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Answer: P; R; Q
## Explanation Distance to Default (DtD) approximates the number of standard deviations to reach the default threshold; thus, the higher the DtD, the least likely to default. Using the simplified formula: $$ DtD \cong \frac{\ln V_a - \ln F}{\sigma_a} = \frac{\ln(V_a/F)}{\sigma_a} $$ Calculating for each company: - **Company P**: DtD = ln(100/60)/0.10 = ln(1.6667)/0.10 = 0.5108/0.10 = **5.11** - **Company Q**: DtD = ln(150/100)/0.07 = ln(1.5)/0.07 = 0.4055/0.07 = **5.79** - **Company R**: DtD = ln(250/160)/0.08 = ln(1.5625)/0.08 = 0.4463/0.08 = **5.58** **Ranking from most likely to least likely to default** (lowest to highest DtD): - P (5.11) - most likely - R (5.58) - middle - Q (5.79) - least likely Therefore, the correct ranking is **P; R; Q**.
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A credit manager in the counterparty risk division of a large bank uses a simplified version of the Merton model to monitor the relative vulnerability of its largest counterparties to changes in their valuation and financial conditions. To assess the risk of default of three particular counterparties, the manager calculates the distance to default assuming a 1-year horizon (t=1). The counterparties: Company P, Company Q, and Company R, belong to the same industry, and are non-dividend-paying firms. Selected information on the companies is provided in the table below:
| 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% |
Using the information above with the assumption that a zero-coupon bond maturing in 1 year is the only liability for each company, and the approximation formula of the distance to default, what is the correct ranking of the counterparties, from most likely to least likely to default?
A
P; R; Q
B
Q; P; R
C
Q; R; P
D
R; Q; P
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