Explanation:
To calculate the Expected Default Frequency (EDF), we first calculate the default threshold (K) and then the Distance to Default (DD). The standard assumption in the KMV model for the default threshold is short-term debt plus 50% of long-term debt: K = Short-term debt + 0.5 × Long-term debt = £6 + 0.5 × £4 = £8 billion.
The Distance to Default (DD) using the real-world expected return (since EDF measures physical default probability) is: Given:
The Expected Default Frequency (EDF) is N(-DD):
An EDF of 0.65% falls within the 0.40% – 0.72% range. Looking at the rating schedule, this corresponds to a rating class of BBB-/BB.
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Q.76 A risk management unit of a bank wishes to estimate the distance to default and expected default frequency for both existing and potential corporate borrowers. One of its clients, ICB Corp, has assets valued at a total of £25 billion, with 45% asset volatility, measured annually. The expected return on the firm’s assets stands at 8% and the risk-free rate is 3% per year. ICB Corp also has short-term debt of £6 billion and long-term debt of £4 billion. The following table gives the rating schedule at a 1-year horizon.
| Expected Default Frequency (EDF) | Rating class |
|---|---|
| 0.02% – 0.04% | AAA |
| 0.04% – 0.10% | AA/A |
| 0.10% – 0.19% | A/BBB+ |
| 0.19% – 0.40% | BBB+/BBB- |
| 0.40% – 0.72% | BBB-/BB |
| 0.72% – 1.01% | BB/BB- |
Determine the credit rating for ICB Corp at a 1-year horizon using the rating schedule provided:
A
AA/A
B
A/BBB+
C
BBB-/BB
D
BB/BB-
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