RDP 9210: Contingent Claim Analysis of Risk-Based Capital Standards for Banks 5. Conclusions and Agenda For Future Research

We have shown within the context of a contingent claim model of banking that risk-based capital standards can be derived to fix the value of the deposit guarantor's liability per dollar of deposits; we call this an LV rule. Alternatively, risk-based capital can place an upper bound on the probability of bank failure during any period, which we refer to as an FP rule. We examine the value-maximising responses of banks facing the constraints imposed by LV and FP risk-based capital standards, assuming that banks maximise the value of equity net of contributed capital. We find that bank behaviour depends on the type of rule imposed. The model suggests that low-risk assets will be chosen under an LV rule, while high-risk assets are likely to be chosen under an FP rule. Thus while the two rules are plausible and are designed to meet related regulatory goals, they have very different implications for bank behaviour.

The LV and FP standards, while desirable in theory, may be too complicated to be feasible in practice. We derive a simple version of the international standards actually being implemented (the BIS/Basle standards) and find that those standards could serve as a good approximation to either an LV rule or an FP rule. However, with either type of rule the “best fit” weight on risky assets is greater than 100 percent under most assumptions; the weight on riskless assets is close to zero for an FP approximation and substantially less than zero for an LV approximation. Judgements regarding the best weightings depend on the range of asset risk believed to be relevant in practice; since this range may vary from one country to the next, capital standards should retain a degree of flexibility to allow national banking authorities to make necessary adjustments.

Further research should explore the sensitivity of the simple linear standards to the number of asset categories. Also, it would be more accurate to allow for non-zero correlation between asset categories, and to treat all assets as risky since even government securities are subject to interest rate risk. For practical applications to banking policy a better sense of the actual variance-covariance matrix for various types of bank assets is needed; estimation of this matrix is the subject of separate work in progress by the authors. Given more precise estimates of the riskiness of various types of assets, it would be interesting to re-examine how close the actual risk weights from the Basle accord come to either of the theoretical possibilities discussed here. Finally, in actual practice regulators probably aim both to prevent failure and to limit the deposit guarantee liability; the authors are exploring the possibility of representing risk-based capital objectives as a weighted average of FP and LV.