Capital Allocation and Bank Management Based on the Quantification of Credit Risk

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1. THE NEED FOR QUANTIFICATION OF CREDIT RISK

Liberalization and deregulation have recently accelerated. It is therefore useful to keep risk within a certain level in relation to capital, considering that financial institutions must control their risk appropriately to maintain the safety and soundness of their operation. In 1988, the Basle Capital Accord--International Convergence of Capital Measurement and Capital Standards--introduced a uniform framework for the implementation of risk-based capital rules. However, this framework applies the same "risk weight" (a ratio applied to assets for calculation of aggregated risk assets) to loans to all the private corporations, regardless of their creditworthiness. Such an approach might encourage banks to eliminate loans that can be terminated easily while maintaining loans with higher risk.

As shareholder-owned companies, banks are expected to maximize return on equity during this competitive era, while performing sound and safe banking functions as financial institutions with public missions. Banks are finding it useful to conduct business according to the management method that requires them to maintain risk within capital and to use risk-adjusted return on allocated capital as an index of profitability based on more accurate quantification of credit risk.

2. OUTLINE OF THE MODEL FOR THE QUANTIFICATION OF CREDIT RISK

2.1. BASIC DEFINITIONS FOR THE QUANTIFICATION OF CREDIT RISK

"Credit risk" (also referred to as maximum loss), in a narrow sense, is defined as the worst expected loss (measured at a 99 percent confidence interval) that an existing portfolio (a specific group) might incur until all the assets in it mature. (We set the longest period at five years here.) Capital should cover credit risk--the maximum loss exceeding the predicted amount.

"Credit cost" (also referred to as expected loss) is defined as the loss expected within one year. Credit cost should be regarded as a component of the overall cost of the loan and accordingly be covered by the loan interest.

"Loss amount" is defined as the cumulative loss we incur over a specific time horizon because of the obligor's default. Loss amount is equal to the decrease in the present value of the cash flows related to a loan caused by setting the value of the cash flows (after the default) at zero: Loss amount equals value in consideration of default less value in case no default occurs.

Here, the loan is regarded as a bond that pays an annual fixed rate. The minimum unit period for a loan is one year; any shorter periods are to be rounded up to the nearest year. The value of each cash flow after default is zero. The discount rate can be determined only for one currency that is applied to all the transactions. Mark-to-market in case of downgrades or upgrades of credit rating is not performed. Loss amount consists of principal plus unpaid interest.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Here, d denotes the year of default, M the maturity of the loan, [D.sub.t] the discount rate for year t, r the interest rate of the loan, P the outstanding balance of the loan, and [Lambda] the recovery rate. We set at zero the discount rate and the interest rate of the loan.

The above measurement does not include new lendings or rollovers that might be extended in the future. Prepayment is not considered, and the risks until the contract matures will be analyzed. (We set the longest period, however, at five years.)

"Recovery rate" is defined as the ratio of 1) the current price of the collateral multiplied by the factors according to the internal rule to 2) the principal amount of each loan on the basis of the present perspective of recovery. In calculations of the loss amount, the amount that can be recovered is deducted from the principal amount of each loan (corresponding to [D.sub.d] [multiplied by] [Lambda] [multiplied by] P in the above formulas). …