OPTIMAL INVESTMENT POLICY AND CAPITAL MANAGEMENT IN A FINANCIAL INSTITUTION

Abstract

This research work considered an asset optimization problem where we examine how a financial institution can optimally allocate its total wealth among three assets namely; treasury, security and loan in stochastic interest rate setting and also determined how a financial institution can manage its capital. The optimal investment policy was derived through the application of stochastic optimization theory for the case of constant relative risk aversion (CRRA) utility function. Also, the Stochastic Differential Equation (SDE) for the capital adequacy ratio under Basel Accord, the SDE for the Total Risk – Weighted Assets (TRWA), the SDEs for the capital required to maintain the capital adequacy ratio under Basel II and Central Bank of Nigeria (CBN) standards were derived and solved numerically to study the capital management problem of the financial institution. Numerical examples using published data obtained from Central Bank of Nigeria (CBN) statistical bulletin and Nigeria Stock Exchange were presented to illustrate the dynamics of the optimal investment policy and how a financial institution can manage its capital. From the results, the optimal investment strategy can be achieved by shifting the financial institution investment away from the risky assets (security and loan) towards the riskless asset (treasury). It was also observed that if a financial institution observes the Basel II standard or Nigeria CBN standard of capital requirement, the financial institution would be considered to be strongly capitalized and guarantees the ability to absorb unexpected losses.