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.
Highlights
Successful bank management can be achieved by addressing four operational concerns
Tier 2 capital is defined as the sum of the following elements: instruments issued by the bank that meet the criteria for inclusion in Tier 2 capital, stock surplus resulting from the issue of instruments included in Tier 2 capital, instruments issued by consolidated subsidiaries of the bank and held by third parties that meet the criteria for inclusion in Tier 2 capital and are not included in Tier 1 capital, certain loan-loss provisions, and regulatory adjustments applied in the calculation of Tier 2 capital
We provide a numerical simulation in order to characterize the behaviour of the Capital Adequacy Ratio (CAR), Λ
Summary
Successful bank management can be achieved by addressing four operational concerns. Firstly, the bank should be able to finance its obligations to depositors. Under the Basel II Accord, banks were required to maintain a CAR, that is, a ratio of total bank capital to total risk-weighted assets (TRWAs), with a minimum value of 8%. Mukuddem-Petersen and Petersen [11] studied a problem related to the optimal risk management of banks in a stochastic setting. The aforementioned authors minimized market and capital adequacy risk that respectively involves the safety of the securities held and the stability of sources of funds In this regard, the authors suggested an optimal portfolio choice and rate of bank capital inflow that will keep the loan level as close as possible to an actuarially determined reference process. The issues of asset portfolio and capital adequacy management for Basel III compliant commercial banks are addressed in a continuous-time setting.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
