Value at Risk and Bank Capital Management

Questions such as How much capital is required to cover potential losses deriving from the risks we are undertaking?, What is the risk-adjusted return on capital produced by each business unit and by each product?, and How should capital be allocated within business units? are crucial for any bank. Yet before discussing them, the word capital must be defined. In fact, there are different notions of capital and different capital constraints that the bank should satisfy at the same time.
One well-known distinction is between regulatory capital and economic capital. Required regulatory capital is calculated according to regulators rules and methodologies, defining for each bank a minimum regulatory capital requirement (MRCR). Regulators also clearly identify which components of the bank s balance sheet can be considered to be eligible as capital (i.e., available regulatory capital). In contrast, economic capital represents an internal estimate of the capital needed to run the business that is developed by the bank itself. This estimate may differ from MRCR since, for instance, the bank may include risks that are not formally subject to regulatory capital or may use different parameters or methodologies. Here we define required economic capital as the amount of capital the bank considers necessary for running the business from its point of view, independent of regulatory constraints. Of course, the bank should also be able to compare it with available economic capital.
According to the broad definition we have adopted, required economic capital is therefore an...