2013 FRM Calendar

# P2.T6.211. Spread-based default probability (PD)

27 Sep 2012   by Suzanne Evans

Exam Relevance: Optional

### Questions:

211.1. The risk-free rate is 2.00% and a corporate bond has a yield of 3.50% per annum. It is estimated that the contribution to the spread by all non-credit factors is 40 basis points; e.g., liquidity risk. The recovery rate estimate is 75.0%. What is an approximation (emphasis on "approximation") for the implied default probability?

1. 1.90%
2. 2.50%
3. 4.40%
4. 6.00%

211.2. The risk-neutral default probability of a one-year corporate BB-rated bond is 5.0% with an estimated loss given default (LGD) of 65.0% while the risk-free rate is 2.0%. If we assume an annual compound frequency, which is nearest to the yield of the corporate bond?

1. 3.57%
2. 4.29%
3. 5.43%
4. 6.60%

211.3. The following three corporate bonds trade

- Bond A has a price of \$97.00, pays no coupon, estimated loss given default (LGD) of 50.0%, and matures in one year
- Bond B has a price of \$95.00, a coupon rate of 1.0% (payable semi-annually), estimated LGD of 45.0%, and matures in 1.5 years
- Bond C has price of \$96.00, a coupon rate of 2.0% (payable semi-annually), estimated LGD of 40.0%, and matures in 2.0 years

The risk-free rate curve includes: 1.0% at one year; 1.5% at 1.5 years; and 2.0% at two years. If the only contribution to spreads is credit risk (unrealistically, non-credit factors do not contribute to the spread), which bond has the highest market-implied probability of default?

1. Bond A
2. Bond B
3. Bond C
4. Cannot determine