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The financial crisis and the shadow price of bank capital

  • S.I.: Application of O. R. to Financial Markets
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Abstract

We employ parametric forms of directional distance functions to obtain shadow prices of bank equity capital for listed and unlisted banks. We exploit cost, revenue and profit maximisation as the optimisation criteria to derive pricing rules, which allow us to find shadow prices for both inputs and outputs by explicitly accounting for the bank’s capital structure choices and hence risk-taking behaviour. We show how knowledge of one input price can be used to price outputs and how knowledge of one output price can be used to price inputs along with information on input and output quantities. We also show how information on total cost or revenue can be used to shadow price inputs and outputs, respectively. We obtain some striking results highlighting the perils of overambitious balance sheet expansions supported by excessive leverage. More specifically, we show that shadow prices for equity capital had reached abnormally high levels in the years leading up to the subprime crisis in the US indicative of excessive risk-taking behaviour.

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Notes

  1. The low risk anomaly refers to an empirical pattern arising from historical returns and thus realised cost of equity being higher, rather than lower, for less risky equity. A similar albeit much weaker pattern arises in debt markets (see Frazzini and Pedersen 2014; Baker and Wurgler 2013; Baker et al. 2017).

  2. The directional distance function was introduced by Chambers et al. (1996, 1998) as a generalisation of the Luenberger (1992) benefit function. Fixler and Zieschang (1992) were the first to measure the shadow value of the opportunity cost of bank capital in a distance function framework using Shephard (1970) distance functions.

  3. See Green et al. (2003), Barnes and Lopez (2006), King (2009), Baker and Wurgler (2013).

  4. Applications using parametric forms of directional distance functions in banking include Fukuyama and Weber (2008), Koutsomanoli-Philippaki et al. (2009).

  5. For example, negative shadow capital prices may result from extensive deleveraging as banks attempt to rebuild their capital above well-capitalised levels after suffering major mortgage-related losses (see Weyman-Jones 2016).

  6. See Spierdijk et al. (2017) for a similar argument in relation to the US banking industry.

  7. Leverage amplifies shocks to the value of banks’ assets, increasing the chance of distress, insolvency, and costly bailouts, thereby raising the required return on equity capital (Kisin and Manela 2016).

  8. Tier 1 (core) capital as a percent of average total assets minus ineligible intangibles. Tier 1 (core) capital includes: common equity plus noncumulative perpetual preferred stock plus minority interests in consolidated subsidiaries less goodwill and other ineligible intangible assets. The amount of eligible intangibles (including mortgage servicing rights) included in core capital is limited in accordance with supervisory capital regulations.

  9. According to the FDIC Vice Chairman of FDIC Thomas Hoenig “The primary measure of capital—the risk adjusted measure - is misleading and overstates the strength of these firms’ balance sheets. No other industry is allowed to make these kinds of adjustments. The tangible leverage ratio provides a more accurate measure of assets and risks than the balance sheet reported under either GAAP or Basel” see https://www.fdic.gov/about/learn/board/hoenig/statement4-2-2015.html.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, 1561836314, Iran

    Maryam Hasannasab

  2. Department of Accounting and Finance, University of Auckland Business School, Auckland, 1010, New Zealand

    Dimitris Margaritis

  3. Member of Greek Parliament, Department of Accounting and Finance, Athens University of Business and Economics, 10434, Athens, Greece

    Christos Staikouras

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  1. Maryam Hasannasab
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  2. Dimitris Margaritis
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  3. Christos Staikouras
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Correspondence to Dimitris Margaritis.

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Hasannasab, M., Margaritis, D. & Staikouras, C. The financial crisis and the shadow price of bank capital. Ann Oper Res 282, 131–154 (2019). https://doi.org/10.1007/s10479-018-2886-z

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