# ps7 - ECO 362 December 6 2007 PROBLEM SET 71 FINANCIAL...

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ECO 362 December 6, 2007 PROBLEM SET 7 1 FINANCIAL INVESTMENTS Professor: Burt Malkiel Exercise 1 The approximate percentage price change due to a change y is P P = D × y = D × 1 1+ y × y . where D and D denote Macaulay and modi f ed duration, respectively. Given the information: y = 10% , D =7 . 194 ,and y =0 . 5% ,wehave P P = 7 . 194 × 1 1+0 . 10 × 0 . 005 = 0 . 0327 . Then, the price would decline by 3 . 27% . Obs : Since the wording did not specify what duration 7 . 194 was, I will consider right those answers that used D =7 . 194 instead, and hence obtained a decrease of 3 . 6% . In any case, you have to be sure of being using the right number in the Final! Exercise 2 A 6% coupon bond making annual coupon payments has a coupon of 60 = 6% × F =6% × 1 , 000 (where F =1 , 000 as usual). Furthermore, we know that y =6% ,sow ehav ea l lth en e ed ed information to compute the Macaulay’s duration. As last week, we can construct the following table: (1) (2) (3) (2) × (3) (4) (1) × (4) Semester Payment Discount rate Disc. Payment (6%) Weight Contrib. to D 1 60 0.9434 56.60 0.0566 0.0566 2 60 0.8900 53.40 0.0534 0.1068 3 1060 0.8396 890.00 0.8900 2.6700 So that the Macaulay duration is D =2 . 833 years. Consequently, the modi f ed duration is D = D 1+ y = 2 . 833 1+0 . 06 =2 . 673 years. If instead, one assumes y = 10% , doing the same as above: (1) (2) (3) (2) × (3) (4) (1) × (4) Semester Payment Discount rate Disc. Payment (10%) Weight Contrib. to D 1 60 0.9091 54.55 0.0606 0.0606 2 60 0.8264 49.59 0.0551 0.1102 3

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ECO 362 December 6, 2007 So that the Macaulay duration is D =2 . 824 years —which is less than the duration at y =6% and the modi f ed duration is D =2 . 567 years. Intuition
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ps7 - ECO 362 December 6 2007 PROBLEM SET 71 FINANCIAL...

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