4. Suppose you decide to immunize against this liability using of type D. Bonds of type 1 have a price of 121.87, a Macaulay Duration of 7.078, a modified duration of 6.621 and a dollar duration of 806.978. Bonds of type 2 have a price of 77.66, a Macaulay Duration of 13.402, a modified duration of 12.537 and a dollar duration of 973.582. The liability has a market value of 5,131,247.32, a Macaulay Duration of 10 , modified duration of 9.355 and a dollar duration of 48,000,442.69. The first equation for finding the immunization portfolio is: . + . = , , . . Which of the following is a correct expression for the second equation? i. 806.9781+ 973.5822= 48,000,442.69 ii. 121.87 6.621 1+ 77.66 12.537 2= 5,131,247.32 9.355 iii. 121.87 7.078 1+ 77.66 13.402 2= 5,131,247.32*10 iv. 7.0781+ 13.4022= 10 v. 6.6211+ 12.5372= 9.355 A. (i) & (ii) only B. (i) & (iii) only C. (i), (ii) & (iii) only D. (ii) & (iii) only E. All of the above are correct

A liability of $10 million is due in 10 year's time. The yield curve is currently flat at 6.9% per annum. The following 5 portfolios are available to invest in. Each portfolio comprises one of Bonds A, B, C and D whose details are given below. Assume annual compounding for all bonds. Term to maturity Coupon Bond Macaulay Duration Face Value ($) (yrs) rate (yrs) A 10 0% 10 100 B 10 10% 7.08 100 16 7.5% 100 D 25 5.0% 13.40 100 10 i. 194,884 bonds of Type A ii. 82,052 bonds of Type B iii. 94,602 bonds of Type C iv. 48,543 bonds of Type C v. 66,075.54 bonds of Type D UZ OM A liability of $10 million is due in 10 year's time. The yield curve is currently flat at 6.9% per annum. The following 5 portfolios are available to invest in. Each portfolio comprises one of Bonds A, B, C and D whose details are given below. Assume annual compounding for all bonds. Term to maturity Coupon Bond Macaulay Duration Face Value ($) (yrs) rate (yrs) A 10 0% 10 100 B 10 10% 7.08 100 16 7.5% 100 D 25 5.0% 13.40 100 10 i. 194,884 bonds of Type A ii. 82,052 bonds of Type B iii. 94,602 bonds of Type C iv. 48,543 bonds of Type C v. 66,075.54 bonds of Type D UZ OM