NO.PZ2024042601000050
问题如下：
An analyst at a financial institution has been asked to assess the quality of estimating credit VaR (CVaR) of a homogenous 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:
• There are 1,000 firms (credits) in the portfolio.
• Each firm represents 0.1% of the portfolio.
• There is no idiosyncratic risk.
• Loss given default is the same for each firm in the portfolio.
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?
选项：
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
解释：
A is correct. Under perfect correlation (beta equal to 1), there are two possibilities: either all the credits default (loss rate equals to 100%), or none of the credits defaults (loss rate equals to 0%).
B is incorrect. The reading explains that correlation to the market factor determines how spread out the defaults are over the range of the market factor such that, if the correlation to the market factor is low (high), then for any probability of default, the number of defaults will be low (high) and the distance to default of credit assets will typically be high (low).
C is incorrect. Given no idiosyncratic risk and a default correlation of zero, the loss rate is likely very close to the probability of default.
D is incorrect. The pairwise asset return correlation is measured by the square of beta.
各项具体公式讲一下呗
