions and key findings
- The correlation bias is a novel channel by which capital structure and control rights affect portfolio composition: junior claimants prefer higher asset correlation, producing higher joint tail risk.
- Because corporate control is usually exercised by the most junior claimants, financial institutions—especially systemic banks—may bias portfolios toward highly correlated assets, increasing institution-level failure probability and systemic risk.
- Many post-crisis regulatory reforms (contingent capital, systemic risk charges, waterfall structures, retention of equity tranche) do not eliminate correlation bias and could in some cases exacerbate it.
- Potentially effective policies to reduce correlation bias risk include:
  - Substantially increasing the share of common equity in the capital structure measured relative to unweighted assets.
  - Enforcing diversification requirements and banning proprietary trading in systemic institutions (Volcker rule).
  - Requiring securitization originators to hold stakes in all tranches of structured products.
  - Giving debt holders greater corporate control through increased long-term debt and board representation.

*Source: _wp1182 - section II, high leverage would bias the bank even more towards highly correlated assets in*

### References .............................................................................................................

### _wp1182 - References .............................................................................................................

### I. INTRODUCTION
- Firms and financial institutions holding portfolios of diverse projects/assets face correlation risk arising from correlation of cash flows across projects/assets.
- Capital structures mix equity and debt, differentiated by seniority; equity is subordinated to debt.
- Correlation bias: different claim holders prefer different levels of asset correlation.
  - Junior claim holders (shareholders) prefer highly correlated assets.
  - Senior claim holders (debt holders) prefer less correlated (more diversified) assets.
- Managers typically act on behalf of the most junior claim holders (shareholders), biasing portfolio choice toward highly correlated assets.
- Bias toward highly correlated assets produces fat tails, increasing likelihood of extreme upside and downside outcomes and raising firm failure probability.
- Widespread dominance of the shareholders’ correlation bias plus herd behavior can cause financial systems to oscillate between tranquility and disruption; fat-tail events exemplified by the recent global financial crisis originating in U.S. subprime problems.
- The paper proposes a copula approach to capital structure (extending Black and Scholes (1973) and Merton (1974)) to analyze the correlation bias and its interaction with systemic risk and regulatory reform.

### II. UNDERSTANDING THE CORRELATION BIAS
A. The Basic Contingent Claim Model
- Black and Scholes (1973) and Merton (1974): payoffs to equity and debt equivalent to options on firm asset value.
- Shareholders hold a long asset volatility position; increased asset volatility increases value of equity (call option), producing a high volatility bias for shareholders and the opposite for debt holders.
- The basic model does not account for the fact that asset value is determined by a portfolio of projects whose mutual dependence (correlation) affects volatility.

B. Tail Risk and Correlation
- Shareholders can increase firm volatility by increasing correlation among projects in the portfolio.
- Illustration: two two-project portfolios (each project requires initial investment of 100).
  - Portfolio 1: projects A and B uncorrelated; each project success/failure probability = ½; zero rate of return; success returns original investment of 100; failure loses original investment.
  - Portfolio 2: projects C and D with similar characteristics but (text indicates difference in correlation; figure shows higher correlation).
  - Three potential profit/loss scenarios: lose 100, break even at 0, or gain 100.
- Both portfolios have expected value of 100.
  - If financed only with equity, shareholders prefer Portfolio 1: standard deviation smaller and probability of losing money is 25 percent.
  - With partial debt financing, shareholders prefer Portfolio 2 as debt share increases: for a 50-50 mix of debt and equity, portfolio 1 yields shareholders an expected profit/loss of 25 while portfolio 2 delivers 50.
- Shareholders’ preference increases debtholders’ probability of total loss (50 percent in Portfolio 2 vs. 25 percent in Portfolio 1); bondholders prefer Portfolio 1.

C. The Copula Capital Structure Model and the Correlation Bias
- Analogizes firm capital structure to tranched structured products: total asset value depends on cash flows from different projects; claims’ values depend on priority/seniority.
- Copula pricing model (Vasicek (1977) and Gaussian copula specialization by Li (2000)) used as framework — termed the copula capital structure model.
  - In copula approach: asset/project value determined by common factor and idiosyncratic factor; asset correlation determined by correlation with the common factor; extendable to multifactor copula models.
- Copula model extends Black-Scholes-Merton by accommodating portfolios of multiple projects and several claim types; equity value equates to a portfolio of options on several projects.
- Main insight: explicit correlation bias—shareholders prefer highly correlated assets, increasing idiosyncratic and systemic risk.
- Effects of changes in project riskiness:
  - Improvement in probability of project success benefits all claims if payoff of success is independent of project riskiness.
  - If payoff increases with project risk, equity benefits more (consistent with Black-Scholes-Merton convexity result).
  - Increase in correlation of cash flows benefits shareholders but not senior debt holders.
- Intuition: high correlation creates binary outcomes (majority succeed or fail); shareholders’ downside limited to equity stake while upside accrues to shareholders due to convexity of their payoff.
- Subordinated debt sensitivity to correlation is non-monotonic:
  - At very low correlation, losses small, absorbed by equity.
  - As correlation increases below a threshold, subordinated debt value declines due to partial losses after equity exhaustion.
  - Once correlation crosses the threshold, subordinated debt value starts increasing because high correlation increases likelihood of either few failures (protecting subordinated tranche) or fully catastrophic loss; above threshold subordinated holders prefer higher correlation.
- Relative size of equity and subordinated debt determines strength of junior claimants’ bias:
  - Smaller subordinated claims strengthen incentive to opt for high correlation.
  - In subordinated debt, smaller equity buffer lowers the threshold correlation.

### III. CORRELATION BIAS, SYSTEMIC RISK AND PRUDENTIAL REGULATION
A. Systemic Risk
- Correlation bias combined with corporate control can induce high portfolio correlation across institutions, raising failure likelihood.
- Excess portfolio correlation at firm level can translate into systemic risk; prudential regulation must consider claim holders’ correlation biases.
- Correlation bias induces upside and downside fat-tail risk, contributing to swings from tranquility to turmoil.
- Asset correlation is procyclical: correlation tends to increase during periods of turmoil.
- Financial system interconnectedness (direct cross-institution claims and indirect linkages from common exposures and similar accounting/risk management practices) means individual failures can create domino effects.
- Herding behavior increases the too-many-to-fail (TMTF) problem by concentrating similar portfolios across institutions; reputational factors and strategy convergence (overcrowding) can prompt herding.
  - Historical examples: losses by credit correlation traders in 2005 and quantitative alternative asset managers in 2007.
- Reducing systemic risk from correlation bias requires corporate governance and regulatory measures to reduce portfolio correlation across financial institutions.

B. Corporate Governance
- Correlation bias risk arises when corporate control is exercised by shareholders (or management acting for shareholders).
- Banks typically have relatively small equity shares in capital structure; high leverage can be a market solution to governance problems in presence of asymmetric information (Kashyap, Rajan and Stein (2008)).
- Managers, as most junior claimants, can be even more biased than shareholders toward highly correlated projects/assets.

*Source: _wp1182 - References .............................................................................................................*

### section II, high leverage would bias the bank even more towards highly correlated assets in

### _wp1182 - section II, high leverage would bias the bank even more towards highly correlated assets in

### Correlation bias and corporate governance
- Definition / mechanism:
  - By viewing the firm as a portfolio of projects and assets funded by claims differentiated by seniority, the copula capital structure model identifies a "correlation bias": the more junior a claim is, the stronger the preference for higher asset correlation in the firm's portfolio.
  - Corporate control exercised by the most junior claimants implies shareholders (as the most junior controllers) have incentives to bias portfolios toward highly correlated assets, increasing default and systemic risk.
- Governance solution proposed:
  - Shift some corporate control to claim holders other than shareholders (debt holders).
  - A simple mechanism: require debt holders to also hold some equity in the firm (observed in bank-based systems in Japan and continental Europe).
  - Caveats: Whether bank portfolios in bank-based systems are less correlated than in market-based systems (UK, USA) is an open empirical question.
- Practical constraints:
  - Debt holders often too diversified and lack expertise to monitor efficiently; deposits and explicit/implicit guarantees undermine monitoring incentives.
  - Absent substantial governance changes, prudential regulation must substitute for debt-holder monitoring.

### Prudential regulation: overview of reforms and limitations
- Post-2008-9 reforms discussed:
  - Contingent capital / hybrid securities.
  - Increases in minimum capital requirements.
  - Systemic risk capital charges.
  - "Skin-in-the-game" requirements for originators of structured/securitized products.
- General conclusion:
  - These reforms, while addressing some aspects of TBTF and recapitalization, are largely ineffective at eliminating the correlation bias because they do not change the ownership-control structure that gives junior claimants incentives to increase asset correlation.

### Contingent capital and hybrid securities
- Structure and rationale:
  - Capital structure should include two subordinated tranches: common equity (most junior) and subordinated debt that converts to equity once a pre-insolvency threshold is crossed (decline in common equity or regulatory capital to RWA ratio).
  - Arguments for contingent capital:
    - Facilitates orderly recapitalization during distress when capital markets are impaired.
    - Risk of dilution in distress provides shareholders incentives to avoid excessive risk taking.
    - Converts ambiguity over bailouts into clearer incentives for subordinated debt holders to price risk.
- Limitations with respect to correlation bias:
  - Functionally, contingent capital and hybrid securities are subordinated debt; convertibility makes them resemble equity more closely.
  - Convertibility increases subordination of equity, strengthening incentives to "gamble" (increase volatility and asset correlation).
  - Therefore contingent capital may increase, not reduce, correlation bias.

### Minimum capital requirements (Basel III) — specifics and loopholes
- Basel III reforms (as stated):
  - Raise minimum common equity requirements to 4½ percent of risk-weighted assets (RWA) from 2 percent.
  - Add a conservation buffer of 2½ percent on top, raising total common equity ratio to 7 percent of RWA.
  - National authorities could impose a countercyclical macroprudential common equity overlay of up to 2 ½ percent of RWA.
  - Tier-1 capital requirements increased to 6 percent.
  - Minimum total capital requirement remains equal to 8 percent of RWA.
- Key limitation related to correlation bias:
  - The increase is relative to RWA rather than to total assets, creating a loophole: banks can concentrate portfolios on highly correlated low risk-weighted assets and satisfy capital ratios while increasing leverage and reducing common equity relative to total assets.
- Leverage ratio note:
  - Introduction of a non-risk based leverage ratio requiring Tier-1 assets to no less than 3 percent of non-weighted assets plus off-balance sheet structures could limit leverage build-up.
  - However, because Tier-1 assets include instruments other than common equity, the leverage ratio may not be sufficient to address shareholders' correlation preferences.
- Table summary (as presented):
  - Common Equity: 4.5 / 2.5 / 7.0
  - Tier 1 capital: 6.0 / 8.0
  - Total capital: 8.0 / 10.5 - 2.5
  - (Table labels: Additional Macroprudential overlay, Countercyclical buffer, Minimum, Conservation buffer, Required Minimum; Source: Caruana (2010))

### Systemic risk capital charges
- Intent:
  - Impose capital charges proportional to each bank’s contribution to systemic risk to incentivize reduced default and spillover risk and encourage relatively diversified bank and trading books.
- Practical difficulties:
  - Measurement challenges: reliance on market-based measures (mark-to-market firm value, equity/bond/CDS prices, distance-to-default, Moody’s KMV expected default frequencies, Altman Z-scores) that may misprice risk.
  - Correlation bias may induce upside fat-tail risk and long tranquil periods; if historical data used spans tranquil periods, systemic charge may understate spillover risks.
  - Harmonization across jurisdictions is difficult for global systemic institutions.
  - Evolving strategies and changing spillover channels mean a bank’s systemic contribution can change over time, undermining static charge calibrations.

### "Skin-in-the-game" measures for securitizations
- Motivation:
  - Require originators of structured vehicles to retain relatively risky claims so they perform due diligence on collateral.
  - Regulatory expectation: total capital held against securitized claims should not be less than capital that would be held against collateral assets.
- Copula-model insight and limitations:
  - The copula capital structure model indicates originators holding junior/subordinated claims in structured products have strong incentives to include highly correlated assets (to benefit junior tranches), thus worsening correlation bias.
  - Standard practice—originator retention of equity tranche and payment waterfall structures—did not prevent origination incentives to increase collateral correlation in 2008-9.
  - Evidence: structured vehicle collateral correlation was much higher in crisis than used for pricing; parameter gaming (e.g., correlation) has occurred (U.S. SEC action referenced; settlement included a $550 million fine).
- Suggested stronger requirement:
  - Require originators to hold stakes in every single tranche of a securitized product ("skin, flesh, and bones") rather than only the equity/subordinated tranche.

### Measures that may work against correlation bias risk (policy recommendations)
- Increase common equity relative to non-weighted assets:
  - Require substantially higher levels of common equity relative to total (unweighted) assets rather than relative to RWA.
  - Note in-source calibration remark: Basel III requirements specify a maximum leverage ratio of 33 for Tier-1 capital; even if Tier-1 comprised only common equity, that recommended leverage ratio implies a very thin equity layer supporting the capital structure. Calibrating a maximum common equity leverage ratio requires assessing acceptable institution risk and the impact of correlation bias, potentially via simulation.
- Enforce the Volcker Rule and portfolio diversification requirements:
  - Ban proprietary trading for systemic financial institutions (Volcker rule) to reduce complex, highly correlated trading book activity.
  - Strengthen concentration and large position limits for banking portfolios and consider quantitative limits guided by regulator-performed risk factor analysis or validated internal models (bearing in mind model risk and gaming incentive concerns).
- Force originators to hold stakes across all securitization tranches:
  - Require originators to retain proportional stakes across every tranche ("skin, flesh, and bones") to align incentives across seniority classes and reduce tranche-driven correlation incentives.
- Enhance corporate control by debt holders:
  - Increase the share of long-term debt in bank liabilities and ensure long-term creditors are represented on boards.
  - Increase long-term debt to strengthen asset-liability management and create stronger creditor monitoring incentives.
  - Careful design required to balance power between directors representing shareholders and those representing debt holders; the copula model could inform design choices.
- Other recommendations noted:
  - Ban proprietary trading in systemic institutions.
  - Enforce diversification requirements in both banking and trading books.

### Conclusions and key findings
- The correlation bias is a novel channel by which capital structure and control rights affect portfolio composition: junior claimants prefer higher asset correlation, producing higher joint tail risk.
- Because corporate control is usually exercised by the most junior claimants, financial institutions—especially systemic banks—may bias portfolios toward highly correlated assets, increasing institution-level failure probability and systemic risk.
- Many post-crisis regulatory reforms (contingent capital, systemic risk charges, waterfall structures, retention of equity tranche) do not eliminate correlation bias and could in some cases exacerbate it.
- Potentially effective policies to reduce correlation bias risk include:
  - Substantially increasing the share of common equity in the capital structure measured relative to unweighted assets.
  - Enforcing diversification requirements and banning proprietary trading in systemic institutions (Volcker rule).
  - Requiring securitization originators to hold stakes in all tranches of structured products.
  - Giving debt holders greater corporate control through increased long-term debt and board representation.

*Source: _wp1182 - section II, high leverage would bias the bank even more towards highly correlated assets in*

### REFERENCES

### _wp1182 - REFERENCES

### Systemic risk, bank regulation, and macroprudential policy
- Acharya, V.V., 2001, “A Theory of Systemic Risk and Design of Prudential Bank Regulation,” working paper (New York: New York University).
- __________, and T. Yorulmazer, 2007, “Too Many to Fail – An Analysis of Time-Inconsistency in Bank Closure Policies,” Journal of Financial Intermediation, Vol. 16, No. 1, pp. 1–31.
- __________, and M. Richardson, editors, 2009, Restoring Financial Stability: How to Repair a Failed System (New York: John Wiley and Sons).
- Basel Committee on Banking Supervision, 2009, Strengthening the Resilience of the Banking Sector, Consultative Document (Basel: Bank for International Settlements).
- __________, 2010a, Proposal to Ensure the Loss Absorbency of Regulatory Capital at the Point of Non-Viability, Consultative Document (Basel: Bank for International Settlements).
- __________, 2010b, “Group of Governors and Heads of Supervision Announces Minimum Global Standards,” press release (September 12).
- Brunnermeier, K., and L. Pedersen, 2008, “Market Liquidity and Funding Liquidity,” Review of Financial Studies, Vol.
- __________, A. Crockett, C. Goodhart, A.D. Persaud, and H.-S. Shin, 2009, “The Fundamental Principles of Financial Regulation,” Geneva reports on the World Economy, Vol. 11 (Geneva: International Center for Monetary and Banking Studies).
- Caruana, J., 2010, “Basel III: Towards a Safer Financial System,” speech delivered at the Third Santander International Banking Conference, Madrid (September).
- Dewatripont, M., J.-C. Rochet, and J. Tirole, 2010, Balancing the Banks (Princeton: Princeton University Press).
- Gauthier, C., A. Lehar, and M. Souissi, 2010, “Macroprudential Regulation and Systemic Capital Requirements,” Working Paper No. 2010-4 (Ottawa: Bank of Canada).
- Kashyap, A.K., R.G. Rajan, and J.C. Stein, 2008, “Rethinking Capital Regulation,” Proceedings of the 2008 Jackson Hole Symposium (Kansas City: Federal Reserve Bank of Kansas City).
- Lester, A., L.H. Pedersen, and T. Philippon, 2008, “Systemic Risk and Macroeconomic Capital,” working paper (New York: New York University).
- Tarashev, N., C. Borio, and C. Tsatsaronis, 2010, “Attributing Systemic Risk to Individual Institutions,” Working Paper No 308.
- Tarullo, D., 2009, “Confronting Too Big to Fail,” speech at The Exchequer Club, Washington, DC (October).
- Corrigan, G., 2009, “Containing Too Big to Fail,” The Charles F. Dolan Lecture Series at Fairfield University (November).
- Strongin, S., A. Hindlian, and S. Lawson, 2009, “Effective Regulation: Part 5 – Ending Too Big to Fail,” Global Markets Institute, Goldman Sachs (December).
- Tucker, P., 2009, “The Crisis Management Menu,” speech at the SUERF, CEPS, and Belgian Financial Forum Conference, Crisis Management at the Cross-Roads, Brussels (November).

### Market liquidity, funding, and contagion
- Adrian, T., and M. Brunnermeier, 2009, “CoVaR,” working paper (New York: Federal Reserve Bank of New York).
- Borio, C., C. Furfine, and P. Lowe, 2001, Procyclicality of the Financial system and Financial Stability: Issues and Policy Options, BIS Paper No. 1 (Basle: Bank for International Settlements).
- Hartmann, P., S. Straetmans, and C. de Vries, 2004, “Asset Market Linkages in Crisis Periods,” The Review of Economics and Statistics, Vol. 86, No. 1, pp. 313–326.
- Forbes, K., and R. Rigobon, 2002, “No Contagion, Only Interdependence: Measuring Stock Market Comovements,” Journal of Finance, Vol. 57, No. 5, pp. 2223–61.
- Cont, R., and J.P. Bouchaud, 1998, “Herd Behavior and Aggregation Fluctuations in Financial Markets,” working paper.
- Hartmann, P., S. Straetmans, and C. de Vries, 2004, “Asset Market Linkages in Crisis Periods,” The Review of Economics and Statistics, Vol. 86, No. 1, pp. 313–326.

### Structured finance, credit risk, and valuation
- Allen, F., and D. Gale, 2000, Comparing Financial Systems (Cambridge, MA: MIT Press).
- Andersen, L., J. Sidenius, and S. Basu, 2003, “All your Hedges in One Basket,” Risk, pp. 67–72.
- Gibson, M., 2004, “Understanding the Risk of Synthetic CDOs,” Finance and Economics Discussion Series 2004-36 (Washington, D.C.: Board of Governors of the Federal Reserve).
- Hull, J., and A. White, 2004, “Valuation of a CDO and n-th to Default CDS without Monte Carlo Simulation,” Journal of Derivatives, Vol. 12, No. 2, pp. 8-23 (Winter).
- Coval, J., J.W. Jurek, and E. Stafford, 2009, “The Economics of Structured Finance,” Journal of Economic Perspectives, Vol. 23, No. 1, pp. 3–25.
- Rajan, A., G. McDermott, and R. Roy, 2007, The Structured Credit Handbook (Wiley).
- Li, D.X., 2000, “On Default Correlation: A Copula Function Approach,” Journal of Fixed Income, Vol. 9, No. 4, pp. 43–54.
- Lando, D., 2004, Credit Risk Modeling (Princeton: Princeton University Press).
- Merton, R.C., 1974, “On the Pricing of Corporate Debt: the Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, No. 2, pp. 449–70.
- Vacisek, O., 1977, “Probability of Loss on Loan Portfolio,” Moody’s KMV (San Francisco).

### Herd behavior, behavioral finance, and market dynamics
- Bikhchandani, S., and S. Sharma, 2001, “Herd Behavior in Financial Markets,” IMF Staff Papers, Vol. 47, 279–310.
- Cont, R., and J.P. Bouchaud, 1998, “Herd Behavior and Aggregation Fluctuations in Financial Markets,” working paper.
- Nirei, M., 2006, “Herd Behavior and Fat Tails in Financial Markets,” working paper (Ottawa: Carleton University).
- Scharfstein, David, and Jeremy Stein, 1990, “Herd Behavior and Investment,” American Economic Review, Vol. 80, pp. 465–479.
- Andersen, L., J. Sidenius, and S. Basu, 2003, “All your Hedges in One Basket,” Risk, pp. 67–72.

### Corporate governance, agency costs, and legal actions
- Chan-Lau, J.A., 2001, “The Impact of Corporate Governance Structures on the Agency Cost of Debt,” available at http://ssrn.com/author=96623.
- __________, 2009, “Default Risk Codependence in the Global Financial System: Was the Bear Stearns Bailout Justified?” in G. Gregoriou, editor, The Banking Crisis Handbook (New York: CRC Press).
- __________, 2010, “Regulatory Capital for Too-Connected-to-Fail Institutions: A Practical Proposal,” forthcoming in Financial Markets, Institutions, and Instruments, Vol. 19, No. 5.
- U.S. Securities and Exchange Commision, 2010, “SEC Charges Goldman Sachs with Fraud in Structuring and Marketing of CDO Tied to Subprimer Mortgages,” press release (April 16).

### Books, reports, and commentary on the crisis and reforms
- Brunnermeier, K., and L. Pedersen, 2008, “Market Liquidity and Funding Liquidity,” Review of Financial Studies, Vol.
- French, K. et al, 2010, The Squam Lake Report: Fixing the Financial System (Princeton: Princeton University Press).
- Shin, H.-S., 2008, Risk and Liquidity, Clarendon Lectures in Finance (Oxford: Oxford University Press).
- Taleb, N., The Black Swan, Basic Books.
- The Economist, 2010, “Third Time’s the Charm?” London (September 13).
- Triana, P., 2010, “Basel III contains seeds of more chaos,” September 19 (London: Financial Times).
- Dudley, W., 2009, “Some Lessons Learned from the Crisis,” speech delivered at the Institute of International Bankers Membership Luncheon, New York City (October).

*Source: _wp1182 - REFERENCES*

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