Basel II versus III: a comparative assessment of minimum capital requirements for internal model approaches

ABSTRACT In this paper, we provide a comparative assessment of the minimum capital requirement (MCR) in three prominent versions of the Basel regulatory framework: Basel II, the 2010 version of Basel III and the current 2013 version of Basel III. For this purpose, we use Cantelli's inequality to compute theoretical MCR violation levels for different unconditional distributional specifications, accounting for skewness and kurtosis. Cantelli's inequality allows us to perform a quantitative comparison of various Basel accords without exact knowledge of the future return process. Therefore, our results are not biased, due to the specific choice of the sample data and/or uncertainty about the underlying return process as well as the "true" risk model. We find that under weak distributional specifications (ie, normal tails), the MCR under the 2013 version of Basel III is only marginally higher than under Basel II. However, this difference increases (decreases) for risk models equipped with heavy-tailed (normal) innovations. In contrast to this, we document that under the 2010 version of Basel III the MCR violation levels during a stress period are adequate, even when using a risk model with weak distributional specifications. However, we also show that the MCR under the 2010 version of Basel III is too conservative in calm periods. ;