Balance sheet and seniority constraints on the repayment value of claims

Padellini, Mauro (2021): Balance sheet and seniority constraints on the repayment value of claims.

Abstract

The problem is addressed of how (different types of) funding transactions may affect the repayment value of (credit or equity) claims; to this purpose a novel prove for the existence and uniqueness of the payment vector, which does not make (explicit) use of the fixed point theorem and allows for the presence of claims with different seniorities (i.e. credit and equity claims), is proposed. Different components of the overall displacement (the reduction of repayment value), related to i) seniority structure, ii) network of bilateral exposure and iii) imbalances between external loss and external capital, are calculated by sequentially relaxing different constraints in the mixed linear program used for calculating overall displacement. The possibility that more credit may reduce overall displacement (due to borrowing-from-Peter-to-pay-Paul effect) and more equity capital may on the contrary increase overall displacement (due to its role in the transmission of financial displacement) is exemplified, along with the possible negative dependence of relative displacement (the ratio between overall displacement and total claims) on total claims.

• Item Type: MPRA Paper
• Language: English
• Keywords: Balance sheet, leverage
• Subjects: G - Financial Economics > G0 - General > G01 - Financial Crises; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M4 - Accounting and Auditing > M41 - Accounting

References

[1] D.Acemoglu, A.Ozdaglar, A.Tahbaz-Salehi, Systemic Risk and Stability in Financial Networks The American Economic Review Vol. 105, No. 2 (February 2015), pp. 564-608.

[2] T.Adrian, H.S.Shin, The Changing Nature of Financial Intermediation and the Financial Crisis of 2007-09 Federal Reserve Bank of New York Staff Reports, no. 439, April 2010.

[3] Banca d'Italia, Financial Stability Report No. 5, April 2013.

[4] Bank for International Settlements, Implications of repo markets for central banks, page 4. Basle, 1999.

[5] A.Barba, G.de Vivo, An ‘unproductive labour’ view of finance Cambridge Journal of Economics (October 2012), 36, 1479-1496.

[6] A.Barba, M.Pivetti, Rising household debt: Its causes and macroeconomic implications-a long period analysis Cambridge Journal of Economics 2009, 33, 113-137.

[7] N.Bertschinger, J.Stobbe, Systemic Greeks: Measuring risk in financial networks arXiv:1810.11849v1 [q-fin.RM] 28 October 2018.

[8] A.A.Bogdanov, Tektology, Centre for Systems Studies Press, Hull, UK, 1996. First published in Russian, 1913-1917 as The Universal Science of Organization (Tektologia).

[9] M.D.Bordo, C.M.Meissner, Does Inequality Lead to a Financial Crisis?, NBER Working Paper 17896, March 2012.

[10] S.Bougheas, A.Kirman, Systemic risk and the optimal seniority structure of banking liabilities, Int. J.Fin. Econ., 2018, pages 47-54.

[11] R.A.Brualdi, Combinatorial Matrix Analysis. In C.F. Floudas and P.M. Pardalos, editors, Encyclopedia of Optimization, pages 377-379. Springer Science+Business Media LLC, NY USA, 2009.

[12] N.I.Bukharin, Imperialism and the Accumulation of Capital, Monthly Review Press, 1972, English translation from the original Russian edition of 1924.

[13] W.K.Chen, On Directed Graph Solutions of Linear Algebraic Equations, SIAM Review, Vol. 9, No. 4 (October, 1967), pp. 692-707.

[14] J.F. Cocco, Portfolio Choice in the Presence of Housing,The Review of Financial Studies Vol. 18, No. 2, 2004.

[15] D.Cooper, Did Easy Credit Lead to Overspending? Home Equity Borrowing and Household Behavior in the Early 2000s.

[16] J.L.Coronado, D.Maki, B.Weitzer, Retiring on the House? Cross-Cohort Differences in Housing Wealth PRCWP (September 2006).

[17] V.Cuciniello, N.di Iasio, Determinants of the credit cycle: a ow analysis of the extensive margin, ECB Working Paper Series No 2445 / July 2020.

[18] F. De Saussure, Course in General Linguistics, p. 81. The Philosophical Library, INC., NY USA, 1959 (translated from the French edition Geneva, July 1915).

[19] M.Eboli, Direct Contagion in Financial Networks with Mark-to-Market and Historical Cost Accounting Rules, International Journal of Economics and Finance Vol. 2, No. 5; (2010), pp.27-34.

[20] M.Eboli, A Flow Network Analysis of Direct Balance-Sheet Contagion in Fi- nancial Networks, Kiel Working Papers 1862, Kiel Institute for the World Economy (IfW), 2013.

[21] ECB, Financial Stability Review, May 2016.

[22] L.Eisenberg and T.H.Noe, Systemic Risk in Financial Systems, Management Science, Vol. 47, No. 2 (February., 2001), pp. 236-249.

[23] A.A. Eliman, M.Girgis, S.Kotob, The Use of Linear Programming in Disentangling the Bankruptcies of Al-Manakh Stock Market Crash, Operations Research, Vol. 44, No. 5 (September - October, 1996), pp. 665-676.

[24] H.Elsinger, Financial Networks, Cross Holdings, and Limited Liability, ONB Working Paper 156, 2009.

[25] K.Fan, Inequalities for M-matrices, Proc. Konig Nederl. Akad. Wetensch. Amsterdam Ser. A 67 (1964), 602-610.

[26] Z.Feinstein, W.Pangz, B.Rudlox, E.Schaanning S.Sturmz, M.Wildmank, Sensitivity of the Eisenberg Noe clearing vector to individual interbank liabilities, NORGES BANK 13, 2017.

[27] M.Fiedler, Matrices and Graphs in Geometry, Cambridge University Press,New York, 2011.

[28] T.Fischer, No-Arbitrage Pricing Under Systemic Risk: Accounting for Cross-Ownership, Mathematical Finance, Vol.24, No.1 (January 2014), pp.97-124.

[29] O.Frécaut, A National Wealth Approach to Banking Crises and Financial Stability, IMF Working Paper 2016/128.

[30] M.Fry, The Fiscal Abuse of Central Banks, IMF Working Paper 1993/58.

[31] D. Graeber, Debt: the first 5,000 years, Melville House, New York, 2011.

[32] J.L.Gross and J. Yellen (edited by), Handbook of Graph Theory, CRC Press, Boca Raton, FL, 2013.

[33] D.Harvey, The New Imperialism, Oxford University Press, 2003.

[34] M.Horkheimer, T.W.Adorno, Dialectic of Enlightenment - Philosophical Fragments, Stanford University Press, Stanford, California, 2002 First published in German, 1944-194.

[35] O.Jordà, B.Richter, M.Schularick, A.M.Taylor, Bank Capital Redux: Solvency, Liquidity, and Crisis, NBER Working Paper 23287, March 2017.

[36] A.S.Karpenko, V.A.Smirnov's Results in the Field of Modern Formal Logic, Studia Logica: An International Journal for Symbolic Logic, Vol. 66, No. 2, In Memory of V. A. Smirnov (November, 2000), Springer, p. 239.

[37] D.B.Kronenfeld, Fanti Kindship and the Analysis of Kinship Terminologies, University of Illinois Press, Urban and Chicago, 2009.

[38] M.Kumhof, R.Ranciére and P.Winant, Inequality, Leverage, and Crises, The American Economic Review , Vol. 105, No. 3 (March 2015), pp. 1217-1245 26.

[39] J.Lubliner, Plasticity Theory, Dover Inc., 2008.

[40] R. Luxemburg, The Accumulation of Capital, trans. A. Schwartzchild, New Havenm Yale University Press, 1951. First German edition, Die Akkumulation des Kapitals: Ein Beitrag zur oekonomischen Erklarung des Imperialismus, 1913.

[41] G.Poole and T.Boullion, A Survey on M-Matrices, J. Soc. Indust. Appl. Math., 16 (1974), pp. 419-427.

[42] G.F.Rose, Equation of Value in Investment Theory, The American Mathematical Monthly, Vol. 55, No. 8 (October, 1948), pp. 495-497.

[43] A.C.Santos and N.Teles (CES), Recent Trends in Household Financial Behaviour, FESSUD Working Paper 171, November 2016.

[44] W.Schoen, Balance Sheet Tests of Solvency Test - of Both?, European Business Organization Law Review 7, 2006. The Hague: T.M.C Asser Press pp. 181-198.

[45] T.Sinai, N.S.Souleles, Net Worth and Housing Equity in Retiremen, NBER Working Paper 13693, March 2017.

[46] H.L.Smith, M.S.Finke, S.J.Huston, Financial Sophistication and Housing Leverage Among Older Households, Journal of Family and Economic Issues (2012).

[47] T.Suzuki, Valuing Coporate Debts: The Effect of Cross-Holdings of Stocks and Debt, Journal of the Operational Research Society of Japan, Vol. 45, No. 2 (June, 2002), pp. 123-144.

[48] L.E.O.Svensson, Housing Prices, Household Debt, and Macroeconomic Risk: Problems of Macroprudential Policy, https://larseosvensson:se/les/papers/housing-prices-household-debtandmacroeconomic- risk:pdf.

[49] A.Tarski, A simplified formalization of predicate logic with identity, Archiv fȗr Mathematische Logik und Grundlagenforschung, Vol.7 (March 1964), pp. 61-79.

[50] K.Thulasiraman and M.N.S.Swamy, Graphs: Theory and Algorithms, John Wiley and Sons, Inc., Hoboken, New Jersey 1992.

[51] J. Tobin, On the Effciency of the Financial System, Lloyds Bank Review (July 1984) pp.1-15.

[52] R.S.Varga, Matrix Iterative Analysis, Springer-Verlag, Berlin, 2000.