Question

A corporate bond pays 10% (annual) coupon and has 2 years left to maturity. Its price in the market is USD 100.75. A fixed-income portfolio manager holds this bond in her portfolio and is required to report the benchmark spread of this bond in her quarterly filings to the SEC. Below is a table showing the available treasury security information she is looking at (from the same website where you got your Chapter 5 homework data, but these are for a different time period):

Bond #	Maturity (in Weeks)	Coupon (%)	Yield (%)
1	4	0	6.45
2	8	0	6.8
3	26	0	6.88
4	52	4	7.22
5	52	4.5	7.32
6	104	10	7.47
7	104	10.5	7.40
8	208	11	7.44
9	208	11.5	7.89

(i) What is the correct treasury bond she should choose to compute the benchmark spread? Write a brief sentence for why you chose this bond.   

(ii) Compute the benchmark spread for the bond based on your answer to part (i) of this question. If you were not able to answer the previous part correctly, assume the hypothetical number 6.5% as the answer to part (i). Remember to present the right units for benchmark spread.

Answer 1

Part 1: The correct treasury bond to use to calculate the benchmark spread is Bond#6 as it matches the maturity of our bond (2 years or 104 weeks) and has the same coupon of 10%.

Part 2: The yield for the treasury bond selected above is 7.47%. Now we will calculate the yield of our 10% coupon bond first and then subtract 7.47 percent from it to calculate the spread. We use the cashflows of the bond below to calculate its IRR or Yield to Maturity at 9.57%. The spread is the difference between this YTM and the treasury bond yield of 7.47%. The spread therefore is 2.10% (i.e. 9.57%-7.47%) Answer

Year 0	Year 1	Year 2
-100.75	10	110
9.57%	IRR