Problem 1

A fixed-income trader observes a three-year, 2.60% annual-pay corporate bond trading at 90.045 per 100 of par value. The research team at the hedge fund determines that the risk-neutral annual probability of default is 2% and the recovery rate to be applied each year is 20%. The government bond yield curve is flat at 4.50%.

1. Based on these assumptions, does the trader deem the corporate bond to be overvalued or undervalued? By how much? (To do this question you will need to calculate the risk-free value of the bond, and then the CVA as shown below.)

1. How does the yield spread of the bond compare to its theoretical spread?

Problem 2

Continuing with the above example, if the trader buys the bond at 105.500, what are the potential projected annual rates of return? (In other words, what are the returns if the bond defaults after 1 to 3 years, and if the bond pays in full for the full 3 years.)

Note: If you cannot calculate the recovery amounts in the final year, assume the following recoveries for the final year:

• 19 for the bond that defaults after year 1
• 20 for the bond that defaults after year 2
• 21 for the bond that defaults after year 3