Explanation

In the single-factor model for credit risk, the asset return correlation between two firms i and j is given by:

$\rho_{ij} = \beta_i \times \beta_j$

Where:

• $\beta_i$ is the correlation of firm i with the market factor
• $\beta_j$ is the correlation of firm j with the market factor

Given:

• Firm 1 (cyclical): $\beta_1 = 0.5$
• Firm 2 (defensive): $\beta_2 = 0.1$

Calculation: $\rho_{12} = \beta_1 \times \beta_2 = 0.5 \times 0.1 = 0.05$

Therefore, the asset return correlation between the two firms is 0.05.

Key Points:

• In the single-factor model, asset correlations are determined solely by their individual correlations with the common market factor
• The correlation between any two firms is the product of their respective beta coefficients
• This model assumes that all systematic risk is captured by a single common factor