Dear David,
I’ve had some confusion, misunderstanding and doubts when doing 09 Level II Annotated Power Practice. Appreciate your kind help on this!
In question 2 from 09 Level II Annotated Power Practice, you seem to have made a mistake in writing the question 2b. I think the assumption should be zero recovery (100% LGB), based on your answer for 2b that:
Probability of repay (p) = 1.05/1.06 = 99.057%
For sub question 2c, you used the formula:
No arbitrage indifference suggests (Saunders p 323):
[(1-p)*recovery*(1+k)] + [p*(1+k)] = 1 + i
Can I just confirm with you that the term (1+k) should be multiplied to (1-p)*recovery as well? I always thought that the formula is [(1-p)*recovery]+ [p*(1+k)] = 1 + i
Below is the question and answer for your reference:
Question 2:
The risk-free rate is 5% per year and a corporate bond yields 6% per year. Assuming a recovery rate of 75% on the corporate bond, what is the approximate market implied one-year probability of default of the corporate bond?
a. 1.33% b. 4.00% c. 8.00% d. 1.60%
2b. [my adds] If we assume full recovery (0% LGD) and flat term structures (i.e., two-year yields are also 5% and 6%, respectively, for the risk-free instrument and the corporate bond), what is the estimated two-year cumulative probability of default (2-year cumulative PD)? 2c. [harder] The question mistakenly sources Saunders but uses an approximation given by Hull. If, instead of the approximation given by Hull, we use the (more accurate) approach given by Saunders, what is the (alternative) market implied one-year probability of default of the corporate bond?
Thank you for your enlightenment and correction!
Cheers
Liming
16/11/09
I’ve had some confusion, misunderstanding and doubts when doing 09 Level II Annotated Power Practice. Appreciate your kind help on this!
In question 2 from 09 Level II Annotated Power Practice, you seem to have made a mistake in writing the question 2b. I think the assumption should be zero recovery (100% LGB), based on your answer for 2b that:
Probability of repay (p) = 1.05/1.06 = 99.057%
For sub question 2c, you used the formula:
No arbitrage indifference suggests (Saunders p 323):
[(1-p)*recovery*(1+k)] + [p*(1+k)] = 1 + i
Can I just confirm with you that the term (1+k) should be multiplied to (1-p)*recovery as well? I always thought that the formula is [(1-p)*recovery]+ [p*(1+k)] = 1 + i
Below is the question and answer for your reference:
Question 2:
The risk-free rate is 5% per year and a corporate bond yields 6% per year. Assuming a recovery rate of 75% on the corporate bond, what is the approximate market implied one-year probability of default of the corporate bond?
a. 1.33% b. 4.00% c. 8.00% d. 1.60%
2b. [my adds] If we assume full recovery (0% LGD) and flat term structures (i.e., two-year yields are also 5% and 6%, respectively, for the risk-free instrument and the corporate bond), what is the estimated two-year cumulative probability of default (2-year cumulative PD)? 2c. [harder] The question mistakenly sources Saunders but uses an approximation given by Hull. If, instead of the approximation given by Hull, we use the (more accurate) approach given by Saunders, what is the (alternative) market implied one-year probability of default of the corporate bond?
Thank you for your enlightenment and correction!
Cheers
Liming
16/11/09
