A credit supervisor within the counterparty risk department of a leading financial institution utilizes a simplified version of the Merton model to assess the relative vulnerability of its largest counterparties to changes in their value and financial stability. To assess the default risk of three specific counterparties, the supervisor calculates the distance to default over a 1-year horizon (t=1). The companies under consideration, named Company P, Company Q, and Company R, are in the same industry and do not distribute dividends. The pertinent details about these companies are summarized in the following table:
| Company | P | Q | R |
|---|---|---|---|
| Market value of assets (EUR million) | 100 | 150 | 250 |
| Face value of debt (EUR million) | 60 | 100 | 160 |
| Annual volatility of asset values | 10.0% | 7.0% | 8.0% |
Based on the provided data, and considering that each company's only financial liability is a zero-coupon bond maturing in 1 year, together with the approximation formula for the distance to default, what is the correct ranking of the counterparties from the highest to the lowest probability of default?
A
P; R; Q
B
Q:P;R
C
Q; R; P
D
R: Q: P
Explanation:
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 using the Merton model. The DtD is a measure that approximates the number of standard deviations away from the default threshold a company is, with a higher DtD indicating a lower likelihood of default.
The formula for DtD, assuming a 1-year horizon and zero drift factors, is simplified to:
[ \text{DtD} = \frac{\text{In}(\frac{\text{Va}}{\text{F}})}{\sigma} ]
where:
Using the provided data:
Based on these calculations:
Therefore, the correct ranking is Q; R; P, which corresponds to option C.
Ultimate access to all questions.