Financial Crisis, Interconnectedness and Regulatory Capital

Introduction

Problems experienced in the U.S. subprime mortgage market in mid-2007 rapidly escalated to a liquidity crisis in the financial system, leading to a full blown financial crisis in 2008-9 and the worst global recession experienced since the Great Depression in 1929. The economic consequences of the crisis have been substantial. Writedowns in the banking sector through the first half of 2009 amounted to $1.3 trillion, and going forward they may increase to $2.8 trillion.[1]

The substantial costs associated with the crisis have raised concerns in regard to whether the financial regulatory framework provides adequate safeguards against externalities affecting the systemic financial stability. One such insidious externality, which arises naturally from the increased interdependence and globalization of the financial system, is associated with the Too-Connected-to-Fail (TCTF) problem. Examples of this problem include the stresses in the payment and settlement systems following the liquidation of Herstatt bank in 1974 and the need for the Federal Reserve Bank of New York to coordinate the rescue of Long Term Capital Management in 1998.

More recently, the TCTF problem was dramatically illustrated by the increased volatility and liquidity shortages affecting financial institutions in the aftermath of the demise of Lehman Brothers, an investment bank, on September 15, 2008. Arguably, motivated by these developments, American International Group (AIG), an insurance company, was bailed out the next day to prevent a disorderly unwinding of AIG’s credit derivatives contracts and its potential negative consequences on the financial system.

Among the academic and policymaking communities, the crisis has prompted calls for adopting higher quality regulatory capital requirements that reflect the systemic risk posed by financial institutions[2] and the risks associated with their market interaction.[3] While there is still ample debate on whether higher capital charges could hamper the efficiency and pace of innovation of the financial system, the Basel Committee is already working on measures aimed at reducing leverage and procyclicality in the banking system.[4]

In line with this debate, it may be appropriate to introduce TCTF capital charges since TCTF has been recognized as one of the contributing factors to the systemic risk of a financial institution.[5] One clear benefit of TCTF capital charge is that it induces institutions to internalize the costs associated with their interconnection with other institutions. Such a charge, hence, will provide managerial incentives to avoid too much homogeneity among financial institutions, which tend to amplify shocks, and to reduce the reliance on a limited number of counterparties. The TCTF capital charge could also be useful for defining the perimeter of regulation, as the capital charge needs to rely on the incremental contribution to systemic risk of the institution. The rest of the article discusses the logic underlying the TCTF capital charge and how it may help to enhance financial regulation.[6]

The Too-Connected-To-Fail Capital Charge: A Simple Concept

The globalization of the financial system and the expansion of large complex financial institutions onto an array of diverse activities that transcend national boundaries have led to stronger linkages and interconnectedness across institutions, whether regulated or not. [7] In a highly interconnected system, the failure of one institution is likely to trigger the failure of other institutions due to either direct or indirect sources of exposures. Direct exposure can arise from interbank claims and/or counterparty exposure from derivatives transactions. An institution may have also accumulated a substantial exposure through credit derivatives contracts to the credit risk of an otherwise unrelated institution, as it was the case with AIG. Among indirect exposures, the similarities of investment portfolios and trading strategies subject them to substantial mark-to-market losses if the bankruptcy of one institution forces a disorderly fire-sale of assets at drastically reduced prices.

Societal loss is the proper risk metric for assessing the TCTF capital charge. Either due to direct or indirect exposures, the externalities associated with the failure of a too-big-to-fail or too-interconnected-to-fail institution force the government to partly assume some of the losses, which are ultimately borne out by taxpayers. It becomes natural, therefore, that the TCTF capital charge reflects the incremental contribution of the default of one institution to the potential societal loss from the surviving institutions.

The definition of societal loss is rather flexible and should be determined by the systemic regulatory agency. The operational definition depends on the dominant features of the financial system it oversees. In a country where the financial system comprises mostly deposit-taking institutions, the measure of societal loss could be associated with potential deposit losses. If pension funds are among the main sources of funding to domestic banks, it may be justified to include as societal losses potential losses faced by pension funds in case financial institutions fail. The recent experience in the U.S. indicates that societal losses could be roughly approximated by the potential losses associated with the bank liabilities since many of the government measures effectively guarantee the claims of banks’ senior creditors. Indeed, the implicit U.S. government guarantee was priced in the market as shown by the convergence of the U.S. sovereign and banks’ credit default swaps following the implementation of support measures.

A Two-Bank Example

The following two-bank example helps to clarify the intuition underlying the TCTF capital charge. Suppose that the two banks, A and B , are identical. Each bank holds $100 million and their unconditional probability of default is 5%. If one bank defaults, all deposits are lost and the probability of default of the surviving bank increases to 6%. Since deposits, in this example, are guaranteed by the government, the societal cost is equal to the losses suffered by the depositors. In isolation, the expected societal loss from the default of any of the two banks is $5 million (5% times the amount of deposits, $100 million). If bank A defaults, the expected societal loss from the subsequent default of bank B increases to $6 million (6% times $100 million).

In this example, the incremental contribution to societal loss of the default of bank A is $1 million, or the increase in the expected losses of bank B ($6 million minus $5 million). The TCTF capital charge should be proportional to the incremental contribution of $1 million. For instance, if capital charges (or provisions, in this example) were set equal to the expected loss, bank A would have to hold $6 million in capital: $5 million corresponding to its unconditional expected loss, and an additional $1 million corresponding to the expected losses its default induces on bank B.

A Practical Approach to Assess TCTF Capital Charges

More generally, the TCTF capital charge for a specific institution should be assessed based on the differences between the conditional societal loss distributions when the institution survives and defaults respectively. Furthermore, in line with current practice established under the Basel Accord, the comparison between the loss distributions should be based on a predetermined confidence level set up by the regulatory authority. This is summarized in Figure 1. The Figure depicts the hypothetical case of N banks or systemic financial institutions of interest to the regulator. The incremental contribution to societal loss of bank J is determined by comparing changes in the loss distribution of the other N-1 banks when the bank J is solvent and when bank J defaults.

Figure 1. The Incremental Contribution of the Default of Institution J to Societal Loss

The figure shows the hypothetical loss distribution for a portfolio of N-1 banks (or financial institutions) that excludes bankJ conditional on whether bank J defaults or not. It also shows the corresponding marginal contribution to societal loss of bank J for a given confidence level α.

The calculations to assess the incremental contribution of bank J on the system, based on known techniques for risk budgeting,[8] are described as follows: The starting point is a portfolio of N-1 banks that excludes bank J. This portfolio is referred to as the incremental portfolio of institution J. The loss distribution over a fixed time horizon conditional on the survival of bank J is calculated for its incremental portfolio using the probability of default, PD_I, exposure at default, EAD_I, and the loss given default, LGD_I of the remaining institutions. Depending on the loss distribution model used, it would also be necessary to specify the degree of association (or dependence) between the probabilities of default of the banks in incremental portfolio of institution J. The loss distribution associated with the survival of institution J is referred to as the hypothetical ex-ante loss distribution, i.e. prior to the failure of the institution.

Similarly, the conditional loss distribution in the event that J defaults, or the hypothetical ex‑post loss distribution, can be calculated using the conditional probability of default, PD_I|J, the conditional exposure at default, EAD_I|J, the conditional LGD_I|J, and the conditional degree of association (or dependence). For instance, in the two bank example above, it was assumed that the exposure at default, equal to the deposits, and the loss given default, 100%, remain the same regardless of whether a bank defaults or not. This is not necessarily the case, as the default of one bank could change the exposure at default of the surviving banks. For instance, in the case of Herstatt risk, or settlement risk, the exposure at default depends on how much the defaulted institution owes to the surviving institutions. Furthermore, the dependence or association measure, such as the default correlation, could increase substantially following the failure of one institution as observed in the aftermath of the bankruptcy of Lehman Brothers on September 15, 2008. More generally, empirical studies have shown that dependence measures are higher during downmarket periods and recessions, which suggests failures of financial institutions could be related to higher default correlation.

For the purpose of determining the incremental contribution to societal losses, it is appropriate to use the difference between the values of both loss distributions at a certain confidence level such that the probability of experiencing a large loss is relatively small. The use of the differences in the expected loss in both distributions is just the particular case of setting the confidence level at 50%. Furthermore, the use of a confidence level is also the standard practice for the calculation of economic and regulatory capital using Value-at-Risk (VaR) models, which facilitates the adoption of the interconnectedness capital charge by regulatory agencies. Alternatively, it is possible to use Expected Shortfall (ES) rather than VaR or other coherent risk measures.[9] For illustration purposes only, the discussion below focuses on VaR but extending the methodology to other risk measures is straightforward.

Consequently, as shown in Figure 1, for a confidence level of 1-α, the incremental contribution to societal loss of bank J is equal to B-A, the difference between the VaR_α values of the conditional and unconditional loss distributions respectively: 

 (1)

Once the incremental contribution to societal loss is calculated, the TCTF capital charge can be calculated simply as the product of the probability of default of bank J times the incremental contribution to societal loss:

 (2)

In the two-bank example above, the interconnectedness capital charge for any of the banks will be $50,000 (5 percent times $1 million). The magnitude of the TCTF capital charge of an institution increases with its incremental contribution to societal loss and with the probability it will default. So imposing this charge provides banks with incentives to either change their business activities to reduce the risk they pose to other banks or to take measures aimed at strengthening their solvency.

Summarizing, the steps for calculating the interconnectedness capital charge for an institution J in relation to a group of connected institutions are:

1. For each institution other than J, specify the probability of default of the remaining institutions in the events that institution J survives or defaults.

2. Similarly, for each one of the institutions in step 1, determine the societal exposure at default and the societal loss given default for each of the two events. Typical choices are the nominal amount of potential losses incurred by the government in case the institutions default.

3. Construct the societal loss distributions for the incremental portfolio that comprises all institutions excluding institution J in the event that J survives, ex-ante loss distribution, or defaults, ex-post loss distribution.

4. Pick up a given confidence level. Typical values correspond to those used for calculating Value-at-Risk (VaR), i.e. 95% , 99%, and 99.5% (alternatively, a tail-risk measure such as Expected Shortfall (ES) can be used).

5. Calculate the VaR in the ex-ante and ex-post societal loss distributions at the specified confidence level.

6. Calculate the incremental contribution to societal loss as the difference between the VaR conditional on the default of institution J (VaR of ex-ante loss distribution) and the VaR conditional on the survival of institution J (VaR of ex-post loss distribution).

7. Calculate the TCTF capital charge as the product of the probability of default of institution J and its incremental contribution to societal loss.

Among the steps above, the most difficult calculations are likely related to step 1, the specification of the probability of default, and to step 2, the determination of the exposure at default and loss given default. Step 3 requires the specification of a loss distribution model and its associated characteristics. Foremost among them is the specification of the degree of association or dependence, i.e., in layman terms, comovement, between the probabilities of default of individual institutions. Steps 4 to 7 are relatively straightforward after the specification of the required elements in steps 1 to 3.[10] But ongoing work by researchers in academia and policymaking institutions may help cope with some of the difficulties outlined above.[11]

The TCTF Capital Charges and Financial Regulation

The proposed Too-Connected-to-Fail capital charge attempts to contribute to the ongoing efforts towards the design of a modern regulatory framework. The proposed capital charge methodology has two important features. First, it builds upon an intuitive principle: the capital charge must be proportional to the incremental contribution to societal losses (or risk) due to the failure of the institution. Second, by relating the concept of incremental contribution to systemic risk to concepts such as Value-at-Risk and Expected Shortfall, the TCTF capital charge is aligned with the spirit of Basel II. This alignment will facilitate its adoption and implementation by supervisory agencies and systemic risk regulators.

Since the TCTF capital charge relies on measuring the systemic risk contribution of an institution, it could also help to determine what institutions should be covered by the perimeter of regulation. The inclusion in the perimeter, for instance, could be based on each institution’s incremental contribution to societal loss. If this contribution exceeds a predetermined threshold, the institution should be included in the perimeter. Under this procedure, some institutions that are not currently regulated may be subsequently included while others may be dropped from it if they no longer present a systemic risk to society. The adoption of a dynamic perimeter of regulation not only responds to changes in market practices and business conditions but also helps to allocate scarce regulatory resources more efficiently by focusing them on the more vulnerable and/or riskier institutions from a societal vantage point.

The discussion above assumes the charge should be applied to the institution that fails. There are valid arguments, however, for applying the charges to the institutions most affected by the failure of the TCTF institution. One argument is that the TCTF capital charge, if applied as suggested in the paper, may potentially penalize efficient institutions. Their efficiency, arguably, is one reason why they have become TCTF. A second argument is that, from the perspective of a TCTF institution, the linkages with other institutions could depend on the business models of the latter. In this case, the TCTF institution would be punished unfairly for factors beyond its control. One potential way to partly address these concerns is to add up the individual TCTF capital charges and distribute them proportionally to each institution’s probability of default.

As with any capital charge, there are some procyclical features in the TCTF capital charge as the probability of default of an interconnected institution increases during economic slowdowns and/or periods of generalized market underperformance. The procyclicality could be reduced to a certain extent by using estimates of the probability of default conditional on the realization of extreme events. In addition, to reduce the risks to the system, it may be possible to design a prompt corrective action (PCA) framework in which different thresholds for the TCTF capital charges trigger potential remedial actions. In this case, even if the TCTF capital charge is procyclical, its use within a PCA framework ensures a ceiling on the maximum probability of default of any given institution.

Finally, the imposition of a TCTF capital charge could go a long way towards internalizing the negative externalities associated with too-connected-to-fail institutions and provide managers the incentives to strengthen an institution’s solvency position, and avoid too much homogeneity and excessive reliance on the same counterparties in the financial industry.

But for the TCTF capital charge to have its intended effects, it would be necessary to harmonize regulatory practices, especially in regard to the measurement of interconnectedness risk, across different jurisdictions since TCTF institutions operate across countries and are subject to the different regulatory regimes. Fortunately, the need to cope with future financial crisis has strengthened the political will to increased harmonization of regulatory principles and supervisory practices.

* This article is an excerpt from J.A. Chan-Lau, “Regulatory Capital Charges for Too-Connected-to-Fail Institutions: A Practical Approach,” working paper, 2009.

[1] International Monetary Fund, Global Financial Stability Report (October 2009).

[2] M. Brunnermeier, A. Crockett, C. Goodhart, A. Persaud, and H.-S. Shin, “The Fundamental Principles of Financial Regulation,” Geneva Reports of the World Economy (2009); B. Bernanke, “Financial Regulation and Supervision after the Crisis – the Role of the Federal Reserve” (speech at the Federal Reserve Bank of Boston 54th Economic Conference, October 23, 2009).

[3] F. Milne, “The Complexities of Financial Risk Management and Systemic Risks,” Bank of Canada Review (Summer 2009): 15–29; D.K. Tarullo, “Regulatory Reform,” (testimony before the Committee on Financial Services, U.S. House of Representatives, Washington, D.C., October 29, 2009).

[4] J.C. Trichet, “Shaping the Future of Global Financial Market Regulation,” transcript of ideo interview at the Netherlands Bank’s Amsterdam Financial Forum, November 28, 2009.

[5] Guidance to Assess the Systemic Importance of Financial Institutions, Markets and Instruments: Initial Considerations , Report to G20 Finance Ministers and Governors.

[6] See Chan-Lau, “Regulatory Capital Charges,” for detailed examples.

[7] For a detailed account on the systemic risks posed by financial globalization and how they contribute to interconnectedness, see J.A. Chan-Lau, “The Globalization of Finance and its Implications for Financial Stability: An Overview of the Issues,” International Journal of Banking, Accounting and Finance 1(1): 3 -29 (2008).

[8] R. Litterman, “Hot SpotsTM and Hedges,” Journal of Portfolio Management 23 (December 1996, special issue): 52–75.

[9] See P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, “Coherent Measures of Risk,” Mathematical Finance 9 (1999): 203–28.

[10] It is worth mentioning that a rigorous calculation of the TCTF capital charge requires an iterative process, or finding a fixed point, as emphasized in C. Gauthier, A. Lehar, and M. Souissi, “Macroprudential Capital Requirements and Systemic Risk,” working paper, Ottawa, Bank of Canada, 2009.. Equation (2) points out that the capital charge depends on the probability of default. The addition of the TCTF capital charge increases the capital of the institution and reduces its leverage. Lower leverage usually contributes to lower asset volatility. As a result, the probability of default of the institution declines and in turn, it reduces the TCTF capital charge. From a regulatory perspective, however, a one iteration of the TCTF capital charge errs on the conservative side and appears to be a second-best solution in a world where optimal solutions are unfeasible due to data quality and model risk.

[11] See T. Adrian and M. Brunnermeier, “CoVaR,” mimeo (New York: Federal Reserve Bank of New York, 2009); Gauthier, Lehar and Souissi, “Macroprudential Capital”; N. Tarashev, C. Borio, and K. Tsatsaronis, “The Systemic Importance of Financial Institutions,” BIS Quarterly Review (September 2009): 75–87;, and especially Chan-Lau, “Regulatory Capital Charges,” for a practical implementation.