Since the default correlation equals 1, the entire portfolio will act as if it is a single credit. Thus, either the entire portfolio defaults, with a probability of π, or it doesn’t. Regardless of the value of n, say 5, 10, 20, 50, etc., the portfolio will behave as if n = 1.

The expected loss is equal to π × total value of the portfolio = 2% × $100,000,000 = $2,000,000

There is a 98% probability that the loss will be zero, because π = 2%. We calculate the credit VaR as the quantile of the credit loss minus the expected loss of the portfolio. At 95%, therefore, the credit VaR is equal to −$2,000,000 (= 0 − $2,000,000)

Things to Remember

• Default Probability: The likelihood that a borrower will be unable to meet its debt obligations.
• Recovery Rate: The percentage of the principal amount that is recovered after a borrower defaults.
• Credit Value at Risk (Credit VaR): A statistical technique used to measure and quantify the level of financial risk within a credit portfolio.
• Default Correlation: The degree to which the defaults of different credits are related or move together.