Credit Risk Management Practice Exam

How is variance of default probability calculated assuming a binomial distribution?

1. σ² = PD × (1 - PD)

2. σ² = PD × 2

3. σ² = (1 - PD)²

4. σ² = PD + (1 - PD)

The correct answer is: σ² = PD × (1 - PD)

The variance of default probability under the assumption of a binomial distribution can be derived based on the formula for variance in a binomial scenario. In such distributions, the variance is calculated using the formula σ² = n × p × (1 - p), where 'n' refers to the number of trials, and 'p' is the probability of success (in this case, the probability of default, PD). In scenarios where the number of trials is 1 (which represents a single observation), the formula simplifies to σ² = PD × (1 - PD). This formulation captures the uncertainty around the probability of default, accounting for the likelihood of both defaulting (PD) and not defaulting (1 - PD). The other options do not accurately represent the correct calculation of variance in this context. For instance, multiplying PD by 2 or adding PD with (1 - PD) does not align with the statistical principles governing variance in a binomial distribution. Understanding this calculation is essential for effective credit risk assessment, as it helps quantify the risk associated with potential defaults.