Question 6 of 13 6 You ane managing a portolio of 1 million

Question 6 (of 13)> 6. You ane managing a portolio of $1 million Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity of 5 years, and a perpebuity, each yieldng 7.6%. What weight of each bond will you hold to immunize your portolio? (Do not round your intermediate calculation. Round your answers to 2 decimal places. Omit the%sign in your response Zero-coupon bond Perpetuity bond b. How wil these weights change next year if target duration is now 9 years? (Do not round your intermedlate calculation. Round your answers to 2 decimal places. Omit the \"sign in your Zero-coupon bond Perpebuity bond esc 20 FS F6 2 3 4

Solution

Duration of zero coupon bond is 5 years Duration of perpetuity bond is as below (1+7.60%)/7.60% 14.15789 years Let the weight of zero bond be w, we would use the relation of portfolio duration 10 = w*5 + (1-w)*14.15789 10= 5w + 14.15789 - 14.15789w 10-14.15789 = 5w - 14.15789w -4.15789 (9.15789)w w 4.15789/9.15789 w 0.454023 The weight for zero coupon bond is 45.20 and for perpuity bond is (1-0.4520) = 54.80 After one year the duration of zero coupon bond will be 4 yrs whereas duration of perpetuity bond would still be 14.15789 yrs 9 = w*4 + (1-w)*14.15789 = 4w + 14.15789 - 14.15789w 9-14.15789 = 10.15789w 5.15789 = 10.15789w w 5.15789/10.15789 0.507772 The weight for zero coupon bond is 50.78 and for perpuity bond is (1-0.5078) = 49.22