Question

17. Suppose that the T-bond futures price is 101-12. Which of the following four bonds is cheapest to deliver? Bond Cash Price esion Factor 1.2131 1.3792 125-05 142-15 1.1149 1.4026 3 115-31 144-02 a, Bond # 1 b, Bond # 2 c, Bond # 3 d, Bond #4 18. What number is closest to the duration of a 12% annual coupon bond maturing in 5 years and yielding i 1967 Assume a $1,000 face value. a. 2.5 years b. 3.0 years c. 3.5 years d. 4.0 years . 4.5 years 19. On August 1, a portfolio manager has a bond portfolio worth S10 million The duration of the portfolio is 7.1 years. The December T-bond futures price is currently 91-12, and the cheapest-to-deliver bond has a duration of 8.8 years. Yields are 9.5% on the futures and 9.5% on the bond portfolio. How should the portfolio manager immunize the portfolio against changes in interest rates over the next two months? a. Long 14 T-bond futures contracts. b. Long 49 T-bond futures contracts. c. Short 9 T-bond futures contracts. d. Short 49 T-bond futures contracts. e. Short 88 T-bond futures contracts 20. In question 19, after the portfolio was immunized against interest rate changes, the duration of the total portfolio including the T-bond futures is: a. b. 6 months c. 7.1 years d. 8.8 years e. None of the above.

Answer 1

17) C

Bond	Cash Price	Conversion Factor	CP*CF	CP-CP*CF
1	125.05	1.2131	151.70	-26.65
2	142.15	1.3792	196.05	-53.90
3	115.31	1.1149	128.56	-13.25
4	144.02	1.4026	202.00	-57.98		Bond C is cheapest to deliver

18) D

Year	C	NPV	nPVC			FV	1000
1	120	108.11	108.1081			YTM	11%
2	120	97.39	194.7894			CP	12%
3	120	87.74	263.2289
4	120	79.05	316.1909
5	120	71.21	356.0708
5	1000	593.45	2967.257
		1036.96	4205.645		4.1

19) E

The treasurer should short Treasury bond futures contract. If bond prices go down, this futures position will provide offsetting gains. The number of contracts that should be shorted is

(10,000,000 x 7.1) / (91375 x 8.8) = 88.30

Rounding to the nearest whole number 88 contracts should be shorted.

20) D