Internal vs. External Risk Measures: How Capital Requirements Differ in Practice

We compare capital requirements derived from tail conditional expectation (TCE) with those derived from the tail conditional median (TCM). In theory, TCE is higher than TCM for most distributions commonly used in finance and at fixed confidence levels; however, we find that in empirical data, there is no clear-cut relationship between the two. Our results highlight the relevance of TCM as a robust alternative to TCE, especially for regulatory control.