QUESTION 1

Assume annual compounding and that the yield curve is flat at 8.50% pa nominal. Suppose we have a liability of $700,000 due in exactly 7 years' time. We want to immunize the liability by investing in a combination of 3-year coupon-paying bonds paying 9.50% annual coupons and 10-year zero coupon bonds

(a) What is the price of the 3-year bond?

*43.50

*44.23

*102.60

*102.55

*None of the above

(b) What is the price of the 10-year bond?

*43.50

*44.23

*102.60

*102.55

*None of the above

(c) What is the present value of the liability?

*548,035.67

*None of the above

*395,448.45

*390,870.73

*309,599.79

(d) What is the Macaulay Duration of the 3-year bond (in years)?

*3

*10

*9.217

*2.751

*None of the above

(e) What is the Macaulay Duration of the 10-year bond (in years)?

*10

*9.217

*None of the above

*7

*6.452

(f) What is the Macaulay Duration of the liability (in years)?

*6.715

*7

*2.765

*6.452

*None of the above

(g) What is the first equation in the system of equations that needs to be solved to find the immunizing portfolio, where q_Z is the number of zero-coupon bonds and q_C is the number of coupon-paying bonds in the immunizing portfolio?

*None of the above

*q_Z*102.55+q_C*44.23=395,448.45

*q_Z*102.55+q_C*44.23=700,000.00

*q_Z*44.23+q_C*102.55=700,000.00

*q_Z*44.23+q_C*102.55=395,448.45

(h) What is the second equation in the system of equations that needs to be solved to find the immunizing portfolio, where q_Z is the number of zero-coupon bonds and q_C is the number of coupon-paying bonds in the immunizing portfolio?

*None of the above

*q_Z*282.08+q_C*442.29=2,768,139.12

*q_Z*132.69+q_C*717.88=2,768,139.12

*q_Z*442.29+q_C*282.08=2,768,139.12

*q_Z*309.60+q_C*307.66=4,900,000.00