Suppose your liability is $100,000,000 par of the 10-year 2.875%-coupon bond above.

Liab. par value

100,000,000

Construct an asset portfolio consisting of the 2-year 2.625%-coupon bond and the 30-year 3%-coupon bond with the same market value and

the same duration/dollar duration as your liability.

That is, what are the par amounts, N2 and N30, of those bonds in the asset portfolio?

N2

xxx

N30

xxx

Selected Treasury coupon bonds a) b) c) d) e) F) g) h) i) i) Actual Assumed From Problem Set 1: $Duration of $Convexity of maturity date maturity Treasury Implied zero Implied Duratior $Duratio $100 par of Duration c Convexity Convexity $100 par of Convexity of Zero rates - 20 bp Zero rates + 20 bp (do not use) Coupon (use this) bond price price per $1; zero rate of zero $1 par of Treasury b Treasury 1 of zero $1 par of ze Treasury bond Treasury bonc New zero pric New bond New zero prices New bond prices 2015/2019 0.750% 0.5 99.26472 0.9889 2.237% 0.4945 0.4890 49.08 0.4945 0.49 0.48 48.54 0.49 0.9899 99.3630 0.9880 99. 1667 7/312019 1.375% 10 98.99218 0.9764 2.402% 0.9881 0.9648 97.48 0.9847 1.46 1.43 144.32 1.46 0.9783 99.1874 0.9745 98.7975 2/15/2020 3.625% 1.5 101.51462 0.9621 2.593% 1.4808 1.4247 147.68 1.4548 2.92 2.81 289.85 2.86 0.9649 101.8106 0.9592 101.2198 8/15/2020 2.625% 2.0 99.94387 0.9486 2.658% 1.9738 1.8723 193.46 1.9357 4.87 4.62 474.19 4.74 0.9523 100.3317 0.9448 99.5579 2015/2021 3.625% 2.5 102.25337 0.9353 2.692% 2.4668 2.3073 243.52 2.3815 7.30 6.83 712.30 6.97 0.9400 102.7418 0.9307 101.7678 8/15/2021 2.750% 3.0 100.08014 0.9220 2.727% 2.9597 2.7287 286.33 2.8610 10.22 9.42 977.40 9.77 0.9274 100.6548 0.9165 99.5094 2/15/2022 2.000% 3.5 97.53649 0.9089 2.747% 3.4526 3.1382 326.75 3.3500 13.62 12.38 1276.26 13.08 0.9152 98. 1925 0.9027 96.8855 77312022 1.875% 4.0 96.68116 0.8961 2.760% 3.9455 3.5358 369.01 3.8167 17.51 15.69 1619.75 16.75 0.9032 97.4224 0.8891 95.9464 2/15/2023 2.000% 4.5 96.80452 0.8838 2.763% 4.4387 3.9230 412.68 4.2631 21.89 19.35 2007.79 20.74 0.8917 97.6339 0.8760 95.9832 71312023 2.750% 5.0 99.88867 0.8711 2.779% 4.9315 4.2958 463.52 4.6403 26.75 23.30 2462.77 24.66 0.8797 100.8206 0.8626 98.9665 2015/2024 2.750% 5.5 99.76700 0.8581 2.802% 5.4240 4.6543 505.76 5.0694 32.09 27.54 2924.30 29.31 0.8675 100.7844 0.8488 98.7613 7/312024 2.125% 6.0 96.20440 0.8452 2.823% 5.9165 5.0007 536.55 5.5771 37.92 32.05 3370.85 35.04 0.8553 97.2843 0.8353 95.1380 2/15/202 2.000% 6.5 95.02909 0.8320 2.850% 6.4087 5.3321 572.87 6.0284 44.23 36.80 3872.73 40.75 0.8427 96.1826 0.8214 93.8910 7/312025 2.875% 7.0 100.22077 0.8204 2.849% 6.9017 5.6620 631.36 6.2997 51.04 41.87 4524.09 45.14 0.8318 101.4926' 0.8091 98.9671 2015/2026 6.000% 7.5 121.32408 0.8095 2.838% 7.3951 5.9862 752.56 6.2029 58.33 47.22 5567.38 45.89 0.8216 122.8404 0.7976 119.8300 8/15/2026 1.500% 8.0 90.30272 0.7961 2.871% 7.8868 6.2788 671.08 7.4314 66.09 52.61 5512.30 61.04 0.8088 91.6560 0.7837 88.9715 2015/2027 6.625% 8.5 128,44946 0.7863 2.849% 8.3806 6.5894 871.55 6.7851 74.37 58.47 7148,62 55.65 0.7996 130, 2069 0.7732 126.720 8/15/2027 2.250% 9.0 95.01352 0.7722 2.893% 8.8717 6.8511 765.02 8.0517 83.08 64.16 6929.90 72.94 0.7861 96.5575' 0.7587 93.4973 111572027 6.125% 9.5 126.82164 0.7606 0 2.901% 9.3642 7.1228 951.64 7.5038 92.30 70.21 8635.73 68.09 0.7750 128.7423 0.7465 124.9355 811572028 2.875% 10.0 99.92230 0.7502 2.895% 9.8573 7.3949 862.47 8.6314 102.02 76.54 8521.79 85.28 0.7651 101.6644 0.7356 98.2143 2015/2029 5.250% 10.5 121.29281 0.7388 2.904% 10.3497 7.6462 1009.26 8.3209 112.22 82.90 10093.00 83.21 0.7542 123, 3317 0.7237 119.2943 8/15/2029 6.125% 11.0 130.29786 0.7275 2.913% 10.8421 7.8879 1098.37 8.4297 122.89 89.41 11317.73 86.86 0.7435 132.5174 0.7119 128. 1236 6.125% 11.5 131.59870 0.7185 2.895% 11.3359 8.1452 % 1149.04 8.7314 134.09 96.35 12306.68 93.52 0.7350 133.9216' 0.7024 129.3250 5/15/2030 6.250% 12.0 133.73453 0.7056 2.927% 11.82698.3456 1201.99 8.9879 145.70 102.82 13329.31 99.67 0.7225 136.1654 0.6892 131.3570 2015/2031 5.375% 12.5 125.73575 0.6954 2.927% 12.3197 8.5672 1195.73 9.5099 157.85 109.77 13892.72 110.49 0.7128 128.1552 0.6785 123.3718 5.250% 13.0 125.48636 0.6879 2.898% 12.8143 8.8152 1235.79 9.8480 170.52 117.31 14886.75 118.63 0.7058 127.9880' 0.6705 123.0443 5.250% 13.5 126.28963 0.6782 2.898% 13.3072 9.0243 1280.39 10.1385 183,64 124.54 15936.70 126.19 0.6965 128.8826 0.6604 123.7604 5.250% 14.0 127.02447 0.6680 2.903% 13.7997 9.2178 % 1323.93 10.4226 197.23 131.75 17003.41 133.86 0.6867 129.7067 0.6498 124.4103 5.000% 14.5 124.80078 0.6580 2.908% 14.2922 9.4037 1346.88 10.7923 211.31 139.03 17897.60 143.41 0.6771 127.5307 ' 0.6394 122.1425 5.000% 15.0 125.42546 0.6480 2.913% 14.7846 9.5806 1388.52 11.0705 225.87 146.37 18996.75 151.46 0.6675 128.2409 0.6291 122.6860 5.000% 15.5 126.03678 0.6382 2.919% 15.2770 9.7493 % 1429.77 11.3441 240.92 153.75 20118.96 159.63 0.6580 128.9370 0.6190 123.2171 4.750% 16.0 123.45424 0.6285 2.924% 15.7695 9.9115 1446.79 11.7192 256.45 161.18 21008.41 170.17 0.6487 126.3903 0.6090 120.6022 4.750% 16.5 123.96281 0.6189 2.929% 16.2618 10.0646 1486.00 11.9875 272.46 168.63 22153.44 178.71 0.6394 126.9796 0.5991 121.0346 4.750% 17.0 124.45977 0.6094 2.935% 16.7542 10.2101 1524.80 12.2513 288.96 176.09 23318.05 187.35 0.6302 127.5565 0.5893 121.4563 2015/2036 4.500% 17.5 121.53858 0.6001 2.939% 17.2465 10.3501 1535.57 12.6344 305.94 183.60 24181.68 198.96 0.6212 124.6586 0.5798 118.5153 4.500% 18.0 121.93989 0.5908 2.945% 17.7388 10.4809 1572.23 12.8935 323.41 191.08 25359.55 207.97 0.6122 0.5703 118.8456 2015/2037 4.750% 18.5 125.88266 0.5815 2.952% 18.2309 10.6020 1638.64 13.0172 341.35 198.51 26920 93 213.86 0.6031 129.2144 0.5607 122.6586 5/15/2037 5.000% 19.0 129.94485 0.5722 2.960% 18.7229 10.7134 1707.01 13.1364 359.77 205.87 28543.37 219.66 0.5941 133.4167 0.5512 126.5872 2015/2038 4.375% 19.5 121.03260 0.5617 2.980% 19.2137 10.7924 1659.06 13.7076 378.63 212.68 28695.48 237.09 0.5837 124.4088' 0.5405 117.7711 5/15/2038 4.500% 20.0 123.25662 0.5530 2.984% 19.7060 10.8968 1710.58 13.8782 398.03 220.10 30144.98 244.57 0.5752 126.7389 0.5316 119.8950 2015/2039 3.500% 20.5 108.14235 0.5433 2.998% 20.1972 10.9740 1599.53 14.7909 417.88 227.05 29429.53 272.14 0.5657 111.4011 0.5218 105.0014 8/15/2039 4.500% 21.0 123.63595 0.5326 3.023% ##### 11.0172 1772.10 14.3332 438.15 233.34 32505.02 262.91 0.5551 127.2460 ' 0.5110 120.1559 201512040 4.625% 21.5 125.88512 0.5234 3.034% 21.1787 11.0848 1823.12 14.4824 458.97 240.22 3400325 270.11 0.5461 129.6003 0.5017 122.3060 8/15/2040 3.875% 22.0 114.12229 0.5151 3.039% 21.6707 11.1615 1736.53 15.2164 480.29 247.38 33579.38 294.24 0.5379 117.6635 0.4932 110.7155 215/2041 4.750% 22.5 128.54077 0.5058 3.052% 22. 1618 11.2101 1908.09 14.8442 502.06 253.96 36837.04 286.58 0.5288 132.4317 0.4839 124.7972 8/15/2041 3.750% 23.0 112.23609 0.4976 3.058% ##### 11.2719 1769.70 15.7677 524.34 260.90 35611.87 317.29 0.5206 115.8478 0.4755 108.7669 2/15/2042 3.125% 23.5 101.85947 0.4903 3.056% 23.1463 11.3481 % 1687.98 16.5716 547.15 268.26 35179.67 345.37 0.5135 105.3069 0.4681 98.5528 8/15/2042 2.750% 24.0 95.33161 0.4818 3.066% ##### 11.3880 164124 17.2161 570.38 274.79 35208.70 369.33 0.5051 98.6856 0.4595 92. 1185 2015/2043 3.125% 24.5 101.72156 0.4740 3.071% 24.1295 11.4366 1732.48 17.0316 594.12 281.59 37382.50 367.50 0.4974 105.2625 0.4516 98.3302 8/15/2043 3.625% 25.0 110.45236 0.4659 3.079% 24.6210 11.4712 1850.95 16.7579 618.32 288.08 40029.35 362.41 0.4894 114.2356 0.4435 106.8293 2015/2044 3.625% 25.5 110.57274 0.4588 3.079% 25.1134 11.5219 1876.91 16.9744 643.05 295.03 41258.96 373.14 0.4824 114.4104 0.4363 106.9001 8/15/2044 3.125% 26.0 101.71888 0.4524 3.074% ##### 11.5849 1801.34 17.7090 668.30 302.35 40842.25 401.52 0.4762 105.4046' 0.4298 98.1966 2015/2045 2.500% 26.5 90.30695 0.4457 3.073% ##### 11.6319 1692.01 18.7363 694.01 309.31 39803.14 440.75 0.4696 0.4230 87.0012 8/15/2045 2.875% 27.0 97.08367 0.4385 3.076% 26.5910 11.6612 1791.03 18.4483 720.17 315.83 42239.55 435.08 0.4625 0.4158 93.5847 2015/2046 2.500% 27.5 90.03677 0.4321 3.075% ##### 11.7028 1728.31 19.1956 746.86 322.72 41942. 19 465.83 0.4562 93.5788 0.4093 86.6626 8/15/2046 2.250% 28.0 85.24617 0.4262 3.069% ##### 11.7539 1690.84 19.8348 774.06 329.92 42067.01 493.48 0.4504 88.7135 0.4034 81.9471 215/2047 3.000% 28.5 99.43010 0.4197 3.070% ##### 11.7804 1882.97 18.9376 801.70 336.47 46250.68 465.16 0.4439 103.2902 0.3968 95.7550 8/15/2047 2.750% 29.0 94.51129 0.4127 3.075% ##### 11.7874 1841.14 19.4806 829.79 342.46 46270.89 489.58 0.4370 98.2878 0.3898 90.9199 2015/2048 3.000% 29.5 99.32102 0.4063 3.076% 29.0531 11.8047 1920.79 19.3392 858.39 348.78 48518.52 488.50 0.4306 103.2615 0.3834 95.5747 8/15/2048 3.000% 30.0 99.35297 0.4006 3.072% 29.5461 11.8369 1941.77 19.5441 887.52 355.56 49730.56 500.54 0.4250 103.3379' 0.3776 95.5671 *no near-maturity bond 125. 1357" 93.7720" 100.7517 Selected Treasury coupon bonds a) b) c) d) e) F) g) h) i) i) Actual Assumed From Problem Set 1: $Duration of $Convexity of maturity date maturity Treasury Implied zero Implied Duratior $Duratio $100 par of Duration c Convexity Convexity $100 par of Convexity of Zero rates - 20 bp Zero rates + 20 bp (do not use) Coupon (use this) bond price price per $1; zero rate of zero $1 par of Treasury b Treasury 1 of zero $1 par of ze Treasury bond Treasury bonc New zero pric New bond New zero prices New bond prices 2015/2019 0.750% 0.5 99.26472 0.9889 2.237% 0.4945 0.4890 49.08 0.4945 0.49 0.48 48.54 0.49 0.9899 99.3630 0.9880 99. 1667 7/312019 1.375% 10 98.99218 0.9764 2.402% 0.9881 0.9648 97.48 0.9847 1.46 1.43 144.32 1.46 0.9783 99.1874 0.9745 98.7975 2/15/2020 3.625% 1.5 101.51462 0.9621 2.593% 1.4808 1.4247 147.68 1.4548 2.92 2.81 289.85 2.86 0.9649 101.8106 0.9592 101.2198 8/15/2020 2.625% 2.0 99.94387 0.9486 2.658% 1.9738 1.8723 193.46 1.9357 4.87 4.62 474.19 4.74 0.9523 100.3317 0.9448 99.5579 2015/2021 3.625% 2.5 102.25337 0.9353 2.692% 2.4668 2.3073 243.52 2.3815 7.30 6.83 712.30 6.97 0.9400 102.7418 0.9307 101.7678 8/15/2021 2.750% 3.0 100.08014 0.9220 2.727% 2.9597 2.7287 286.33 2.8610 10.22 9.42 977.40 9.77 0.9274 100.6548 0.9165 99.5094 2/15/2022 2.000% 3.5 97.53649 0.9089 2.747% 3.4526 3.1382 326.75 3.3500 13.62 12.38 1276.26 13.08 0.9152 98. 1925 0.9027 96.8855 77312022 1.875% 4.0 96.68116 0.8961 2.760% 3.9455 3.5358 369.01 3.8167 17.51 15.69 1619.75 16.75 0.9032 97.4224 0.8891 95.9464 2/15/2023 2.000% 4.5 96.80452 0.8838 2.763% 4.4387 3.9230 412.68 4.2631 21.89 19.35 2007.79 20.74 0.8917 97.6339 0.8760 95.9832 71312023 2.750% 5.0 99.88867 0.8711 2.779% 4.9315 4.2958 463.52 4.6403 26.75 23.30 2462.77 24.66 0.8797 100.8206 0.8626 98.9665 2015/2024 2.750% 5.5 99.76700 0.8581 2.802% 5.4240 4.6543 505.76 5.0694 32.09 27.54 2924.30 29.31 0.8675 100.7844 0.8488 98.7613 7/312024 2.125% 6.0 96.20440 0.8452 2.823% 5.9165 5.0007 536.55 5.5771 37.92 32.05 3370.85 35.04 0.8553 97.2843 0.8353 95.1380 2/15/202 2.000% 6.5 95.02909 0.8320 2.850% 6.4087 5.3321 572.87 6.0284 44.23 36.80 3872.73 40.75 0.8427 96.1826 0.8214 93.8910 7/312025 2.875% 7.0 100.22077 0.8204 2.849% 6.9017 5.6620 631.36 6.2997 51.04 41.87 4524.09 45.14 0.8318 101.4926' 0.8091 98.9671 2015/2026 6.000% 7.5 121.32408 0.8095 2.838% 7.3951 5.9862 752.56 6.2029 58.33 47.22 5567.38 45.89 0.8216 122.8404 0.7976 119.8300 8/15/2026 1.500% 8.0 90.30272 0.7961 2.871% 7.8868 6.2788 671.08 7.4314 66.09 52.61 5512.30 61.04 0.8088 91.6560 0.7837 88.9715 2015/2027 6.625% 8.5 128,44946 0.7863 2.849% 8.3806 6.5894 871.55 6.7851 74.37 58.47 7148,62 55.65 0.7996 130, 2069 0.7732 126.720 8/15/2027 2.250% 9.0 95.01352 0.7722 2.893% 8.8717 6.8511 765.02 8.0517 83.08 64.16 6929.90 72.94 0.7861 96.5575' 0.7587 93.4973 111572027 6.125% 9.5 126.82164 0.7606 0 2.901% 9.3642 7.1228 951.64 7.5038 92.30 70.21 8635.73 68.09 0.7750 128.7423 0.7465 124.9355 811572028 2.875% 10.0 99.92230 0.7502 2.895% 9.8573 7.3949 862.47 8.6314 102.02 76.54 8521.79 85.28 0.7651 101.6644 0.7356 98.2143 2015/2029 5.250% 10.5 121.29281 0.7388 2.904% 10.3497 7.6462 1009.26 8.3209 112.22 82.90 10093.00 83.21 0.7542 123, 3317 0.7237 119.2943 8/15/2029 6.125% 11.0 130.29786 0.7275 2.913% 10.8421 7.8879 1098.37 8.4297 122.89 89.41 11317.73 86.86 0.7435 132.5174 0.7119 128. 1236 6.125% 11.5 131.59870 0.7185 2.895% 11.3359 8.1452 % 1149.04 8.7314 134.09 96.35 12306.68 93.52 0.7350 133.9216' 0.7024 129.3250 5/15/2030 6.250% 12.0 133.73453 0.7056 2.927% 11.82698.3456 1201.99 8.9879 145.70 102.82 13329.31 99.67 0.7225 136.1654 0.6892 131.3570 2015/2031 5.375% 12.5 125.73575 0.6954 2.927% 12.3197 8.5672 1195.73 9.5099 157.85 109.77 13892.72 110.49 0.7128 128.1552 0.6785 123.3718 5.250% 13.0 125.48636 0.6879 2.898% 12.8143 8.8152 1235.79 9.8480 170.52 117.31 14886.75 118.63 0.7058 127.9880' 0.6705 123.0443 5.250% 13.5 126.28963 0.6782 2.898% 13.3072 9.0243 1280.39 10.1385 183,64 124.54 15936.70 126.19 0.6965 128.8826 0.6604 123.7604 5.250% 14.0 127.02447 0.6680 2.903% 13.7997 9.2178 % 1323.93 10.4226 197.23 131.75 17003.41 133.86 0.6867 129.7067 0.6498 124.4103 5.000% 14.5 124.80078 0.6580 2.908% 14.2922 9.4037 1346.88 10.7923 211.31 139.03 17897.60 143.41 0.6771 127.5307 ' 0.6394 122.1425 5.000% 15.0 125.42546 0.6480 2.913% 14.7846 9.5806 1388.52 11.0705 225.87 146.37 18996.75 151.46 0.6675 128.2409 0.6291 122.6860 5.000% 15.5 126.03678 0.6382 2.919% 15.2770 9.7493 % 1429.77 11.3441 240.92 153.75 20118.96 159.63 0.6580 128.9370 0.6190 123.2171 4.750% 16.0 123.45424 0.6285 2.924% 15.7695 9.9115 1446.79 11.7192 256.45 161.18 21008.41 170.17 0.6487 126.3903 0.6090 120.6022 4.750% 16.5 123.96281 0.6189 2.929% 16.2618 10.0646 1486.00 11.9875 272.46 168.63 22153.44 178.71 0.6394 126.9796 0.5991 121.0346 4.750% 17.0 124.45977 0.6094 2.935% 16.7542 10.2101 1524.80 12.2513 288.96 176.09 23318.05 187.35 0.6302 127.5565 0.5893 121.4563 2015/2036 4.500% 17.5 121.53858 0.6001 2.939% 17.2465 10.3501 1535.57 12.6344 305.94 183.60 24181.68 198.96 0.6212 124.6586 0.5798 118.5153 4.500% 18.0 121.93989 0.5908 2.945% 17.7388 10.4809 1572.23 12.8935 323.41 191.08 25359.55 207.97 0.6122 0.5703 118.8456 2015/2037 4.750% 18.5 125.88266 0.5815 2.952% 18.2309 10.6020 1638.64 13.0172 341.35 198.51 26920 93 213.86 0.6031 129.2144 0.5607 122.6586 5/15/2037 5.000% 19.0 129.94485 0.5722 2.960% 18.7229 10.7134 1707.01 13.1364 359.77 205.87 28543.37 219.66 0.5941 133.4167 0.5512 126.5872 2015/2038 4.375% 19.5 121.03260 0.5617 2.980% 19.2137 10.7924 1659.06 13.7076 378.63 212.68 28695.48 237.09 0.5837 124.4088' 0.5405 117.7711 5/15/2038 4.500% 20.0 123.25662 0.5530 2.984% 19.7060 10.8968 1710.58 13.8782 398.03 220.10 30144.98 244.57 0.5752 126.7389 0.5316 119.8950 2015/2039 3.500% 20.5 108.14235 0.5433 2.998% 20.1972 10.9740 1599.53 14.7909 417.88 227.05 29429.53 272.14 0.5657 111.4011 0.5218 105.0014 8/15/2039 4.500% 21.0 123.63595 0.5326 3.023% ##### 11.0172 1772.10 14.3332 438.15 233.34 32505.02 262.91 0.5551 127.2460 ' 0.5110 120.1559 201512040 4.625% 21.5 125.88512 0.5234 3.034% 21.1787 11.0848 1823.12 14.4824 458.97 240.22 3400325 270.11 0.5461 129.6003 0.5017 122.3060 8/15/2040 3.875% 22.0 114.12229 0.5151 3.039% 21.6707 11.1615 1736.53 15.2164 480.29 247.38 33579.38 294.24 0.5379 117.6635 0.4932 110.7155 215/2041 4.750% 22.5 128.54077 0.5058 3.052% 22. 1618 11.2101 1908.09 14.8442 502.06 253.96 36837.04 286.58 0.5288 132.4317 0.4839 124.7972 8/15/2041 3.750% 23.0 112.23609 0.4976 3.058% ##### 11.2719 1769.70 15.7677 524.34 260.90 35611.87 317.29 0.5206 115.8478 0.4755 108.7669 2/15/2042 3.125% 23.5 101.85947 0.4903 3.056% 23.1463 11.3481 % 1687.98 16.5716 547.15 268.26 35179.67 345.37 0.5135 105.3069 0.4681 98.5528 8/15/2042 2.750% 24.0 95.33161 0.4818 3.066% ##### 11.3880 164124 17.2161 570.38 274.79 35208.70 369.33 0.5051 98.6856 0.4595 92. 1185 2015/2043 3.125% 24.5 101.72156 0.4740 3.071% 24.1295 11.4366 1732.48 17.0316 594.12 281.59 37382.50 367.50 0.4974 105.2625 0.4516 98.3302 8/15/2043 3.625% 25.0 110.45236 0.4659 3.079% 24.6210 11.4712 1850.95 16.7579 618.32 288.08 40029.35 362.41 0.4894 114.2356 0.4435 106.8293 2015/2044 3.625% 25.5 110.57274 0.4588 3.079% 25.1134 11.5219 1876.91 16.9744 643.05 295.03 41258.96 373.14 0.4824 114.4104 0.4363 106.9001 8/15/2044 3.125% 26.0 101.71888 0.4524 3.074% ##### 11.5849 1801.34 17.7090 668.30 302.35 40842.25 401.52 0.4762 105.4046' 0.4298 98.1966 2015/2045 2.500% 26.5 90.30695 0.4457 3.073% ##### 11.6319 1692.01 18.7363 694.01 309.31 39803.14 440.75 0.4696 0.4230 87.0012 8/15/2045 2.875% 27.0 97.08367 0.4385 3.076% 26.5910 11.6612 1791.03 18.4483 720.17 315.83 42239.55 435.08 0.4625 0.4158 93.5847 2015/2046 2.500% 27.5 90.03677 0.4321 3.075% ##### 11.7028 1728.31 19.1956 746.86 322.72 41942. 19 465.83 0.4562 93.5788 0.4093 86.6626 8/15/2046 2.250% 28.0 85.24617 0.4262 3.069% ##### 11.7539 1690.84 19.8348 774.06 329.92 42067.01 493.48 0.4504 88.7135 0.4034 81.9471 215/2047 3.000% 28.5 99.43010 0.4197 3.070% ##### 11.7804 1882.97 18.9376 801.70 336.47 46250.68 465.16 0.4439 103.2902 0.3968 95.7550 8/15/2047 2.750% 29.0 94.51129 0.4127 3.075% ##### 11.7874 1841.14 19.4806 829.79 342.46 46270.89 489.58 0.4370 98.2878 0.3898 90.9199 2015/2048 3.000% 29.5 99.32102 0.4063 3.076% 29.0531 11.8047 1920.79 19.3392 858.39 348.78 48518.52 488.50 0.4306 103.2615 0.3834 95.5747 8/15/2048 3.000% 30.0 99.35297 0.4006 3.072% 29.5461 11.8369 1941.77 19.5441 887.52 355.56 49730.56 500.54 0.4250 103.3379' 0.3776 95.5671 *no near-maturity bond 125. 1357" 93.7720" 100.7517