Credit Risk Management Practice Exam

What is the formula to calculate default correlation for a two credit portfolio assuming Bernoulli-distributed random variables?

1. P12 = (π12−π1π2) / [Sqrt(π1*(1-π1)) * Sqrt(π2 * (1-π2))]

2. P12 = (π1 + π2) / Sqrt(π1 * π2)

3. P12 = π12 / (π1 + π2)

4. P12 = π1 * π2 / (1 - π1 * π2)

The correct answer is: P12 = (π12−π1π2) / [Sqrt(π1*(1-π1)) * Sqrt(π2 * (1-π2))]

The formula for calculating default correlation in a two-credit portfolio is derived from the concept of how the default events of these credits are statistically related to each other. The correct choice utilizes the joint probability of defaults, represented by π12, and the marginal probabilities of defaults for each of the individual credits, denoted as π1 and π2. The formula expresses default correlation as a comparison between the observed joint default probability (π12) and the product of the individual default probabilities (π1 and π2). This relationship captures how much the presence of a default in one credit informs about the likelihood of a default in the other. Specifically, the formula effectively quantifies how the actual joint probability deviates from what would be expected if the two defaults were independent occurrences. The use of the square roots in the denominator, calculated from the variances of the individual probabilities, normalizes this correlation measure. This normalization is crucial because it ensures the correlation value remains within a bounded range, typically between -1 and 1, making it interpretable under standard correlation metrics. This approach is essential in credit risk management as it helps practitioners understand and manage the interdependencies between different credit exposures, which is particularly relevant in diversified portfolios.