A Contingent Claim Analysis of Risk-based Capital Standards for Banks

Many countries are implementing capital adequacy standards developed under the auspices of the Bank for International Settlements (BIS), which explicitly link each bank’s minimum capital-to-asset ratio to the riskiness of its operations. In this paper, we use a contingent claim framework to examine the general questions of what goals a risk-based capital framework might be designed to achieve and how risk-based standards might be expected to influence bank behaviour. We identify two related but distinct regulatory policy goals, and derive a capital adequacy rule to achieve each goal: a liability-value (LV) rule designed to limit the contingent liability borne by the deposit guarantor per dollar of deposits; and a failure-probability (FP) rule designed to limit the probability of bank insolvency. We show that an LV rule is likely to push banks toward low-risk, low-capital combinations, whereas an FP rule is likely to encourage high risk and high capital ratios. The results suggest that restrictions on bank asset holdings and on overall financial leverage may be desirable in conjunction with risk-based capital standards. We then consider the extent to which the BIS standards reflect either an FP or an LV approach to capital regulation. The BIS standards assign risk weights to various types of assets, and establish a minimum ratio of capital to the sum of risk-weighted assets. We find that a BIS-type standard with appropriately chosen weights could be an extremely close approximation to a rule designed to achieve either goal, but that the actual weightings contained in the accord are most consistent with an FP rule. However, we show that the weight assigned to riskless assets should be negative if regulatory goals make an LV rule desirable; we also find that under either LV or FP rules the weight given to risky assets probably should be substantially higher than established in the BIS agreement. The optimal weights also depend on the typical range of risks in bank portfolios. Since this range may vary from one financial system to the next, it may be desirable to retain a degree of national discretion in setting the precise weightings.