固定收益证券的小组作业2

Group Assignment 2

Due on October 18th

1. A 5-year ordinary annuity with a par value of $10,000 and a coupon rate of 5%

has an expected cash flow of $2,309.75 per year, assuming there are no principal prepayments. The annual cash flow includes interest and principal payment. What is the present value of this ordinary annuity assuming a discount rate of 6%? What would the present value of an annuity due with same features be assuming the same discount rate of 6%?

[Note: Ordinary annuity is an annuity with cash flows occurring at the end of each period; Annuity due is an annuity with cash flows occurring at the

beginning of each period.]

ing the Treasury spot rates shown in the following table, what is the

arbitrage-free value of a 7.4% coupon 8-year Treasury security? Compared with its traditional present value at a 5.65% discount rate, what is the arbitrage profit that can be obtained from stripping this 7.4% 8-year Treasury? How does the

dealer arbitrage? [Hint: Should the dealer buy the Treasury and sell the strips or buy strips and sell the Treasury?]

Years Periods Annual Spot Rate (%) Years Periods Annual Spot Rate (%)

0.5 1 3.0000 4.5 9 5.1701

1 2 3.3000 5 10 5.2772

1.5 3 3.5053 5.5 11 5.3864

2 4 3.9164 6 12 5.4976

2.5 5 4.4376 6.5 13 5.6108

3 6 4.7520 7 1

4 5.6643

3.5 7

4.9622 7.5 15

5.7193

4 8 5.0650 8 16 5.7755

3.Suppose that a bond is purchased between coupon periods. The days between the

settlement date and the next coupon period is 58. There are 183 days in the

coupon period. Suppose that the bond purchased has a coupon rate of 7% and

there are 10 semiannual coupon payments remaining. What is the full price for this bond if a 5% annual discount rate is used? What are the accrued interest and the clean price for the bond?

4.Given the spot rates in Question 2, compute the 2-year forward rate 1.5 years from

now. Verify your answer.

[Hint: To verify your answer, you need to demonstrate that the total returns of

investing same $s computed using either spot rates or forward rates are

identical.]