O. Paste 822 28 29 Geneva A. 8% coupon bond 30 31 BIU x ✓ fx 10 B. Zero-coupon bond 11 12 13 14 Sum: Sum B Period 1 2 3 4 1 2 3 4 ✓ 0.05 10 A A ✓ & v A v C Time until Payment (Years) 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 D Cash flow 40 40 40 1040 0 0 0 1000 = I PV of CF (Discount rate- 5% per period) 38.095 36.281 34.554 15 16 Semiannual int rate: 17 18 "Weight - Present value of each payment (Column E) divided by the bond price 19 20 21 22 23 24 25 26 27 855.611 964.540 0.000 0.000 0.000 822.702 822.702 F Weight 0.0395 0.0376 0.0358 0.8871 1.0000 0.0000 0.0000 0.0000 1.0000 1.0000 Wrap Text Merge & Center Column (C) times Column (F) 0.0197 0.0376 0.0537 1.7741 1.8852 0.0000 0.0000 0.0000 2.0000 2.0000 H General $%9 1 ←8 98 J H Cell Conditional Format Formatting as Table Styles K L M Insert v Delete Format N OM 28. 0. Sort & Find & Filter Select 0 P O Analyze Data O Jasperactive for Office Q
You are thinking of pursuing an actuarial career, so you have agreed to serve as an intern at Love Actuaries LLP.
The managing partner, Karen Thompson, has asked you to do some quick calculations for her. She wants you to use the current yield curve, flat at 6%, in your calculations.
Client Annie Inc. has a pension plan that pays pension benefits annually at a rate of $10 million per year, starting one year from today. The pension obligation will end in 40 years. Karen wants to know the duration of these required pension payments.
Client Billy Mack Co. wants to immunize its pension obligations (present value = $150 million with a duration of 22 years) with two $1000 face
Thirdly, client Colin Limited’s pension plan obligation has a duration of 16 and a convexity of 29. Colin’s immunization strategy will use 3 bonds, issued by firms named Eleonore, Frissel, and Greta, respectively.
The bonds have the following parameters:
|
Bond |
|
Duration |
|
Convexity |
|
Eleonore |
|
9.00 |
|
29.00 |
|
Frissel |
|
21.00 |
|
35.00 |
|
Greta |
|
28.00 |
|
56.00 |
Required:
- What is the duration of Annie’s required pension payments?
Hint: Starting with Spreadsheet 16.1 of Bodie_9Ce_Ch16.xlsx, copy the formulas for coupon bonds, adjusting them to extend for the full 40 years of payments, and determine the duration. - Calculate the money Billy Mack should allocate to each of these bonds to immunize its pension against interest rate risk. (Again, modify Spreadsheet 16.1 for the coupon bond’s duration.)
- What weights should Ms. Thompson recommend for Colin’s strategy?
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