Question

Now suppose market interest rates have risen over the course of the year. Specifically, the bonds in your portfolio experienced the following changes. Interest Rate a Year Ago (96) Interest Rate Now (96) 12 10 5.5 3. Calculate the approximate change in the price of each bond in your portfolio. (Hint) You may want to use the Equation (2) in the Web Appendix to Cho4. %A in P

Answer 1

% change in price -13% 0.25% -6% -1%

с 2 3 A. A $1000 twenty year 15% coupon bond with interest rate at 12% Interest Rate a year ago Interest Rate Now (%) % change in Price 12% 7 Price of Bond $1,224.08 |--PV(C6,19,1000*15%,1000,0) PV(rate, nper, pmt, [fv], [type]) 9 B. A $1000 eight year discount bond with the interest rate of 7%

1 Workings % change in price 3 A. A $1000 twenty year 15% coupon bond with interest rate at 12% 4 5 Interest Rate a year ago Interest Rate Now (%) % change in Price 12% 14% $1,224.08 $1,065.50 -13% 7 Price of Bond B. A $1000 eight year discount bond with the interest rate of 7% Interest Rate a year ago Interest Rate Now (%) % change in Price 7% 8% 3 Price Of Bond $582.01 $583.49 0.25% 5 C. A $1000 ten year 12% coupon bond with the interest rate of 9% Interest Rate a year ago Interest Rate Now (%) % change in Price 9% 10% $1,192.53 $1,115.18 -6% 9 Price Of Bond 2 D. A $1000 five year 4% coupon bond with the interest rate of 5% Interest Rate a year ago Interest Rate Now (%) % change in Price 5% 5.50% $956.71 $947.42 -1% 6 Price of Bond

1 Duration of Bond A S o 1 150 2 150 3 150 4 150 5 150 6 150 7 150 8 150 9 150 10 150 11 150 12 150 13 150 14 150 15 150 16 150 17 150 18 150 19 150 20 1150 4. Payments 6 PV of Payments 133.9286 119.5791 106.767 95.32771 85.11403 75.99467 67.85238 60.58248 54.0915 48.29599 43.12142 38.50126 34.37613 30.69297 27.40444 24.46825 21.84665 19.50594 17.41602 119.2168 3 Weights of each payment 0.11 0.10 0.09 0.08 0.07 0.06 0.06 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.01 0.10 0 =weight*n 0.109411 0.195377 0.261666 0.311507 0.347664 0.372498 0.388018 0.395937 0.397705 0.394548 0.387503 0.377438 0.365081 0.35104 0.335816 0.319825 0.303405 0.286833 0.270328 1.947854 2 Duration of the bond 8.12 Years

5 Duration Bond B 8 1000 582.0091 8 Payments 9 PV 0 Weights 1 Duration 8 years

4 Duration C. C6 Payments 7 PV 8 Weights -9 =weights*n 1 2 3 4 5 6 7 8 9 10 120 120 120 120 120 120 120 120 120 1120 110.0917 101.0016 92.66202 85.01103 77.99177 71.55208 65.64411 60.22395 55.25133 473.1001 0.092318 0.084695 0.077702 0.071286 0.0654 0.06 0.055046 0.050501 0.046331 0.39672 0.092318 0.16939 0.233106 0.285145 0.327001 0.360001 0.385323 0.404008 0.416981 3.967198 1 Duration 6.640472 years

Duration D Payments PV Weights =weights*n 1 2 4 5 40 40 40 40 1040 38.09524 36.28118 34.5535 32.9081 814.8672 0.039819 0.037923 0.036117 0.034397 0.851743 0.039819 0.075846 0.108352 0.137589 4.258716 Duration 4.620322

A B 1 Duration of Bond A C D G H I J K L M N O P Q R S T U V W S o 1 150 2 150 3 150 4 150 5 150 6 150 7 150 8 150 9 150 10 150 11 150 12 150 13 150 14 150 15 150 16 150 17 150 18 150 19 150 20 1150 4. Payments 6 PV of Payments Ī 133.92861 119.5791 106.767 95.32771 85.11403 75.99467 67.85238 60.58248 54.0915 48.29599 43.12142 38.50126 34.37613 30.69297 27.40444 24.46825 21.84665 19.50594 17.41602 119.2168 3 Weights of each payment 0.03 0.02 0.02 0.02 0.02 0.01 0.10 I=D6/SUM(D6:W6) 0.09 0.08 0.07 0.06 0.06 0.05 0.04 0.04 0.04 0.03 0.03 SUM(number1, [number2], ...) 0.109411 0.195377 0.261666 0.311507 0.347664 0.372498 0.388018 0.395937 0.397705 0.394548 0.387503 0.377438 0.365081 =weight*n 0.35104 0.335816 0.319825 0.303405 0.286833 0.270328 1.947854 2 Duration of the bond 8.12 Years 3

4. A B C D E F G H I J K L M N O P Q R S T U V W L 1 Duration of Bond A 3 I o r I 2 150 3 150 4 150 5 150 6 150 7 150 8 150 9 150 10 150 11 150 12 150 13 150 14 150 15 150 16 150 17 150 18 150 19 150 20 1150 4 Payments 150 5 6 PV of Payments 133.9286 119.5791 106.767 95.32771 85.11403 75.99467 67.85238 60.58248 54.0915 48.29599 43.12142 38.50126 34.37613 30.69297 27.40444 24.46825 21.84665 19.50594 17.41602 119.2168 1 8 Weights of each payment 0.11 0.10 0.09 0.08 0.07 0.06 0.06 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.01 0.10 10 =weight*n =D8*3 0.195377 0.261666 0.311507 0.347664 0.372498 0.388018 0.395937 0.397705 0.394548 0.387503 0.377438 0.365081 0.35104 0.335816 0.319825 0.303405 0.286833 0.270328 1.947854 11 12 Duration of the bond 8.12 Years 73