Answer: 0.05

## 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

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