723873

Research Article An Optimal Portfolio and Capital Management Strategy for Basel III Compliant Commercial Banks Grant E. Muller and Peter J. Witbooi Univer sity of the West ern Cape, Private Bag X, Bellville , South Africa Correspondence should be addressed to Peter J. Witbooi; [email protected] .za Received October ; Accepted January ; Published February Academic Editor: Francesco Pellicano Copy right © G. E. Muller and P . J. Witb ooi. Tis is an openaccess artic le distri bute d underthe Crea tiveCommons At tribu tion Licen se, whichpermits unre strict ed use, distr ibuti on, andreprod uctio n in anymedium, pro videdthe origi nal workis pro perlycited. We model a Basel III complian t commercial bank that operates in a nancial market consisting o a treasury security , a marketable securi ty , and a loa n and we reg ar d the interestratein the mar ke t as bein g st och ast ic. We ndthe inves tme nt str at egy tha t maximizes an expected utility o the bank’s asset portolio at a uture date. Tis entails obtaining ormulas or the optimal amounts o bank capital invested in different assets. Based on the optimal investment strategy, we derive a model or the Capital Adequacy Ratio (CAR), whic h theBasel Committeeon Ban kin g Superv ision (BCB S) int rod uce d as a measure aga inst banks ’ sus cep tib ili ty to ai lur e. Furthe rmo re, we consi der the op timal inv est men t strat egy sub jec t to a constant CAR at the minimu m pr esc ribe d lev el. We der ive a ormula or the bank’ s asset portolio at constan t (minimum) CAR value and present numerical simulation s on different scenarios. Un der theoptimal inves tme nt str ategy , the CARis abo ve the minimum pr escribed lev el.Te val ue o theasset por to lio is imp roved i the CAR is at its (constant) minimum value. 1. Introduction Successul bank management can be achieved by addressing our operational concerns. Firstly, the bank should be able to nance its obligations to depositors. Tis aspect o bank management is called liquidity management. It involves the bank acquiring sufficient liquid assets to meet the demands rom deposi t withd rawal s and depos itor paymen ts. Secon dly , banks mus t eng age in lia bil ity man age men t. Tis aspect o bank management entails the sourcing o unds at an accep table cost. Tirdly, banks are required to inve st in asset s that have a reasonably low level o risk associated with them. Tis process is reerred to as asset management. It aims to encourage the bank to invest in assets that are not likely to be deaulted on and to adopt investment strategies that are sufficiently diverse. Te ourth and nal operational concern is capital adequacy management. Capital adequacy management invol ves the decis ion about the amoun t o capital the bank should hold and how it should be accessed. From a shareholder’ s perspective, utilizing more capital will increase ass et ear nin gs and will lea d to high er returns on equity . From the regulator’ s perspective, banks should increase their buffer capital to ensure the saety and soundness in the case where earnings may end up below an expected level. In this paper, we address problems associated with asset and capital adequacy management. Te Basel Committee on Banking Supervision (BCBS) regulates and supervises the international banking industry by imposing minimal capital requirements and other measures. Te Basel Capital Accord, also known as the Basel I Accord, aimed to assess the bank’s capital in relation to its credit risk, or the risk o a loss occurring i a party does not ulll its obligations. Te Basel I Accord launched the trend toward increasing risk modeling research. How- ever, its oversimplied calculations and classications have simultaneously called or its disappearance. Tis paved the way or the Basel II Capital Accord and urther agreements as the symbol o the conti nuous rene ment o ris k and capital. Te (revised) ramework o the Basel II Capital Accord (see [ ]) laid down regulations seeking to provide incentiv es orgre at er awaren es s o diff er ences in ris k thr oug h more risk- sensi tive minimum capi tal requirements based on numerical ormulas. Te otal Capital Ratio or Capital Adequacy Ratio (CAR) (see or instance [ –]) measures the amount o the bank’s capital relative to its amount o cred it exposu res.International ly , a stan dardhas been adop ted Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2014, Article ID 723873, 11 pages http://dx.doi.org/10.1155/2014/723873

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