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Answer: P; R; Q
The correct ranking of the counterparties from most likely to least likely to default is determined by calculating the Distance to Default (DtD) for each company. The DtD measures the number of standard deviations to reach the default threshold, with a higher DtD indicating a lower likelihood of default. The formula for DtD is simplified to: \[ \text{DtD} = \frac{\ln(\frac{\text{Va}}{\text{F}})}{\sigma} \] where: - \(\text{Va}\) is the market value of assets, - \(\text{F}\) is the face value of debt, - \(\sigma\) is the annual volatility of asset values. Using the provided data: - For Company P: \( \text{DtD} = \frac{\ln(\frac{100}{60})}{0.10} = 5.11 \) - For Company Q: \( \text{DtD} = \frac{\ln(\frac{150}{100})}{0.07} = 5.79 \) - For Company R: \( \text{DtD} = \frac{\ln(\frac{250}{160})}{0.08} = 5.58 \) Based on these calculations: - Company Q has the highest DtD (5.79), indicating it is least likely to default. - Company R has a DtD of 5.58, placing it in the middle in terms of default likelihood. - Company P has the lowest DtD (5.11), making it the most likely to default. Therefore, the correct answer is A. P; R; Q, with Company P being the most likely to default, followed by Company R, and then Company Q being the least likely.
Author: LeetQuiz Editorial Team
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In the context of credit risk assessment, the Merton model is often used to estimate the default risk of firms by calculating the 'distance to default.' Consider the following data derived from the Merton model for three counterparties, Company P, Company Q, and Company R. These companies operate within the same industry and do not pay dividends. Based on the calculated distance to default over a 1-year period, how should a credit manager rank these companies in terms of their likelihood of defaulting?
A
P; R; Q
B
Q; P; R
C
Q; R; P
D
R; Q; P
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