Factor Value portfolio replication

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Create for each date in your sample a long-short value factor using the data under the ”carry” table. Prior to using these carry data, turn them into a z-score (substract the mean and divide by the standard deviation). The value factor will oppose the assets with a z-score higher than the median of that month to the assets with a score lower than that median value. For each date, compute the factor allocation and the performance of the factor for a 2% ex ante volatility budget (give an equal weight to your longs and your short and scale the portfolio up or down to obtain a 2% volatility). Chart the historical cumulated performance and comment. This is question 1 of Part 2

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Prices Dates World Equities World Bonds US Investment Grade US High Yield Gold Energy Copper 31.10.2000 1282.14 101.57 348.778 390.235 265.15 171.0312 74.2191 30.11.2000 1203.05 103.39 353.744 378.009 270.45 200.4858 74.2632 29.12.2000 1221.25 104.76 360.663 386.206 272.25 212.143 74.54 31.01.2001 1244.22 105.98 370.17 409.237 265.85 199.2194 75.9267 28.02.2001 1137.88 107.03 373.802 415.7 267.15 196.6439 73.2996 30.03.2001 1061.26 107.74 376.7 410.2 257.95 193.3921 68.9111 30.04.2001 1138.09 107.01 374.727 405.719 264.05 209.145 70.9887 31.05.2001 1121.09 107.57 378.556 413.527 265.85 200.8408 69.8542 29.06.2001 1084.79 108.18 380.266 404.998 270.85 176.5319 65.5896 31.07.2001 1069.67 109.5 390.916 411.292 266.65 177.6523 62.4965 31.08.2001 1016.73 110.46 395.157 415.279 274.4 184.4006 61.4975 28.09.2001 926.02 111.37 396.247 388.64 293.25 157.5356 57.6336 31.10.2001 943.2 113.45 404.948 400.085 279.65 145.0308 54.9045 30.11.2001 997.93 112.42 401.629 413.085 274.4 129.8769 62.6748 31.12.2001 1003.52 111.61 399.263 410.169 278.95 128.7 58.5132 31.01.2002 972.42 111.89 401.328 412.464 282.55 123.0475 61.8779 28.02.2002 962.73 112.32 404.352 408.494 296.55 132.5681 61.6934 29.03.2002 1003.6 111.25 396.814 418.199 302.65 164.9156 64.0688 30.04.2002 968.25 112.65 401.96 424.849 308.45 173.886 63.0161 31.05.2002 967.85 112.98 407.141 422.549 326.55 156.925 63.1316 28.06.2002 907.81 114.45 407.19 392.511 314.45 161.0252 63.651 31.07.2002 830.55 115.89 407.413 376.893 303.55 157.236 58.168 30.08.2002 830.58 117.56 418.179 386.317 312.75 171.0546 58.3215 30.09.2002 738.18 119.25 426.283 380.124 323.55 184.7243 56.498 31.10.2002 791.88 118.95 420.84 376.92 317.75 170.3398 60.6025 29.11.2002 833.47 118.84 426.651 399.499 318.15 169.5816 62.1494 31.12.2002 792.21 120.8 439.868 405.475 348.05 196.3532 59.2308 31.01.2003 767.48 121.4 441.391 417.146 368.15 223.2228 64.8415 28.02.2003 752.86 122.53 450.599 422.51 349.95 255.5341 64.819 31.03.2003 748.63 122.38 451.007 433.454 337.45 220.1076 60.1536 30.04.2003 813.3 122.78 459.581 457.812 338.55 205.4413 61.1306 30.05.2003 857.65 125.09 474.231 462.76 364.45 233.8159 64.652 30.06.2003 871.07 124.42 473.452 475.376 346.4 230.3024 62.0931 31.07.2003 887.78 122.06 453.467 468.589 354.35 223.9492 67.6188 29.08.2003 905.32 121.58 457.025 474.718 375.55 231.4051 66.241 30.09.2003 909.64 123.43 473.339 487.398 385.35 218.8155 67.0162 31.10.2003 962.71 122.15 468.02 497.353 384.25 217.2699 75.1478 28.11.2003 976.02 122.31 470.301 504.199 398.15 222.134 73.9142 31.12.2003 1036.32 123.33 476.42 515.873 415.45 255.9819 84.1474 30.01.2004 1052.29 124.02 481.55 523.896 402.45 251.9482 86.827 27.02.2004 1068.65 125.25 487.148 523.711 396.15 271.7681 94.0504 31.03.2004 1059.16 125.75 492.144 527.395 426.45 280.7751 93.6329 30.04.2004 1035.66 124.09 476.851 523.589 386.75 292.8242 85.5624 31.05.2004 1042.63 123.86 473.473 515.229 395.55 314.5057 89.2305 30.06.2004 1062.51 123.82 475.774 522.753 394.25 296.6437 88.825 30.07.2004 1026.99 124.51 481.522 529.898 391.05 329.5241 90.4798 31.08.2004 1029.63 126.43 492.815 539.481 409.85 304.9127 88.1709 30.09.2004 1047.86 127.01 495.391 546.999 418.25 361.8528 98.7588 29.10.2004 1072.7 127.87 500.398 557.384 428.55 388.7701 94.4712 30.11.2004 1127.34 128.33 495.198 563.027 450.95 353.1159 99.1007 31.12.2004 1169.34 129.19 502.218 571.4 438.45 300.7146 103.9563 31.01.2005 1142.35 130.25 506.28 570.921 422.6 326.4827 101.0201 28.02.2005 1176.7 129.67 503.02 578.963 435.65 343.695 106.8353 31.03.2005 1151.18 130.26 497.603 563.199 428.35 379.7654 107.8665 29.04.2005 1123.64 131.93 504.528 557.362 434.4 331.515 102.8708 31.05.2005 1140.68 133.19 510.747 567.589 417.25 326.2363 101.4086 30.06.2005 1148.81 134.4 514.865 578.371 435.5 352.8817 100.7378 29.07.2005 1188.17 133.65 509.531 587.38 429.8 380.1898 106.759 31.08.2005 1194.81 134.91 517.834 589.519 435.2 475.5177 108.7282 30.09.2005 1224.31 134.38 509.642 583.609 469.3 508.749 110.3877 31.10.2005 1193.88 133.63 504.398 579.463 465.19 436.8217 115.2919 30.11.2005 1231.41 134.31 507.103 582.204 493.08 420.955 125.6001 30.12.2005 1257.78 135.42 512.122 587.583 517 414.0502 134.3885 31.01.2006 1313.21 135.2 511.046 596.926 568.9 397.8235 149.5554 28.02.2006 1309.45 135.54 513.079 600.731 561.55 326.1896 146.3851 31.03.2006 1335.07 134.44 506.614 604.352 583.65 347.7954 156.9021 28.04.2006 1373.38 133.83 504.602 607.945 654.43 353.791 191.0301 31.05.2006 1322.25 134.45 504.197 607.482 645.2 343.5898 206.9953 30.06.2006 1319.93 134.43 504.575 605.256 615.85 341.7125 195.4873 31.07.2006 1327.23 135.89 512.053 611.713 636.75 363.0433 207.1458 31.08.2006 1358.87 137.98 521.63 621.664 627.3 320.4398 209.2962 29.09.2006 1373.37 138.95 527.298 629.737 598.3 260.2272 211.0268 31.10.2006 1422.93 139.58 531.846 638.833 606.6 249.5354 226.8521 30.11.2006 1455.17 140.66 539.379 648.919 648 268.2792 227.4692 29.12.2006 1483.58 140.05 534.533 655.984 636.7 231.2062 220.7889 31.01.2007 1500.23 139.99 534.707 662.853 653.2 235.5751 210.5532 28.02.2007 1490.44 141.6 545.56 672.042 669.35 240.4789 221.5675 30.03.2007 1514.18 141.59 542.903 673.528 663.8 252.9156 233.2848 30.04.2007 1577.86 141.96 546.919 682.438 678.45 251.5652 253.2889 31.05.2007 1616.87 141.05 541.503 687.24 660.5 245.829 244.8228 29.06.2007 1602.36 140.62 538.902 675.635 649.65 240.7471 231.7863 31.07.2007 1565.81 142.44 540.441 654.564 664.3 242.1767 234.4349 31.08.2007 1561.59 144.22 545.762 661.769 673.3 224.1142 216.0663 28.09.2007 1633.58 144.74 548.822 677.969 743.6 243.0593 221.5736 31.10.2007 1682.35 145.87 554.787 682.037 796.8 273.5914 216.7587 30.11.2007 1610.94 147.75 559.665 668.222 783.55 251.4852 199.8245 31.12.2007 1588.8 148.07 559.351 670.215 833.7 266.6686 190.1941 31.01.2008 1466.35 150.78 565.962 661.232 926.1 264.0858 207.3065 29.02.2008 1455.56 151.69 566.372 653.553 973.9 295.9496 236.9014 31.03.2008 1437.4 151.88 558.853 650.24 916.9 305.4722 225.6355 30.04.2008 1508.99 150.33 562.051 677.232 877.55 335.1564 222.0858 30.05.2008 1525.73 148.74 556.936 680.038 886.5 371.8309 206.7001 30.06.2008 1402.13 148.6 554.798 661.924 925.4 410.7958 216.2556 31.07.2008 1366.7 150.27 550.021 651.435 914.1 328.2905 203.2403 29.08.2008 1344.87 151.85 553.882 653.594 831.15 298.3612 190.191 30.09.2008 1182.44 152.12 513.241 599.187 870.95 262.5684 164.6904 31.10.2008 957.25 153.18 475.356 501.798 723.85 195.0614 120.3269 28.11.2008 892.93 157.49 493.794 459.66 818.05 166.0576 107.6625 31.12.2008 920.23 161.27 521.217 494.528 882.05 138.3418 96.9222 30.01.2009 838.83 159.13 522.953 520.848 927.85 121.0712 91.4754 27.02.2009 750.86 159.51 514.808 503.419 942.32 112.0617 91.3219 31.03.2009 805.22 161.01 513.742 520.533 919.35 112.6715 101.3781 30.04.2009 893.02 160.57 529.585 579.192 888.2 105.8879 111.1074 29.05.2009 970 159.35 552.543 619.522 979.18 129.7531 117.4022 30.06.2009 964.05 160.46 569.313 637.898 926.5 132.2582 124.0901 31.07.2009 1044.75 161.53 591.789 676.181 954 129.9092 143.0807 31.08.2009 1085.6 162.82 604.588 689.962 951.19 121.8468 150.0599 30.09.2009 1126.98 163.71 616.696 730.269 1007.7 126.5759 148.9763 30.10.2009 1106.17 163.56 621.734 742.921 1045.45 131.1303 154.757 30.11.2009 1149.01 165.07 630.533 750.336 1179.63 127.9727 161.9442 31.12.2009 1168.47 163.49 624.21 772.844 1096.98 130.7939 174.165 29.01.2010 1119.54 164.66 636.749 784.608 1081.2 120.0519 158.907 26.02.2010 1133.35 165.52 639.136 785.762 1117.59 123.9138 168.528 31.03.2010 1200.53 165.51 641.353 810.303 1113.25 119.9249 184.7845 30.04.2010 1198.56 166.17 652.626 827.929 1179.03 122.7881 178.8061 31.05.2010 1079.8 168.05 648.898 799.438 1216.3 110.7221 158.5499 30.06.2010 1041.32 169.39 662.25 810.19 1242.38 112.5089 149.5011 30.07.2010 1124.83 170.35 675.804 838.227 1181 117.1766 165.4341 31.08.2010 1080.7 173.47 690.598 840.185 1247.4 102.9519 163.0674 30.09.2010 1179.19 172.92 694.674 864.843 1308.54 107.6767 179.8542 29.10.2010 1222.23 172.27 696.132 885.552 1359.4 106.3417 182.9805 30.11.2010 1193.56 170.16 690.18 875.567 1386.23 107.9969 179.5454 31.12.2010 1280.07 169.45 683.635 890.606 1421.4 116.8364 202.1788 31.01.2011 1308.08 168.66 685.255 909.089 1332.68 118.062 205.5616 28.02.2011 1351.65 168.64 690.11 921.128 1411.33 116.4192 210.5632 31.03.2011 1334.93 168.43 690.3 924.896 1432.2 124.882 202.5515 29.04.2011 1388.62 169.63 702.022 938.812 1563.7 132.2374 201.5192 31.05.2011 1354.61 171.24 712.072 943.459 1535.73 122.6315 195.9826 30.06.2011 1331.18 171.03 706.142 934.197 1500.18 114.7882 195.1089 29.07.2011 1306.05 172.63 722.343 945.629 1627.05 113.8291 203.9429 31.08.2011 1211.22 175.63 723.086 908.679 1825.55 108.218 188.6714 30.09.2011 1104.06 177.38 722.119 876.637 1623.79 96.0663 150.8244 31.10.2011 1217.3 176.23 734.787 928.156 1714.7 104.5089 164.8809 30.11.2011 1184.6 175.86 721.075 908.085 1746.35 103.9248 159.9072 30.12.2011 1182.59 178.65 734.965 930.709 1564.91 98.1255 153.1071 31.01.2012 1240.89 179.88 751.007 957.037 1737.76 94.7213 169.819 29.02.2012 1298.72 180.15 757.382 978.688 1696.76 99.3239 171.1413 30.03.2012 1312.01 179.66 752.911 977.673 1668.15 92.129 161.9081 30.04.2012 1293.99 180.72 762.52 987.716 1664.75 92.0526 162.3979 31.05.2012 1177.64 183.16 766.932 976.25 1560.51 81.812 146.7192 29.06.2012 1235.72 182.53 770.759 996.012 1597.45 83.8777 147.2718 31.07.2012 1250.57 184.47 792.396 1015.275 1614.58 90.4975 143.6127 31.08.2012 1279.21 184.66 795.564 1027.233 1691.85 91.7503 144.0036 28.09.2012 1311.5 185.23 801.44 1041.591 1772.25 93.8201 159.8674 31.10.2012 1301.52 185.38 811.989 1050.253 1720.65 91.681 145.0272 30.11.2012 1315.49 186.61 811.323 1057.792 1714.98 90.6316 155.1549 31.12.2012 1338.5 186.6 811.165 1074.366 1675.35 88.862 154.0011 31.01.2013 1405.47 185.71 805.344 1088.854 1663.7 91.892 157.5117 28.02.2013 1405.18 186.79 811.039 1093.97 1579.61 89.5426 148.6306 29.03.2013 1434.51 188.05 811.575 1105.217 1597.5 95.1659 141.8936 30.04.2013 1476.14 189.94 825.371 1125.77 1476.71 93.7752 134.699 31.05.2013 1471.93 187.24 806.544 1119.633 1387.8 89.3573 136.86 28.06.2013 1433.55 185.25 784.285 1090.042 1234.53 87.0716 127.1304 31.07.2013 1507.91 185.84 790.079 1110.458 1325.07 90.7397 128.3007 30.08.2013 1472.74 185.27 784.797 1103.666 1395.27 93.5471 130.5253 30.09.2013 1543.67 186.55 791.261 1114.853 1329.03 89.5114 132.5752 31.10.2013 1602.86 188.01 803.104 1142.265 1323.06 87.1612 133.1249 29.11.2013 1628.42 187.87 800.793 1147.36 1253.35 89.1442 126.7338 31.12.2013 1661.07 186.69 799.355 1153.635 1201.64 93.4243 132.9276 31.01.2014 1598.46 189.36 813.617 1162.185 1244.55 96.5953 126.39 28.02.2014 1675.4 190.09 822.545 1185.578 1326.39 99.0975 128.8786 31.03.2014 1673.87 190.35 823.13 1188.167 1284.01 97.3346 126.8625 30.04.2014 1687.74 191.42 832.727 1196.013 1291.6 100.237 130.6445 30.05.2014 1715.18 192.97 845.462 1207.473 1249.68 99.5703 134.1878 30.06.2014 1743.42 193.71 846.877 1217.706 1327.33 101.5739 137.6371 31.07.2014 1714.35 194.46 845.882 1201.512 1282.59 93.6498 140.6914 29.08.2014 1748.69 196.86 857.951 1219.836 1287.32 93.4396 141.3574 30.09.2014 1698.41 196.53 847.286 1194.406 1208.15 89.3184 131.957 31.10.2014 1708.09 197.82 855.193 1208.207 1172.94 81.1915 133.8956 28.11.2014 1739.5 200.02 860.624 1199.634 1167.38 72.6867 129.379 31.12.2014 1709.67 201.58 859.418 1181.853 1184.37 56.6487 123.7539 30.01.2015 1677.54 205.56 882.97 1189.91 1283.79 52.8309 117.1188 27.02.2015 1772.86 204.03 875.587 1218.377 1213.18 57.2827 118.4395 31.03.2015 1740.81 205.45 878.842 1211.713 1183.57 52.0018 117.1676 30.04.2015 1778.4 203.99 874.147 1226.361 1184.37 59.198 126.3123 29.05.2015 1779.31 202.94 869.73 1230.041 1190.58 57.9351 116.5882 30.06.2015 1735.61 200.56 855.472 1211.238 1172.35 57.6803 110.9364 31.07.2015 1765.6 202.88 860.082 1204.037 1095.8 49.3306 102.8322 31.08.2015 1645.43 202.43 854.312 1182.788 1134.93 49.6983 99.9505 30.09.2015 1581.92 204.06 858.789 1152.154 1115.09 44.7861 98.6015 30.10.2015 1705.8 204.59 863.393 1183.864 1142.11 43.2976 95.8342 30.11.2015 1694.4 204.68 861.46 1157.523 1064.77 38.6853 87.5033 31.12.2015 1662.79 204.4 853.99 1128.039 1061.1 34.6081 90.4397 29.01.2016 1562.18 208.18 857.737 1110.254 1118.21 32.0714 89.1619 29.02.2016 1547.17 210.7 864.038 1115.552 1238.67 29.09 92.123 31.03.2016 1648.12 211.79 887.49 1164.487 1232.75 31.3633 92.4441 29.04.2016 1670.8 211.61 899.562 1210.751 1293.53 35.5691 99.062 31.05.2016 1674.61 212.79 898.978 1218.746 1215.32 36.6546 91.8382 30.06.2016 1653.23 217.44 918.571 1231.77 1321.9 37.7191 98.0239 29.07.2016 1721.79 218.15 931.892 1263.021 1351.28 33.6782 101.1115 31.08.2016 1719.52 217.52 934.447 1291.161 1308.97 34.8671 96.9322 30.09.2016 1725.67 217.5 931.756 1299.571 1315.87 36.3098 101.9501 31.10.2016 1690.92 214.93 924.044 1303.467 1277.21 35.3089 103.2591 30.11.2016 1712.09 211.68 899.287 1298.308 1173.2 36.7979 113.8871 30.12.2016 1751.22 212.07 904.913 1323.671 1147.5 40.1069 108.0971 31.01.2017 1792.4 210.68 908.625 1341.455 1210.72 37.0426 116.099 28.02.2017 1838.7 212.41 918.902 1362.431 1248.44 36.0213 118.6558 31.03.2017 1853.69 212.3 917.771 1359.527 1249.2 35.4768 116.1565 28.04.2017 1878.28 213.63 926.927 1374.963 1268.28 34.3946 112.1336 31.05.2017 1911.74 214.62 937.701 1387.421 1268.92 33.2406 110.8737 30.06.2017 1916.43 213.85 940.003 1388.861 1241.61 31.9701 114.5103 31.07.2017 1961.1 214.19 947.027 1404.897 1269.44 33.3986 119.1177 31.08.2017 1959.74 216.26 955.047 1404.615 1321.43 33.8454 130.4838 29.09.2017 2000.55 214.98 952.868 1417.258 1279.75 35.0059 125.4804 31.10.2017 2036.8 215.91 956.714 1422.608 1271.45 35.8341 132.6628 30.11.2017 2077.36 216.54 955.37 1418.623 1275.01 36.6282 127.0243 29.12.2017 2103.45 216.72 963.517 1422.703 1302.8 38.0155 138.51 31.01.2018 2213.24 215.33 954.613 1431.785 1345.14 39.6775 138.626 28.02.2018 2117.99 215.55 940.328 1418.265 1318.31 36.7949 135.4536 30.03.2018 2066.84 217.91 942.35 1409.379 1325.48 38.5358 129.3761 30.04.2018 2086.51 217.22 934.324 1418.731 1315.39 40.4066 133.7187 31.05.2018 2092.92 217.89 938.53 1418.501 1298.51 41.4158 136.7506 29.06.2018 2089.3 218.67 933.466 1423.502 1252.6 42.4697 130.0354 31.07.2018 2153.1 218.31 940.381 1439.456 1224.15 40.5455 123.7156 31.08.2018 2175.5 218.66 945.496 1449.798 1201.15 41.9994 118.127 28.09.2018 2184.01 217.82 942.422 1458.227 1190.88 44.1066 120.47 31.10.2018 2021.98 218.03 929.687 1434.356 1214.76 41.5928 113.5887 30.11.2018 2041.36 219.49 927.914 1421.61 1220.52 40.1243 115.4721 31.12.2018 1883.9 222.81 941.843 1390.537 1282.49 32.5358 109.3356 31.01.2019 2028.49 224.67 961.557 1454.409 1321.25 35.4612 117.8872 28.02.2019 2085.84 224.72 965.015 1478.905 1313.32 37.3221 121.8024 29.03.2019 2107.74 228.67 989.041 1493.404 1292.38 37.4967 122.6583 30.04.2019 2178.67 228.35 994.549 1514.326 1283.53 39.0241 118.216 31.05.2019 2046.25 232.03 1008.817 1495.015 1305.58 34.2816 111.0366 28.06.2019 2178.35 235.09 1032.018 1531.791 1409.55 35.5751 113.1152 31.07.2019 2187.56 237.02 1038.782 1539.571 1413.78 35.5513 114.4857 30.08.2019 2138.52 243.01 1070.321 1545.812 1520.38 33.4704 114.8777 30.09.2019 2180.02 241.7 1063.7 1550.638 1472.49 33.7862 115.2728 31.10.2019 2233.53 240.62 1070.206 1554.303 1512.99 34.2816 117.1549 29.11.2019 2292.26 240.02 1072.525 1558.428 1463.98 33.3568 111.2753 31.12.2019 2358.47 238.92 1075.904 1590.769 1517.27 35.6061 114.5192 31.01.2020 2342.41 243.52 1101.465 1590.889 1589.16 30.3045 105.9967 28.02.2020 2141.12 246.96 1115.678 1566.349 1585.69 26.7556 103.1638 31.03.2020 1852.73 246.58 1032.292 1382.957 1577.18 17.358 93.1017 30.04.2020 2052.85 248.95 1086.719 1435.504 1686.5 16.7555 95.2171 29.05.2020 2147.88 248.65 1105.717 1501.213 1730.27 18.656 97.8393 30.06.2020 2201.79 248.95 1128.001 1515.496 1780.96 19.0597 104.5337 31.07.2020 2304.98 250.74 1163.541 1587.976 1975.86 19.4491 111.7919 31.08.2020 2455.51 248.49 1150.113 1603.675 1967.8 21.998 119.5398 30.09.2020 2367.27 249.95 1147.075 1587.042 1885.82 19.8809 116.184 30.10.2020 2292.93 249.88 1145.107 1594.536 1878.81 19.7707 119.7046 30.11.2020 2583.14 250.27 1175.633 1657.762 1776.95 20.4528 132.3 31.12.2020 2690.04 250.87 1181.409 1689.467 1898.36 20.316 132.7034 29.01.2021 2661.69 249.4 1166.997 1694.817 1847.65 21.426 132.7205 26.02.2021 2726.91 245.02 1144.176 1700.481 1734.04 24.7239 146.1697 31.03.2021 2811.7 244.58 1128.306 1703.152 1707.71 23.8324 142.62 30.04.2021 2938.76 244.75 1141.732 1721.787 1769.13 25.5175 155.1929 VIX Dates VIX 31.10.2000 23.63 30.11.2000 29.65 29.12.2000 26.85 31.01.2001 22.02 28.02.2001 28.35 30.03.2001 28.64 30.04.2001 25.48 31.05.2001 22.64 29.06.2001 19.06 31.07.2001 21.62 31.08.2001 24.92 28.09.2001 31.93 31.10.2001 33.56 30.11.2001 23.84 31.12.2001 23.8 31.01.2002 21.09 28.02.2002 21.59 29.03.2002 17.4 30.04.2002 21.91 31.05.2002 19.98 28.06.2002 25.4 31.07.2002 32.03 30.08.2002 32.64 30.09.2002 39.69 31.10.2002 31.14 29.11.2002 27.5 31.12.2002 28.62 31.01.2003 31.17 28.02.2003 29.63 31.03.2003 29.15 30.04.2003 21.21 30.05.2003 19.47 30.06.2003 19.52 31.07.2003 19.49 29.08.2003 18.63 30.09.2003 22.72 31.10.2003 16.1 28.11.2003 16.32 31.12.2003 18.31 30.01.2004 16.63 27.02.2004 14.55 31.03.2004 16.74 30.04.2004 17.19 31.05.2004 15.5 30.06.2004 14.34 30.07.2004 15.32 31.08.2004 15.29 30.09.2004 13.34 29.10.2004 16.27 30.11.2004 13.24 31.12.2004 13.29 31.01.2005 12.82 28.02.2005 12.08 31.03.2005 14.02 29.04.2005 15.31 31.05.2005 13.29 30.06.2005 12.04 29.07.2005 11.57 31.08.2005 12.6 30.09.2005 11.92 31.10.2005 15.32 30.11.2005 12.06 30.12.2005 12.07 31.01.2006 12.95 28.02.2006 12.34 31.03.2006 11.39 28.04.2006 11.59 31.05.2006 16.44 30.06.2006 13.08 31.07.2006 14.95 31.08.2006 12.31 29.09.2006 11.98 31.10.2006 11.1 30.11.2006 10.91 29.12.2006 11.56 31.01.2007 10.42 28.02.2007 15.42 30.03.2007 14.64 30.04.2007 14.22 31.05.2007 13.05 29.06.2007 16.23 31.07.2007 23.52 31.08.2007 23.38 28.09.2007 18 31.10.2007 18.53 30.11.2007 22.87 31.12.2007 22.5 31.01.2008 26.2 29.02.2008 26.54 31.03.2008 25.61 30.04.2008 20.79 30.05.2008 17.83 30.06.2008 23.95 31.07.2008 22.94 29.08.2008 20.65 30.09.2008 39.39 31.10.2008 59.89 28.11.2008 55.28 31.12.2008 40 30.01.2009 44.84 27.02.2009 46.35 31.03.2009 44.14 30.04.2009 36.5 29.05.2009 28.92 30.06.2009 26.35 31.07.2009 25.92 31.08.2009 26.01 30.09.2009 25.61 30.10.2009 30.69 30.11.2009 24.51 31.12.2009 21.68 29.01.2010 24.62 26.02.2010 19.5 31.03.2010 17.59 30.04.2010 22.05 31.05.2010 32.07 30.06.2010 34.54 30.07.2010 23.5 31.08.2010 26.05 30.09.2010 23.7 29.10.2010 21.2 30.11.2010 23.54 31.12.2010 17.75 31.01.2011 19.53 28.02.2011 18.35 31.03.2011 17.74 29.04.2011 14.75 31.05.2011 15.45 30.06.2011 16.52 29.07.2011 25.25 31.08.2011 31.62 30.09.2011 42.96 31.10.2011 29.96 30.11.2011 27.8 30.12.2011 23.4 31.01.2012 19.44 29.02.2012 18.43 30.03.2012 15.5 30.04.2012 17.15 31.05.2012 24.06 29.06.2012 17.08 31.07.2012 18.93 31.08.2012 17.47 28.09.2012 15.73 31.10.2012 18.6 30.11.2012 15.87 31.12.2012 18.02 31.01.2013 14.28 28.02.2013 15.51 29.03.2013 12.7 30.04.2013 13.52 31.05.2013 16.3 28.06.2013 16.86 31.07.2013 13.45 30.08.2013 17.01 30.09.2013 16.6 31.10.2013 13.75 29.11.2013 13.7 31.12.2013 13.72 31.01.2014 18.41 28.02.2014 14 31.03.2014 13.88 30.04.2014 13.41 30.05.2014 11.4 30.06.2014 11.57 31.07.2014 16.95 29.08.2014 11.98 30.09.2014 16.31 31.10.2014 14.03 28.11.2014 13.33 31.12.2014 19.2 30.01.2015 20.97 27.02.2015 13.34 31.03.2015 15.29 30.04.2015 14.55 29.05.2015 13.84 30.06.2015 18.23 31.07.2015 12.12 31.08.2015 28.43 30.09.2015 24.5 30.10.2015 15.07 30.11.2015 16.13 31.12.2015 18.21 29.01.2016 20.2 29.02.2016 20.55 31.03.2016 13.95 29.04.2016 15.7 31.05.2016 14.19 30.06.2016 15.63 29.07.2016 11.87 31.08.2016 13.42 30.09.2016 13.29 31.10.2016 17.06 30.11.2016 13.33 30.12.2016 14.04 31.01.2017 11.99 28.02.2017 12.92 31.03.2017 12.37 28.04.2017 10.82 31.05.2017 10.41 30.06.2017 11.18 31.07.2017 10.26 31.08.2017 10.59 29.09.2017 9.51 31.10.2017 10.18 30.11.2017 11.28 29.12.2017 11.04 31.01.2018 13.54 28.02.2018 19.85 30.03.2018 19.97 30.04.2018 15.93 31.05.2018 15.43 29.06.2018 16.09 31.07.2018 12.83 31.08.2018 12.86 28.09.2018 12.12 31.10.2018 21.23 30.11.2018 18.07 31.12.2018 25.42 31.01.2019 16.57 28.02.2019 14.78 29.03.2019 13.71 30.04.2019 13.12 31.05.2019 18.71 28.06.2019 15.08 31.07.2019 16.12 30.08.2019 18.98 30.09.2019 16.24 31.10.2019 13.22 29.11.2019 12.62 31.12.2019 13.78 31.01.2020 18.84 28.02.2020 40.11 31.03.2020 53.54 30.04.2020 34.15 29.05.2020 27.51 30.06.2020 30.43 31.07.2020 24.46 31.08.2020 26.41 30.09.2020 26.37 30.10.2020 38.02 30.11.2020 20.57 31.12.2020 22.75 29.01.2021 33.09 26.02.2021 27.95 31.03.2021 19.4 30.04.2021 18.61 Carry World Equities World Bonds US Investment Grade US High Yield Gold Energy Copper 31.10.2000 3.9203 4.257575 7.818 13.328 0.4393339425 4.3692647872 1.5975180278 30.11.2000 4.1746 4.058779 7.619 14.195 0.439894628 4.5582285402 1.5643397813 29.12.2000 3.9931 3.924361 7.324 13.92 0.4414952149 4.1094316808 1.5493951613 31.01.2001 4.087 3.767103 6.894 12.547 0.3992130448 4.6821885914 1.566139347 28.02.2001 4.4596 3.628153 6.783 12.204 0.3981459869 4.2376910017 1.482628139 30.03.2001 4.627 3.572246 6.675 12.534 0.4525173893 3.9324022346 1.4152404972 30.04.2001 4.2953 3.729391 6.794 12.734 0.4604618117 3.9941891178 1.361852572 31.05.2001 4.3591 3.608784 6.728 12.414 0.4251224391 3.906512605 1.3124888333 29.06.2001 4.1601 3.612797 6.744 12.8 0.4486100573 3.7118736383 1.2549537649 31.07.2001 4.2252 3.46969 6.307 12.499 0.4224667173 3.7988795518 1.2429245283 31.08.2001 4.4266 3.333706 6.21 12.144 0.4607160102 3.971474704 1.2698665604 28.09.2001 4.1589 3.152335 6.085 13.724 0.479239209 3.657518582 1.267351646 31.10.2001 4.259 2.908198 5.833 12.884 0.4858891886 3.446571958 1.2644230769 30.11.2001 4.0084 3.106525 6.076 12.275 0.463680134 3.0750481078 1.2800912721 31.12.2001 3.0145 3.474885 6.267 12.385 0.4855208988 3.0608584241 1.2286902287 31.01.2002 3.112 3.524533 6.312 12 0.5009420138 2.8950777202 1.263356617 28.02.2002 3.135 3.50065 6.277 12.081 0.5763031191 3.1021538462 1.2575082348 29.03.2002 2.5842 3.762752 6.756 11.617 0.4297659383 3.3826891671 1.250729927 30.04.2002 2.6943 3.549084 6.557 11.102 0.4341275188 3.460547504 1.2549990478 31.05.2002 2.7025 3.547927 6.227 11.468 0.4373199895 3.3791208791 1.249356381 28.06.2002 2.7706 3.362616 6.244 12.625 0.3776219707 3.4201902748 1.2435991222 31.07.2002 3.0176 3.125816 6.162 13.198 0.325808047 3.4320465362 1.1928746929 30.08.2002 3.0499 2.939968 5.852 12.861 0.3633084107 3.704 1.189287888 30.09.2002 3.7486 2.730999 5.534 13.17 0.4454377496 3.9969434539 1.174857625 31.10.2002 3.4864 2.770615 5.776 13.539 0.4464274837 3.5374609781 1.2040332147 29.11.2002 3.3479 2.864848 5.634 12.207 0.4373840304 3.6022727273 1.2246763138 31.12.2002 3.6872 2.626505 5.114 11.835 0.5748745247 4.2629984856 1.1972318339 31.01.2003 3.8231 2.608822 5.103 11.442 0.6643954373 4.3638033992 1.2122965642 28.02.2003 3.9238 2.456141 4.781 11.263 0.5796197719 4.8122520934 1.2245581395 31.03.2003 4.1571 2.515028 4.803 10.788 0.4352236053 4.574777309 1.1929118002 30.04.2003 3.8386 2.51617 4.578 9.61 0.4321840393 4.1222114452 1.192627824 30.05.2003 3.7611 2.288179 4.136 9.489 0.4386292669 4.8085700978 1.2069927469 30.06.2003 4.0871 2.379333 4.167 9.063 0.3626731431 4.9579418345 1.192017051 31.07.2003 4.0278 2.713271 4.899 9.358 0.3930716059 5.0087145969 1.2634066533 29.08.2003 3.9722 2.833114 4.905 9.217 0.4746857402 5.0899742931 1.2031363968 30.09.2003 4.3078 2.605947 4.347 8.762 0.4254676368 4.6851286524 1.1803513804 31.10.2003 4.0796 2.834868 4.632 8.447 0.4188573872 4.5400428266 1.2270347454 28.11.2003 4.0174 2.892742 4.657 8.329 0.4280315115 4.8290456432 1.2126963351 31.12.2003 4.3796 2.777793 4.472 7.936 0.4929688075 4.8633879781 1.2740524781 30.01.2004 4.335 2.713403 4.374 7.731 0.441431271 5.079401611 1.375120011 27.02.2004 4.2291 2.581489 4.231 7.79 0.4196137139 5.3761500354 1.4541097532 31.03.2004 4.7646 2.538505 4.126 7.752 0.3969535859 5.1273601099 1.4548689361 30.04.2004 4.9241 2.852937 4.753 8.008 0.375555447 5.2402597403 1.4879396308 31.05.2004 4.8532 2.958703 4.989 8.486 0.3896939246 5.3102102102 1.4008941878 30.06.2004 5.1759 3.025315 5.034 8.308 0.3830190053 4.8464081755 1.3637192343 30.07.2004 5.3805 2.992056 4.92 8.167 0.3759557271 5.2387218045 1.423255814 31.08.2004 5.3718 2.770037 4.597 7.933 0.4408116702 5.1309938387 1.3549810072 30.09.2004 5.7217 2.801326 4.622 7.83 0.3510319871 5.4628924833 1.5390819594 29.10.2004 5.6242 2.712801 4.535 7.573 0.3526153307 5.2028199566 1.3968631179 30.11.2004 5.3648 2.732115 4.838 7.458 0.3465529407 4.9327156409 1.4645669291 31.12.2004 5.6969 2.786441 4.751 7.35 0.3025775121 4.7481212121 1.2678328271 31.01.2005 5.869 2.740486 4.773 7.54 0.2533100901 4.5428384565 1.2169919633 28.02.2005 5.6997 2.883886 4.985 7.4 0.2932179471 4.4723901653 1.1946508172 31.03.2005 6.1588 2.910239 5.27 8.093 0.2918633948 4.0742249779 1.1458313065 29.04.2005 6.2754 2.741135 5.116 8.44 0.2999452424 3.6437744277 1.1306913167 31.05.2005 6.186 2.644221 4.93 8.231 0.2898671278 3.6467864419 1.2974492452 30.06.2005 6.344 2.601704 4.887 7.986 0.3459054791 3.5058784567 1.5161797047 29.07.2005 6.1831 2.78465 5.161 7.825 0.3236214784 3.4000925783 1.4353626456 31.08.2005 6.1494 2.698259 4.944 7.921 0.3306700523 3.570480226 1.3563508519 30.09.2005 6.1449 2.886535 5.279 8.103 0.2631274578 3.5172814406 1.3598984772 31.10.2005 6.3535 3.075643 5.538 8.371 0.2532843185 3.4660869565 1.3912193533 30.11.2005 6.1744 3.087379 5.563 8.442 0.2421635913 3.2423559704 1.4026806527 30.12.2005 6.1858 3.060275 5.43 8.383 0.2924868261 3.2319891255 1.3331538565 31.01.2006 5.9548 3.15826 5.545 8.209 0.4210021187 3.2564628642 1.1924394566 28.02.2006 5.9895 3.216592 5.598 8.24 0.3923546348 2.9380569129 1.0867355879 31.03.2006 5.9112 3.459227 5.86 8.239 0.2090972879 3.0119444444 0.9918878317 28.04.2006 5.7522 3.565117 5.978 8.25 0.2034158955 2.8382447561 1.1167101523 31.05.2006 6.011 3.577269 6.102 8.418 0.1873538541 2.8155630865 1.1891643059 30.06.2006 6.2701 3.714425 6.201 8.652 0.1269810882 2.829717041 1.2177940462 31.07.2006 6.2997 3.61773 6.038 8.583 0.1595673399 2.6750462107 1.1874130737 31.08.2006 6.1381 3.458074 5.822 8.416 0.1374694034 2.5852658552 1.0338826901 29.09.2006 6.1848 3.45089 5.727 8.285 0.1763448522 2.5092162657 1.0398115269 31.10.2006 5.9927 3.470935 5.677 8.136 0.1742254352 2.2542323409 0.9373421609 30.11.2006 5.8696 3.418953 5.532 7.93 0.190666779 2.1949295775 0.7412422528 29.12.2006 5.9595 3.600122 5.749 7.89 0.163492866 2.1904413914 0.7388096041 31.01.2007 5.9114 3.682092 5.827 7.828 0.1888692282 2.1492444306 0.8118643347 28.02.2007 5.966 3.545264 5.569 7.665 0.2152567127 2.0935356778 0.7627575277 30.03.2007 6.1594 3.619015 5.689 7.777 0.148656837 2.0544889893 0.8339436169 30.04.2007 5.9344 3.673236 5.66 7.659 0.1488340825 1.9667732518 0.8297563439 31.05.2007 5.7928 3.889713 5.931 7.661 0.1469018112 1.9503434459 0.7840114483 29.06.2007 6.0669 4.019583 6.063 8.16 0.1197330791 2.0948654585 0.7680132219 31.07.2007 6.2531 3.864627 6.062 9.002 0.1471469427 2.3598541132 0.7349351074 31.08.2007 6.2786 3.656978 5.961 9.058 0.1519133869 2.3257425743 0.6630495442 28.09.2007 6.0925 3.662445 5.926 8.682 0.1287080643 2.45916634 0.652239064 31.10.2007 5.9466 3.619497 5.854 8.763 0.1319665262 2.5695159629 0.537301358 30.11.2007 6.2014 3.384528 5.705 9.445 0.1144163708 2.4110612855 0.4708250743 31.12.2007 6.127 3.432495 5.799 9.642 0.1834821275 2.4688542227 0.4498183104 31.01.2008 6.6404 3.048168 5.485 10.024 0.3025633955 2.3597402597 0.4967513826 29.02.2008 6.6881 2.941898 5.47 10.474 0.3685268806 2.4107562696 0.550189419 31.03.2008 6.6361 2.977317 5.798 10.83 0.1510094046 2.4934663342 0.5122642996 30.04.2008 6.2974 3.276359 5.885 10.056 0.1364015106 2.5368449294 0.5132665929 30.05.2008 6.2708 3.54929 6.09 10.066 0.1165455243 2.402159761 0.4382147009 30.06.2008 6.4216 3.652735 6.257 10.786 0.1626349243 2.3142486693 0.4707346814 31.07.2008 6.56 3.494196 6.443 11.331 0.1437429362 2.3040832049 0.459760251 29.08.2008 6.6619 3.322233 6.41 11.482 0.0355961552 2.2435059631 0.4332754646 30.09.2008 7.1527 3.250629 7.639 13.87 0.1161949035 2.5675927652 0.3745670784 31.10.2008 8.764 2.978304 8.924 18.864 0.1385289432 2.2971354167 0.3262961657 28.11.2008 9.7012 2.550313 8.351 21.596 0.160889143 2.031062425 0.289889019 31.12.2008 6.4825 2.211356 7.499 19.387 0.2534486456 1.210455988 0.3003014812 30.01.2009 7.511 2.308642 7.286 17.833 0.3132966431 1.1161616162 0.2889167188 27.02.2009 8.3223 2.323624 7.579 19.13 0.3332499464 1.3111446351 0.2865226028 31.03.2009 6.2092 2.240299 7.592 18.231 0.1518403296 1.2707765668 0.2969837587 30.04.2009 5.5662 2.305548 6.972 15.202 0.1491054327 1.2461564742 0.3600280177 29.05.2009 5.248 2.425395 6.259 13.552 0.1806033693 1.4989666371 0.342358682 30.06.2009 4.0375 2.417491 5.891 12.648 0.1168951539 1.4871362294 0.3150195329 31.07.2009 3.5037 2.35486 5.34 11.348 0.1481737997 1.3697731621 0.3285667741 31.08.2009 3.3593 2.270501 5.044 11.018 0.1454034344 1.4104005622 0.3230019625 30.09.2009 2.903 2.230554 4.81 9.867 0.1386882266 1.4493329549 0.2947149703 30.10.2009 2.9344 2.277625 4.705 9.619 0.1403115763 1.4663083377 0.2757330797 30.11.2009 2.8442 2.138695 4.482 9.351 0.1534224563 1.3618794998 0.2561663663 31.12.2009 4.5058 2.366812 4.747 8.854 0.0694264984 1.4243513999 0.2508463196 29.01.2010 4.7696 2.260364 4.425 8.741 0.0561574396 1.4086545151 0.2666872587 26.02.2010 4.711 2.172576 4.428 8.855 0.0903654375 1.4901753923 0.2456601939 31.03.2010 5.483 2.275465 4.478 8.304 0.1339058469 1.5152671756 0.2459228716 30.04.2010 5.5204 2.280922 4.303 8.024 0.1364794142 1.3903850697 0.2272486108 31.05.2010 6.1175 2.079592 4.465 8.998 0.1341442072 1.3058630586 0.2119768731 30.06.2010 6.946 1.928729 4.244 8.885 0.1629808763 1.3706526257 0.1981158827 30.07.2010 6.4927 1.886766 3.951 8.272 0.1031358386 1.3522892202 0.2186269232 31.08.2010 6.7815 1.671691 3.721 8.342 0.1652719 1.2396064302 0.2212871009 30.09.2010 6.5967 1.770909 3.627 7.852 0.1430700558 1.2934669443 0.2314875023 29.10.2010 6.3821 1.802829 3.576 7.535 0.1459890312 1.3177314211 0.238097668 30.11.2010 6.5465 2.014433 3.8 7.919 0.1570923884 1.3490735975 0.241544927 31.12.2010 6.6043 2.12733 4.037 7.655 0.1865610391 1.3351498638 0.2496112647 31.01.2011 6.6138 2.232606 4.003 7.348 0.1131927345 1.2259766502 0.2175648703 28.02.2011 6.4155 2.294509 3.998 7.226 0.1760839311 1.2590015463 0.1806462345 31.03.2011 6.577 2.393248 4.061 7.292 0.1316395208 1.316368924 0.157447174 29.04.2011 6.3565 2.337423 3.845 7.128 0.138177218 1.3311440055 0.1479858344 31.05.2011 6.459 2.203422 3.68 7.17 0.1421056654 1.2561685905 0.1418320712 30.06.2011 6.8015 2.2507 3.849 7.471 0.116835643 1.1863028953 0.1485706849 29.07.2011 6.9662 2.12313 3.58 7.379 0.2105410638 1.1933214206 0.1436580673 31.08.2011 7.5252 1.864683 3.688 8.41 0.3586394437 1.224399804 0.1283540072 30.09.2011 8.3347 1.787771 3.907 9.357 0.1389411254 1.2280484448 0.1022312373 31.10.2011 7.5708 1.91532 3.705 8.277 0.1406854898 1.2752417085 0.1176947435 30.11.2011 7.7773 1.92855 4.033 8.833 0.1560992243 1.2868758589 0.1186589524 30.12.2011 7.3268 1.704924 3.845 8.272 0.0348989856 1.2504578755 0.1162478522 31.01.2012 6.9805 1.608687 3.506 7.73 0.147444094 1.1890414016 0.1114645815 29.02.2012 6.6813 1.618802 3.403 7.375 0.1282584605 1.2095683827 0.1105592129 30.03.2012 6.6514 1.689172 3.465 7.503 0.1301229568 1.1523900169 0.1081042038 30.04.2012 6.7561 1.618631 3.357 7.36 0.1318263218 1.1641571022 0.1237688613 31.05.2012 7.4332 1.479051 3.4 7.899 0.1413331483 1.1119430925 0.1042555519 29.06.2012 6.8804 1.538642 3.345 7.591 0.1705233673 1.0787244644 0.1056410527 31.07.2012 6.8 1.403674 3.018 7.321 0.174838498 1.1006220271 0.0983421251 31.08.2012 6.6478 1.381814 2.964 7.156 0.2279511961 1.1296777841 0.1015003471 28.09.2012 6.3141 1.364884 2.856 6.976 0.1296627674 1.0856373008 0.1087235091 31.10.2012 6.3768 1.378506 2.741 6.899 0.1287376219 1.041268675 0.0976874525 30.11.2012 6.3145 1.317594 2.754 6.837 0.1250185394 1.045112782 0.0924344266 31.12.2012 6.3011 1.347318 2.776 6.667 0.1007803676 1.0684995888 0.0899392166 31.01.2013 6.0195 1.438545 2.873 6.476 0.0904724418 1.1034365815 0.0826999237 28.02.2013 6.0179 1.364857 2.805 6.471 0.0354188771 1.0676236802 0.0671947978 29.03.2013 5.9525 1.335017 2.83 6.371 0.1278757905 1.108154803 0.0559852276 30.04.2013 5.8209 1.241156 2.682 6.079 0.1300397501 1.0970176069 0.0686006728 31.05.2013 5.842 1.433433 3.009 6.274 0.1307472686 1.0800627943 0.0734892026 28.06.2013 5.9985 1.601557 3.438 6.915 -0.0066783508 1.1860161443 0.083303151 31.07.2013 5.7027 1.563511 3.339 6.562 0.0650026148 1.2517710559 0.086046994 30.08.2013 5.8388 1.635391 3.481 6.774 0.1325140281 1.2663938958 0.0922864618 30.09.2013 5.5705 1.579092 3.376 6.695 0.1267223135 1.1787353106 0.0988215488 31.10.2013 5.3648 1.494027 3.217 6.289 0.1308970693 1.0607772255 0.1096629469 29.11.2013 5.2806 1.512967 3.26 6.304 0.1426955642 0.9933752142 0.1260244999 31.12.2013 5.1768 1.649357 3.37 6.3 0.0987359316 1.0608569191 0.1656925032 31.01.2014 5.7824 1.484014 3.201 6.283 0.1330099485 1.1068913771 0.1402905425 28.02.2014 5.5288 1.462417 3.11 6.006 0.2077628299 1.1178145188 0.1681344598 31.03.2014 5.5018 1.531773 3.215 6.061 0.1270955494 1.0872124714 0.1445993031 30.04.2014 5.4883 1.490566 3.122 5.923 0.1324931231 1.0562275253 0.1717076836 30.05.2014 5.384 1.404442 2.958 5.784 0.1187807877 1.0610298792 0.1827720839 30.06.2014 5.434 1.38186 2.997 5.717 0.1870247241 1.0293730376 0.1564292048 31.07.2014 5.5312 1.380991 3.089 6.115 0.1500442481 1.0038947368 0.1534184032 29.08.2014 5.4264 1.270752 2.971 5.87 0.1541714635 1.0227320787 0.130806591 30.09.2014 5.6658 1.317856 3.178 6.394 0.1204803698 1.048343778 0.1345001725 31.10.2014 5.644 1.261217 3.111 6.232 0.1248059869 0.974218655 0.1511388456 28.11.2014 5.5489 1.165417 3.082 6.481 0.1052328641 0.8850722771 0.1359660747 31.12.2014 5.5958 1.134433 3.226 6.834 0.1133239047 0.7183559849 0.1385185928 30.01.2015 5.703 0.920487 2.927 6.72 0.2015195369 0.6209842789 0.1443478921 27.02.2015 5.3666 1.010937 3.002 6.337 0.1394388896 0.574374797 0.1609623976 31.03.2015 5.4032 0.965968 2.959 6.57 0.1218290556 0.6109341826 0.1620687271 30.04.2015 5.287 1.045856 3.026 6.378 0.1204134152 0.7594816688 0.1517661309 29.05.2015 5.2583 1.105822 3.112 6.424 0.1229189422 0.8035366645 0.1370532182 30.06.2015 5.2763 1.243165 3.352 6.863 0.1059312217 0.7771400459 0.1426471116 31.07.2015 5.1986 1.143239 3.358 7.178 0.032883196 0.6337432744 0.1279848688 31.08.2015 5.5786 1.174797 3.493 7.481 0.0680750008 0.6955868545 0.1537655217 30.09.2015 5.4514 1.09049 3.448 8.157 0.1211394514 0.6970954357 0.1638827098 30.10.2015 5.0652 1.094671 3.44 7.685 0.1225139289 0.675463336 0.1595922528 30.11.2015 5.1241 1.124708 3.517 8.24 0.1293300608 0.5533159948 0.1388035755 31.12.2015 4.9816 1.168252 3.699 8.806 0.1239285249 0.4852269998 0.1458894135 29.01.2016 5.2928 0.954503 3.637 9.265 0.1829735408 0.326937642 0.1513434473 29.02.2016 5.389 0.830642 3.569 9.214 0.3080084045 0.2942247659 0.1493518025 31.03.2016 4.8377 0.821201 3.224 8.468 0.1176755756 0.3399111988 0.1399024137 29.04.2016 4.7736 0.846821 3.094 7.688 0.1140150625 0.401965163 0.1411042945 31.05.2016 4.7382 0.8207 3.16 7.546 0.1082385384 0.4024571065 0.1289974847 30.06.2016 4.6613 0.593378 2.918 7.461 0.2020874919 0.3337510443 0.1298143054 29.07.2016 4.4971 0.587943 2.795 7.052 0.2282452723 0.260210035 0.1287418793 31.08.2016 4.4938 0.649176 2.818 6.646 0.187216918 0.289874552 0.1285772783 30.09.2016 4.5817 0.617376 2.868 6.494 0.0970774908 0.2991308035 0.1323680603 31.10.2016 4.6958 0.770518 2.993 6.539 0.0939488991 0.2851545494 0.1347377472 30.11.2016 4.6664 0.995794 3.422 6.738 0.0725885647 0.2788321168 0.1402859424 30.12.2016 4.8848 0.998387 3.416 6.402 0.0523069431 0.2719657121 0.1313940683 31.01.2017 4.7837 1.077421 3.399 6.203 0.1043460618 0.2669338677 0.1219740909 28.02.2017 4.6434 1.01502 3.305 5.971 0.1430913444 0.2935853609 0.105490524 31.03.2017 4.8324 1.063865 3.372 6.132 0.0767576535 0.2606564365 0.0895744154 28.04.2017 4.7818 1.01355 3.293 6.016 0.0774141212 0.2788966725 0.0951207134 31.05.2017 4.706 0.983115 3.207 5.928 0.0819492941 0.2800450958 0.0922727938 30.06.2017 4.9048 1.081767 3.25 6.004 0.0538712616 0.2390502536 0.0967255115 31.07.2017 4.8199 1.070129 3.171 5.899 0.0744876271 0.3190129985 0.0827613258 31.08.2017 4.8382 0.988125 3.12 6.015 0.115439502 0.2514489523 0.083443505 29.09.2017 4.8561 1.099778 3.206 5.936 0.0652679957 0.3158121499 0.0732732347 31.10.2017 4.7856 1.090355 3.207 5.976 0.0634575117 0.3315251408 0.0769277883 30.11.2017 4.7112 1.077092 3.322 6.135 0.0421546013 0.3442392613 0.067606686 29.12.2017 4.9832 1.129287 3.298 6.164 0.068759166 0.3392959087 0.0637997173 31.01.2018 4.7493 1.251692 3.504 6.134 0.0924379657 0.3680959302 0.0505564764 28.02.2018 5.058 1.261529 3.754 6.386 0.0719428702 0.3676694593 0.0364087212 30.03.2018 5.4129 1.197841 3.819 6.539 0.0325519819 0.3546824543 0.0293915757 30.04.2018 5.3837 1.291513 3.979 6.49 0.0313182552 0.3521628499 0.0210805313 31.05.2018 5.3838 1.337936 3.95 6.544 0.0338898381 0.3041876047 0.0196447876 29.06.2018 5.657 1.340896 4.084 6.656 -0.0058860155 0.3958500885 0.0213108421 31.07.2018 5.4974 1.413593 4.062 6.551 -0.0302988619 0.353372434 0.0124215262 31.08.2018 5.4405 1.418995 4.018 6.522 -0.0515334048 0.3614267677 0.0084645457 28.09.2018 5.6106 1.523833 4.136 6.507 0.0184871578 0.3381114231 0.0315047672 31.10.2018 5.9833 1.544209 4.344 6.988 0.0188405349 0.2728853755 0.0189779436 30.11.2018 5.9284 1.486697 4.437 7.34 0.016404134 0.2462492498 0.0402670415 31.12.2018 6.3866 1.326982 4.263 7.977 0.0622559137 0.1662738376 0.0342971679 31.01.2019 5.9259 1.276488 4.008 7.091 0.0933838705 0.2139737991 0.029389126 28.02.2019 5.7652 1.314702 3.996 6.785 0.085880015 0.1955869373 0.0349921981 29.03.2019 5.6754 1.165613 3.709 6.71 0.0151011492 0.2310236769 0.032495422 30.04.2019 5.4869 1.222903 3.675 6.501 0.0141013261 0.2624874288 0.0146522597 31.05.2019 5.7891 1.072155 3.517 6.916 0.0379554994 0.2203685742 0.0303344953 28.06.2019 5.3803 0.951573 3.25 6.434 0.1191783366 0.2306296498 0.0252106893 31.07.2019 5.3638 0.928404 3.236 6.375 0.1281081683 0.2245449631 0.0173074817 30.08.2019 5.4799 0.687932 2.905 6.346 0.1999628543 0.2497564777 0.0187080698 30.09.2019 5.273 0.794383 3.006 6.332 0.0147991957 0.243825331 0.0190461737 31.10.2019 5.1493 0.868054 2.938 6.377 0.0157373758 0.2157813106 0.0274074626 29.11.2019 4.9922 0.945205 2.97 6.366 0.020981745 0.2184761905 0.0109979333 31.12.2019 4.8393 1.016185 2.939 6.022 0.0559205097 0.2660663842 0.0174035582 31.01.2020 4.8756 0.840117 2.686 6.105 0.0969332849 0.1793022803 0.0112403403 28.02.2020 5.314 0.673244 2.511 6.494 0.0822896379 0.1249734325 0.0180914667 31.03.2020 5.5541 0.627164 3.698 9.264 0.0113136392 -0.3281075028 0.014757865 30.04.2020 5.015 0.546906 2.816 8.173 0.0067171901 -0.4079355239 0.0145298786 29.05.2020 4.8204 0.571452 2.527 7.137 0.0096960984 -0.0314981472 0.0039562392 30.06.2020 3.7576 0.582197 2.262 6.959 0.0378278023 0.0161697827 0.0082614682 31.07.2020 3.5851 0.536487 1.976 6.013 0.1308888373 -0.0169047619 0.002956749 31.08.2020 3.3617 0.647888 2.043 5.805 0.1289416932 0 0.0070933524 30.09.2020 3.3985 0.623082 2.104 6.076 -0.0208108912 -0.0124461465 0.0131795717 30.10.2020 3.5075 0.646469 2.127 6.009 -0.0221127175 -0.0399789584 0.0145674071 30.11.2020 3.1222 0.648229 1.903 5.256 -0.0243894451 0.0438437074 0.0125595116 31.12.2020 3.0608 0.626545 1.846 4.911 0.0381726476 0.0572477857 0.0149130075 29.01.2021 3.1071 0.69063 1.957 4.879 -0.0192405412 0.0906450944 0.02892362 26.02.2021 3.0204 0.866449 2.168 4.872 -0.022191346 0.1180731619 0.032736395 31.03.2021 3.3267 0.900854 2.352 4.857 -0.0202729713 0.0804221252 0.0163016049 30.04.2021 3.1983 0.904246 2.251 4.734 -0.0186531949 0.0803738318 0.0180668473
Quantitative Asset and Risk Management Florian Ielpo 2021 The due date is the 21st of May at midnight CET. The only accepted format is a PDF file. Assignments pro- vided after this deadline will not be considered. This assignment pushes you to develop your own multi-asset investment process. You are in charge of creating a model portfolio for a new client interested in your multi-asset investment skill- set. She asks you to design an investment process that will combine a SAA component with a TAA component. The investment universe is the following: - World equities (equities) - World bonds (bonds) - US investment grade bonds (bonds) - US high yield bonds (bonds) - Gold (commodities) - Energy commodities (commodities) - Industrial Metals (commodities). You have at hand a dataset of returns on each of these asset classes that cover the 2000-2021 period. Use it as much as possible to create a successful investment process. Important elements: • We are on the 31st of December 2010. The product will be launched on that day: you are investing your client’s money at the close of that trading day. The period prior to that date is the ”in-sample” period. The period that follows that date is the out-of-sample period. • The client will benchmark your performance vs. a 50% equities and 50% bonds portfolio, rolled on a monthly basis (benchmark weights are drifted during the month, re-aligned at the end of the month). The data you will use is in the Excel file associated. It is monthly data. Your project will lead you to complete three different tasks: create an SAA and analyze its performance, create a TAA and do the same; finally, invest the money and try to replicate your portfolio model. Part 1: The SAA (2 points) 1 1. You are in December 2010. Using the data available at that point in time, propose a strategic asset alloca- tion that you think can beat the client’s benchmark over the longer run, using one or several of the technics presented during the class. It must be (1) fully systematic and (2) exploit the information available up to December 2010. Explain your choices in terms of (1) allocation scheme and (2) selected asset classes in which you wish to see her money invested. Your SAA must include at least three asset classes and must include world bonds and US investment grade. Explain your choices and show the in-sample performance of your SAA (charts and performance figures: annualized performance, annualized volatility, Sharpe ratio with risk free rate at zero, maximum drawdown and hit ratio). 2. Let’s fast forward to the last date of your sample: analyze the out-of-sample performance of your investment solution: compute the performance, the volatility, the Sharpe ratio, the maximum drawdown and the hit ratio of your strategy on a standalone basis, and then as a comparison to the benchmark. Highlight its strength and its weaknesses. Show charts comparing your out of sample SAA with the benchmark. Part 2: The TAA (2.5 points) 1. You are in December 2010. Using the data available at that point in time, you want to create a TAA alloca- tion that would be fully systematic and based on a ”value” and ”momentum” tilting: - Create for each date in your sample a long-short value factor using the data under the ”carry” table. Prior to using these carry data, turn them into a z-score (substract the mean and divide by the standard deviation). The value factor will oppose the assets with a z-score higher than the median of that month to the assets with a score lower than that median value. For each date, compute the factor allocation and the performance of the factor for a 2% ex ante volatility budget (give an equal weight to your longs and your short and scale the portfolio up or down to obtain a 2% volatility). Chart the historical cumulated performance and comment. - Using the past 12-month performance, do the same with a long-short momentum factor (same ex ante risk budget). • Explain why you are computing long-short factors rather than long-only factors (in the case of a TAA). 2. Analyze the performance of these two long-short factors as a function of the standardized VIX level (the VIX index centered and scaled). Devise a dynamic tilt that uses what you have uncovered: how would you do it? (parametric allocation vs. FLAM allocation or anything else of your own invention). Can you compute an expected IR to your tilt? 3. Now, analyze the out-of-sample performance of your investment solution: compute the performance, the volatility, the Sharpe ratio, the maximum drawdown and the hit ratio of your strategy on a standalone basis, and then as a comparison to the benchmark. Highlight its strength and its weaknesses, show charts and a table that summarizes best the added value of your overlay. Part 3: Implementation (1.5 points) Finally, time has come for an real-life implementation. Good news, the client likes your investment process. Bad news: she will not let you invest in US investment grade but insists on still having the portfolio model’s per- formance. Explain how your real portfolio will be adjusted to accommodate for that, showing how you are going to handle the replication risk that should arise. Is this risk large? From December 2010 onwards, run a replication of your full portfolio model (SAA + TAA with the constraint of no US investment grade) and compute your ex ante and ex post tracking error. Do a performance attribution 2 of your replication errors depending on the following sectors: (1) bonds, (2) equities and (3) commodities. What explains your deviation from the model portfolio? Allocation or Selection? Conclude by explaining what lessons you have gathered from that exercise. 3

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