Questions 1-8 refer to the following information

A liability of $40 million is due in 14 year's time. The yield curve is currently flat at 6% per annum. The following 5 portfolios are available to invest in. Each portfolio comprises one of Bonds A, B, C and D whose details are given below. Assume annual compounding for all bonds.

BondTerm to maturity (yrs)Coupon rateMacaulay Duration (yrs)Face Value ($)A140.00%14100B145.00%10.19100C213.44%14100D284.50%15.05100

i. 904,362 bonds of type A

ii. 195,050 bonds of Type B

iii. 572,377 bonds of Type C

iv. 253,163 bonds of Type C

v. 500,684 bonds of Type D

1. Which of the following portfolios is suitable for immunizing this liability against a shift in interest rates today:

[ Select ]

["

Portfolio (iv)

", "

Portfolio (v)

", "

Portfolio (i)

", "

Portfolio (ii)

", "

Portfolio (iii)

"]

2. You consider immunizing against the liability by investing in 221,452.89 bonds of Type D. This portfolio has a present value, today, equal to the present value of the liability. If the yield curve increases to 7%, what is the new present value of this immunizing portfolio?

[ Select ]

["

11,687,207.53

", "

19,505,027.77

", "

19,605,027.77

", "

None of the other answers are correct

", "

15,425,793.36

"]

3. If the yield curve shifts to 7% and you invest in 221,452.89 bonds of Type D today and hold these bonds for the next 14 years, what is the value at t=14 (i.e. the liability due date) of this portfolio?

[ Select ]

["

None of the other answers are correct

", "

30,135,863.74

", "

39,775,934.97

", "

50,394,380.21

", "

50,294,380.21

"]

4. Suppose you decide to immunize against this liability using q_B bonds of type B and q_D bonds of type D. Bonds of type B have a price of 90.71, a Macaulay Duration of 10.19, a modified duration of 9.61 and a dollar duration of 871.94. Bonds of type D have a price of 79.89, a Macaulay Duration of 15.05, a modified duration of 14.2 and a dollar duration of 1,134.65. The liability has a market value of 17,692,038.58, a Macaulay Duration of 14 , modified duration of 13.21 and a dollar duration of 233,668,434.01. The first equation for finding the immunization portfolio is: 90.71q_s + 79.89q_l= 17,692,038.58. Which of the following is a correct expression for the second equation?

[ Select ]

["

9.61q_B + 14.2q_D=13.21

", "

90.71*10.19*q_B + 79.89*15.05*q_D=233,668,434.01*13.21

", "

871.94q_B + 1,134.65q_D=17,692,038.58*14

", "

10.19q_B + 15.05q_D=14

", "

871.94q_B + 1,134.65q_D=233,668,434.01

"]

5. Assume you are going to set up an immunization portfolio with weight , w_B, on bonds of type B and weight, w_D, on bonds of type D. Assuming a flat yield curve, the first equation for finding the immunization portfolio is: w_B+w_D=1 . Which of the following is a correct expression for the second equation?

[ Select ]

["

15.05w_B+10.19w_D=14

", "

10.19w_B+15.05w_D=13.21

", "

14.2w_B+9.61w_D=13.21

", "

9.61w_B+14.2w_D=14

", "

9.61w_B+14.2w_D=13.21

"]

6. It can be shown that the solution to the above immunization problem is to invest in: 42,285.89 Bonds of Type B and 173,443.05 Bonds of Type D. What is the modified duration of this portfolio?

[ Select ]

["

11.24

", "

13.21

", "

14.00

", "

None of the answers provided are correct

", "

10.61

"]

7. It can be shown that the solution to the above immunization problem is to invest in: 42,285.89 Bonds of Type B and 173,443.05 Bonds of Type D. What is the standardized convexity of this portfolio?

[ Select ]

["

122.52

", "

153.37

", "

262.79

", "

264.91

", "

None of the answers provided are correct

"]

8. It can be shown that the solution to the above immunization problem is to invest in: 42,285.89 Bonds of Type B and 173,443.05 Bonds of Type D. Based on the concept of duration and convexity, what is the percentage change in this portfolio if interest rates decrease by 1% at all maturities?

[ Select ]

["

Increase by 13.208%

", "

Increase by 14.521%

", "

None of the other answers provided are correct

", "

Increase by 9.564%

", "

Increase by 10.176%

"]

Question 9 is not related to Questions 1-8.

9. Consider a bullet portfolio comprising a 19 year zero coupon bond with a face value of 80,000 and a barbell portfolio comprising a 9 year zero coupon bond with a face value of 20,344.76 and a 29 year zero coupon bond with a face value of 86,626.55. The 9-year rate is 5.90% p.a. nominal, the 19-year rate is 6.40% p.a. nominal and the 29-year rate is 6.90% p.a. nominal. These portfolios have the same market value today. Assuming semi-annual compounding and that the yield curve shifts upwards by 100 basis points at all maturities then:

[ Select ]

["

The barbell outperforms the bullet by $93.19

", "

The barbell outperforms the bullet by $135.94

", "

The barbell outperforms the bullet by $25.58

", "

The bullet outperforms the bullet by $135.94

", "

The bullet outperforms the barbell by $93.19

"]

Question 10 is not related to Questions 1-8 or to Q9.

10. Assuming semi-annual compounding and that the yield curve is flat at 6.40%pa nominal. Consider a bullet portfolio with a face value of $80,000 and a maturity of 19 years. A barbell portfolio is to be created which has the same market value and the same dollar duration as this bullet portfolio. Assume that this barbell portfolio has a weight of w_s in 9-year zero-coupon bonds and a weight of w_l in 29 year zero-coupon bonds. Which of the following statements is incorrect?