Elsevier

Journal of Banking & Finance

Volume 45, August 2014, Pages 117-139
Journal of Banking & Finance

Liquidity, leverage, and Lehman: A structural analysis of financial institutions in crisis

https://doi.org/10.1016/j.jbankfin.2014.04.018Get rights and content

Abstract

This paper presents a flexible, lattice-based structural credit risk model that uses equity market information and a detailed depiction of a financial institution’s liability structure to analyze default risk. The model is applied to examine the term structure of default probabilities for Lehman Brothers prior to its demise. The results indicate, as early as March, that the firm would likely lose access to external capital within two years. The model can be used as both a diagnostic tool for the early detection of financial distress and a prescriptive tool for addressing the sources of risk in large, complex financial institutions.

Introduction

The recent financial crisis has demonstrated the pressing need for new tools to both measure and manage the risks of financial institutions. Perhaps no single event better illustrates the lapses in risk management and financial oversight than the dramatic failure of Lehman Brothers in September 2008. In only a few months, Lehman went from a leading and respected bulge bracket investment bank to a firm struggling to find external financing, and ultimately to a firm in throes of bankruptcy. This paper introduces a structural credit risk model to examine the interrelated and endogenous factors that served as the main catalysts of Lehman’s default and bankruptcy: (1) excessive leverage, (2) over-reliance on short-term debt, (3) under-collateralization, and (4) inability to raise capital. The flexible, lattice-based model makes use of equity market information along with a detailed depiction of Lehman Brothers’ liability structure to analyze the evolution of the firm’s default probabilities on a month-by-month basis throughout 2008. The model allows for the identification of the early warning signs of rapidly escalating default risk. These warning signs may be useful to regulators and risk managers as a diagnostic tool to preemptively identify at-risk financial institutions (such as Lehman Brothers) that may be in need of intervention, before it is too late.

In response to the financial crisis, there has been increased attention on the importance of the liability structure of financial institutions (Kashyap et al., 2008, Squam Lake Working Group, 2009). An overreliance on short-term debt makes financial institutions more vulnerable to liquidity shocks; not necessarily in the sense of traditional depositor bank runs (as in Diamond and Dybvig, 1983), but instead, as shown by Gorton and Metrick (2012), as runs on other short-term debt instruments (i.e., repos). This paper focuses on economic default, or insolvency that arises from the value of distressed assets being insufficient to support long-term illiquid liabilities, rather than liquidity-driven failure. The underlying reason for the inability of a financial institution to renew repo contracts and the decision by lending institutions to curtail financing is thus the leverage and credit quality.

Economic default is defined endogenously in our model as the point at which the financial institution can no longer raise capital (debt or equity) in a perfect market. Of course, this definition abstracts real-world market imperfections and frictions that exacerbate the insolvency problems. Nevertheless, even using this strict definition of economic default, the model still provides substantial insight into how the specific makeup of a financial institution’s balance sheet – from the liability structure in terms of both maturity and seniority to the liquidity of both assets and liabilities – amplifies the risk of distress resulting from their high degree of leverage.

Our analysis also highlights the importance of distinguishing between different quality assets on a financial institution’s balance sheet. Berger and Bouwman (2009) argue that the assets of a financial institution, in addition to its liabilities, can also be classified into three liquidity class – liquid, semi-liquid, and illiquid. Since the value of the liquid assets is independent of the credit risk of the financial institution, it would be incorrect to include them in the estimation. Our model assumes that the most liquid assets can be sold at book value which can then be used to cover the most liquid liabilities. What remains is a form of Net Debt made up primarily of the least liquid, publicly-traded debt.

Our model incorporates the complex nature of the illiquid liabilities of financial institutions as well. The impact of the detailed liability structure on financial institution risk can only been seen in a multi-period model and not in a single period model such as the Black–Scholes–Merton model (see Black and Scholes, 1973, Merton, 1974) or the popular KMV implementation (see Crosbie et al., 2003). In a single period, there is no place for the modeler to allow debt to rollover or reduce debt through de-leveraging. Our model, which builds upon this option-theoretical framework presented by Geske (1979) and Leland (1994), allows for refinancing of debt and provides an endogenous and structural analysis of credit risk. Our model includes a flexible refinancing parameter which allows for different assumptions about how the bank funds its maturing debt, nesting both the Leland (1994) and Geske (1977) approaches. The Leland (1994) model, and its extensions, assumes that the firm replaces the maturing debt with an identical new debt, which results in a constant level of debt over time. Such models, which assume that firms rollover debt, capture some elements of the real world in which financial institutions continue to operate with high degrees of leverage. Alternatively, models based on the Geske (1977) compound option pricing model assume that the firm issues equity to fund maturing debt and implicitly de-leverages over time.

We apply our model to the case of Lehman Brothers to demonstrate both its diagnostic ability and corrective potential for regulators and risk managers. To this end we utilize a comprehensive data set of all publicly traded bonds ever issued by Lehman Brothers. The bond data, collected from FactSet, is supplemented with data from financial statements and regulatory filings; thus we create a detailed picture of the liability structure at the end of each month from December 2007 to August 2008.4 We also use the market value of equity at month end and equity volatility as inputs in the model to estimate the market value of assets and asset volatility.

We implement a debt refinancing strategy that is intermediate between rollover of all debt and the paydown of debt with the issuance of new equity. Our attempt is to capture Lehman Brothers’ (or any financial institution’s) funding strategy in times of crisis, by choosing an intermediate value for the flexible refinancing parameter. We find that this generates a reasonable term structure of default probabilities, whose evolution we are able to study on a monthly basis leading up to the firm’s bankruptcy filing in September 2008. From the term structure we are able to compute the forward default probabilities, which we find contains considerable information about future economic distress. The analysis of Lehman Brothers indicates as early as March 2008 that Lehman Brothers would likely lose access to external capital (debt or equity) within the next year.

We argue that the model’s default probability estimates can be a very useful prognostic tool for regulators and risk managers. Our results demonstrate that markets clearly anticipated the financial crisis at Lehman Brothers well before the firm actually failed. The ex-ante increase in the forward default probability can be used to flag at-risk institutions. Our results confirm that the meager capital infusion in the Spring of 2008 was not sufficient to reduce Lehman Brothers’ default risk to acceptable levels.

The rest of the paper is as follows: Section 2 reviews the relevant literature. Section 3 provides an overview of the model framework and uses a numerical example to help develop the intuition. Section 4 contains our analysis of Lehman Brothers. We first discuss the institutional background of Lehman Brothers including a timeline of the events during 2008, details on the balance sheet – assets, liabilities, and net debt – as well as some preliminary analysis of the firm’s financial condition. We then present the model results and comprehensive analysis of Lehman Brothers’ default risk; we show that our model is able to predict the distress that Lehman would encounter and demonstrates the need for equity capital; we also estimate the collateral that should have been required by senior creditors. Section 5 concludes.

Section snippets

Related literature

Our paper is related to three strands of literature: (1) research on the financial crisis, specifically papers that deal with the link between leverage and liquidity; (2) the role of market information in supervising and regulating financial institutions; and (3) the structural credit risk literature with applications to the analysis of banking firms. We review each of these in turn.

Model framework

In this section we discuss our dynamic lattice based structural model for estimating default risk in financial institutions. Structural models are especially well-suited for managing and monitoring credit risk, either internally or externally, as they use the most recent inputs from financial statements and market data. We first review the role of capital structure assumptions in structural models and next present our lattice model.

Analysis of Lehman Brothers

On September 15, 2008, Lehman Brothers Holding Inc. (Lehman hereafter) filed the largest bankruptcy in the U.S. history with gross assets over $600 billion. Lehman was the 4th largest investment bank in the USA behind Goldman Sachs, Morgan Stanley, and Merrill Lynch prior to its bankruptcy. The C.E.O. of Lehman was Richard (Dick) Fuld who began his career with Lehman Brothers in 1969 and has been characterized as a stereotypical Wall Street investment banker: aggressive, ruthless, and

Conclusion

This paper presents new generalized binomial lattice, structural credit risk model which incorporates elements from both the Geske (1977) and Leland and Toft (1996) frameworks. The model is applied in a clinical analysis of the distress and failure of Lehman Brothers. The model uses market inputs, namely equity value and equity volatility, in order to estimate the forward default probabilities that serve as an “early warning signal” for financial institutions in distress. Additional insights

References (52)

  • V. Acharya et al.

    Cash holdings and credit risk

    Rev. Financ. Stud.

    (2012)
  • V. Acharya et al.

    Capital shortfall: a new approach to ranking and regulating systemic risks

    Am. Econ. Rev.

    (2012)
  • Adrian, T., Begalle, B., Copeland, A., Martin, A., 2012. Repo and securities lending, Working Paper 18549 National...
  • Allen N. Berger et al.

    Bank liquidity creation

    Rev. Financ. Stud.

    (2009)
  • Berk, Jonathan, DeMarzo, Peter, 2010. Corporate Finance (Pearson), second...
  • Sreedhar T. Bharath et al.

    Forecasting default with the merton distance to default model

    Rev. Financ. Stud.

    (2008)
  • Fischer Black et al.

    Valuing corporate securities: some effects of bond indenture provisions

    J. Finance

    (1976)
  • Fischer Black et al.

    The pricing of options and corporate liabilities

    J. Political Econ.

    (1973)
  • P. Bond et al.

    Market-based corrective actions

    Rev. Financ. Stud.

    (2010)
  • Markus K. Brunnermeier

    Deciphering the liquidity and credit crunch of 2007–2008

    J. Econ. Perspect.

    (2009)
  • Markus K. Brunnermeier et al.

    Market liquidity and funding liquidity

    Rev. Financ. Stud.

    (2009)
  • Pierre Collin-Dufresne et al.

    Do credit spreads reflect stationary leverage ratios?

    J. Finance

    (2001)
  • Peter J. Crosbie et al.

    Modeling Default Risk

    (2003)
  • Sergei A. Davydenko

    What triggers default? A study of the default boundary

    SSRN eLibrary

    (2012)
  • Delianedis, Gordon, Geske, Robert, 2003. Credit risk and risk neutral default probabilities: information about rating...
  • Douglas W. Diamond et al.

    Bank runs, deposit insurance, and liquidity

    J. Political Econ.

    (1983)
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    We thank participants at the Conference on Risk Management and Reform of Bank Regulation sponsored by Peking University, Fordham University, and the Journal of Banking and Finance, especially Zhuo (Albert) Huang [discussant], Ho-Mou Wu, and Ike Mathur. We would also like to thank an anonymous referee. This paper benefitted from earlier discussions with Sanjiv Das, Mark Flannery, Nikunj Kapadia, C.F. Lee, Joe Mason, Biljana Nikolic, Darius Palia, Dilip Patro, Jun “Jonathan” Wang, as well as seminar participants at the Office of the Comptroller of the Currency, the Indian School of Business, the Korea Advanced Institute of Science and Technology, Louisiana State University, the Securities and Exchange Commission, the 2009 Financial Economics and Accounting Conference, the 2009 Triple Crown Conference, and the 2010 FMA Doctoral Consortium. We thank the Whitcomb Center for Research in Financial Services for their generous support. Sopranzetti gratefully acknowledges financial support for the project provided by a Faculty Research Grant from Rutgers Business School-Newark and New Brunswick.

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