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Answer: When the firm's beta to the market factor is equal to 1, the loss rate of the credits is either 0% or 100%.
## Explanation **A is correct.** Under the single-factor model with perfect correlation (beta equal to 1), there are only two possible outcomes: - All credits default (loss rate = 100%) - No credits default (loss rate = 0%) This occurs because when beta = 1, all firms move perfectly together with the market factor, so they either all default together or all survive together. **B is incorrect.** When correlation to the market factor is low, defaults are more spread out and independent. For a given probability of default, the distance to default (a measure of how far a firm is from default) will typically be **high** when correlation is low, not low. **C is incorrect.** When asset return correlation to the market factor is zero (no systematic risk), defaults occur independently. With no idiosyncratic risk and 1,000 firms, the loss rate should be very close to the individual probability of default due to the law of large numbers. **D is incorrect.** The pairwise asset return correlation between firms is measured by the **square of beta** (β²), not the square root of beta. **Key Concept:** In the single-factor credit risk model, beta represents the sensitivity to the systematic market factor, and the correlation between firms is β². Perfect correlation (β=1) leads to extreme outcomes where all firms default together or survive together.
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An analyst at a financial institution has been asked to assess the quality of estimating credit VaR (CVaR) of a homogeneous portfolio of firms (credits) using the single-factor model, under which default correlation varies with the firm's beta to the market factor. The analyst examines the portfolio under the following assumptions:
Based on the information provided, which of the following observations, if made by the analyst, would be correct regarding the application of the single-factor model and its parameters?
A
When the firm's beta to the market factor is equal to 1, the loss rate of the credits is either 0% or 100%.
B
The distance to default of a firm will typically be low if the correlation to the market factor is low, for a given probability of default.
C
When the asset return correlation to the market factor is equal to zero, the loss rate is typically higher than the probability of default of a firm in the portfolio.
D
The asset return correlation to the market factor is measured by the square root of beta.