Value at Risk and Bank Capital Management

When measuring the impact of credit risk, the bank has to estimate the distribution of potential losses that can be generated by its credit portfolio. The two key concepts are represented by expected losses, i.e., the statistical mean of the loss distribution, and unexpected losses, which can be defined as the amount of losses in some extreme percentile of the loss distribution (e.g., 99%, 99.9%) minus expected losses. Expected losses represent a cost of being in the lending business and hence should be covered by provisions, while capital assuming an adequate amount of provisions should be used to cover unexpected losses. The main determinants of the dynamics of the expected and unexpected losses for a given exposure are represented by exposure at default (EAD), probability of default (PD), and the ratio of the loss in the event of default to the exposure at default, i.e., the loss given default (LGD). Agency rating companies support financial institutions and investors in evaluating the riskiness of a borrower by issuing independent judgments on a borrower s credit quality, which are expressed by classifying the borrower in a given rating class. Rating agencies historical data, such as transition matrixes describing the evolution patterns of borrowers ratings through time and cumulative and marginal default rates, may represent very important sources of information for a risk manager. Similarly to rating agencies, even if often with different methodologies, banks usually classify borrowers in internal rating classes with different probabilities of...