XYZ Ltd., whose bonds are rated as BBB on the market, would like to apply for a 3-year loan from your bank. Related corporate bond returns and government bond returns are presented in the following two tables. What is the cumulative probability of default on this loan at the maturity date? (1 mark) Table 1 Corporate bond ratings and yields with different maturities 1-year2-year3-yearAAA2.45%3.15%3.65%AA2.65%3.59%4.30%A3.21%3.95%4.60%BBB4.30%4.60%5.22%BB4.80%5.50%6.55%B5.70%6.50%7.80%CCC6.50%7.10%8.20%CC7.80%8.80%9.60% Table 2 Government bond yields with different maturitiesMaturity1-year2-year3-yearReturns1.45%2.25%2.75%Question 8Answera.6.88%b.4.72%c.93.12%d.94.68%
Question
XYZ Ltd., whose bonds are rated as BBB on the market, would like to apply for a 3-year loan from your bank. Related corporate bond returns and government bond returns are presented in the following two tables. What is the cumulative probability of default on this loan at the maturity date? (1 mark) Table 1 Corporate bond ratings and yields with different maturities 1-year2-year3-yearAAA2.45%3.15%3.65%AA2.65%3.59%4.30%A3.21%3.95%4.60%BBB4.30%4.60%5.22%BB4.80%5.50%6.55%B5.70%6.50%7.80%CCC6.50%7.10%8.20%CC7.80%8.80%9.60% Table 2 Government bond yields with different maturitiesMaturity1-year2-year3-yearReturns1.45%2.25%2.75%Question 8Answera.6.88%b.4.72%c.93.12%d.94.68%
Solution
The question seems to be asking for the cumulative probability of default on a loan at the maturity date. However, the information provided in the tables is about bond yields, not default probabilities.
In general, the probability of default can be estimated using the difference between the yield of a corporate bond and the yield of a comparable government bond (considered risk-free). This difference is often referred to as the credit spread.
For a BBB-rated company like XYZ Ltd., the 3-year yield is 5.22% (from Table 1). The 3-year government bond yield is 2.75% (from Table 2). The credit spread is therefore 5.22% - 2.75% = 2.47%.
However, this is not a probability. It's a measure of the additional yield that investors demand for taking on the credit risk of the BBB-rated company, compared to a risk-free government bond.
To convert this into a default probability would require additional information or assumptions, such as the recovery rate in the event of default.
Therefore, based on the information provided, it's not possible to calculate the cumulative probability of default on the loan at the maturity date.
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