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On the Fractal Geometry of the Balance Sheet and the Fractal Index of Insolvency Risk

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  • A. K. M. Azhar
  • Vincent B. Y. Gan
  • W. A. T. Wan Abdullah
  • H. Zainuddin

Abstract

This paper reviews the economic and theoretical foundations of insolvency risk measurement and capital adequacy rules. The proposed new measure of insolvency risk is constructed by disentangling assets, debt and equity at the micro-prudential firm level. This new risk index is the Firm Insolvency Risk Index (FIRI) which is symmetrical, proportional and scale invariant. We demonstrate that the balance sheet can be shown to evolve with a fractal pattern. As such we construct a fractal index that can measure the risk of assets. This index can differentiate between the similarity and dissimilarity in asset risk, and it will also possess the properties of being self-similar and invariant to firm characteristics that make up its asset composition hence invariant to all types of risk derived from assets. Self-similarity and scale invariance across the cross section allows direct comparison of degrees of risk in assets. This is by comparing the risk dissimilarity of assets. Being naturally bounded to its highest upper bound, (0,2], the fractal index is able to serve like a risk thermometer. We assign geometric probabilities of insolvency P (equity is equal or less than 0 conditional on debt being greater than 0).

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  • A. K. M. Azhar & Vincent B. Y. Gan & W. A. T. Wan Abdullah & H. Zainuddin, 2015. "On the Fractal Geometry of the Balance Sheet and the Fractal Index of Insolvency Risk," Papers 1512.09280, arXiv.org.
    • Handle: RePEc:arx:papers:1512.09280
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    1. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and multifractality in the term structure of LIBOR interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 603-614.
    2. Fengzhong Wang & Shwu-Jane Shieh & Shlomo Havlin & H. Eugene Stanley, 2009. "Statistical analysis of the overnight and daytime return," Papers 0903.0993, arXiv.org.
    3. Abdul Azhar & Robert Elliott & Chris Milner, 1998. "Static and dynamic measurement of intra-industry trade and adjustment: A geometric reappraisal," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 134(3), pages 404-422, September.
    4. Abdul K. M. Azhar & Robert J. R. Elliott, 2006. "On the Measurement of Product Quality in Intra-Industry Trade," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 142(3), pages 476-495, October.
    5. Moyano, L.G. & de Souza, J. & Duarte Queirós, S.M., 2006. "Multi-fractal structure of traded volume in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 118-121.
    6. Grubel, Herbert G & Lloyd, P J, 1971. "The Empirical Measurement of Intra- Industry Trade," The Economic Record, The Economic Society of Australia, vol. 47(120), pages 494-517, December.
    7. B. B. Mandelbrot, 2001. "Scaling in financial prices: I. Tails and dependence," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 113-123.
    8. Zunino, Luciano & Figliola, Alejandra & Tabak, Benjamin M. & Pérez, Darío G. & Garavaglia, Mario & Rosso, Osvaldo A., 2009. "Multifractal structure in Latin-American market indices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2331-2340.
    9. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393-393.
    10. Benoit B. Mandelbrot, 2005. "The inescapable need for fractal tools in finance," Annals of Finance, Springer, vol. 1(2), pages 193-195, October.
    11. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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