The individual loans here follow a Binomial distribution.

We know that the variance of default probability in the context of a binomial distribution is given by:

$$\text{Var}(X) = n * PD * (1 - PD) \\ = 500 * 0.015 * (1 - 0.015) \\ = 7.3875$$

Things to Remember

• The variance of default probability is critical to measuring the credit risk volatility within a loan portfolio.
• Binomial distribution assumes independence of default events among individual loans, which simplifies the calculation of variance.
• Financial professionals involved in credit risk management should be adept at using the appropriate statistical formulas to inform their risk assessments.