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An Optimal Portfolio and Capital Management Strategy for Basel III Compliant Commercial Banks

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  • Grant E. Muller
  • Peter J. Witbooi

Abstract

We model a Basel III compliant commercial bank that operates in a financial market consisting of a treasury security, a marketable security, and a loan and we regard the interest rate in the market as being stochastic. We find the investment strategy that maximizes an expected utility of the bank’s asset portfolio at a future date. This entails obtaining formulas for the optimal amounts of bank capital invested in different assets. Based on the optimal investment strategy, we derive a model for the Capital Adequacy Ratio (CAR), which the Basel Committee on Banking Supervision (BCBS) introduced as a measure against banks’ susceptibility to failure. Furthermore, we consider the optimal investment strategy subject to a constant CAR at the minimum prescribed level. We derive a formula for the bank’s asset portfolio at constant (minimum) CAR value and present numerical simulations on different scenarios. Under the optimal investment strategy, the CAR is above the minimum prescribed level. The value of the asset portfolio is improved if the CAR is at its (constant) minimum value.

Suggested Citation

  • Grant E. Muller & Peter J. Witbooi, 2014. "An Optimal Portfolio and Capital Management Strategy for Basel III Compliant Commercial Banks," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:723873
    DOI: 10.1155/2014/723873
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    References listed on IDEAS

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    1. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    2. Thakor, Anjan V, 1996. "Capital Requirements, Monetary Policy, and Aggregate Bank Lending: Theory and Empirical Evidence," Journal of Finance, American Finance Association, vol. 51(1), pages 279-324, March.
    3. Gao, Jianwei, 2008. "Stochastic optimal control of DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1159-1164, June.
    4. Cox, John C. & Ingersoll Junior, Jonathan E. & Ross, Stephen A., 2007. "A theory of the term structure of interest rates," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 47(2), April.
    5. Jean-Charles Rochet, 2004. "Rebalancing the three pillars of Basel II," Economic Policy Review, Federal Reserve Bank of New York, issue Sep, pages 7-21.
    6. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    7. von Thadden, Ernst-Ludwig, 2004. "Bank capital adequacy regulation under the new Basel Accord," Journal of Financial Intermediation, Elsevier, vol. 13(2), pages 90-95, April.
    8. J. Mukuddem-Petersen & M. A. Petersen & I. M. Schoeman & B. A. Tau, 2007. "Maximizing Banking Profit on a Random Time Interval," Journal of Applied Mathematics, Hindawi, vol. 2007, pages 1-22, June.
    9. Jung, Eun Ju & Kim, Jai Heui, 2012. "Optimal investment strategies for the HARA utility under the constant elasticity of variance model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 667-673.
    10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    11. Xiao, Jianwu & Hong, Zhai & Qin, Chenglin, 2007. "The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 302-310, March.
    12. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    13. Heid, Frank & Porath, Daniel & Stolz, Stéphanie, 2003. "Does capital regulation matter for bank behavior? Evidence for German savings banks," Kiel Working Papers 1192, Kiel Institute for the World Economy.
    14. Gao, Jianwei, 2010. "An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 511-530, June.
    15. J. Mukuddem-Petersen & M. A. Petersen & I. M. Schoeman & B. A. Tau, 2007. "Maximizing Banking Profit on a Random Time Interval," Journal of Applied Mathematics, John Wiley & Sons, vol. 2007(1).
    16. Gao, Jianwei, 2009. "Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 9-18, August.
    17. Decamps, Jean-Paul & Rochet, Jean-Charles & Roger, Benoit, 2004. "The three pillars of Basel II: optimizing the mix," Journal of Financial Intermediation, Elsevier, vol. 13(2), pages 132-155, April.
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    1. Grant E. Muller, 2018. "An Optimal Investment Strategy and Multiperiod Deposit Insurance Pricing Model for Commercial Banks," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).

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