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Re-sample returens & portfolio value Summary Stats

Year Stocks T-Bills inflation (CPI) Real Gross Portfolio Return Age Return Wealth Path Sim# Final Wealth Mean 1048178.162 1 1928 0.44 0.03 -0.01 1.248893855 26 1.09751331 10975.1331 1 651518.4716 Std 475762.7555 2 1929 -0.08 0.03 0.01 0.968645672 27 1.072306671 21768.70844 2 677169.5416 25 pct 721316.3586 3 1930 -0.25 0.05 -0.06 0.958426539 28 0.885034684 29266.06201 3 745471.4715 75 pct 1257132.837 4 1931 -0.44 0.02 -0.09 0.873769337 29 1.24520574 46442.26839 4 1736289.591 Min 294547.6521 5 1932 -0.09 0.01 -0.10 1.072306671 30 0.957069274 54448.46808 5 1240729.8 Max 4046098.153 6 1933 0.50 0.01 0.01 1.24520574 31 0.851963138 56388.0877 6 817961.6215 7 1934 -0.01 0.00 0.02 0.98080893 32 1.12027075 73169.92531 7 1206962.656 8 1935 0.47 0.00 0.03 1.198792262 33 1.136119695 93129.79323 8 867348.7991 9 1936 0.32 0.00 0.01 1.143987522 34 1.090884354 111593.8343 9 785463.4396 10 1937 -0.35 0.00 0.03 0.801916944 35 0.978931668 119242.7383 10 578440.3332 bins Frequency 11 1938 0.29 0.00 -0.03 1.179566506 36 0.94004602 122093.6615 11 1640998.873 294547.65 1 12 1939 -0.01 0.00 0.00 0.994699677 37 1.0724005 140933.3036 12 774889.8067 369578.66 2 13 1940 -0.11 0.00 0.01 0.94004602 38 1.009438289 152263.4728 13 718213.6981 444609.67 25 14 1941 -0.13 0.00 0.10 0.851963138 39 0.958426539 155933.3532 14 799164.5267 519640.68 40 15 1942 0.19 0.00 0.09 1.00663449 40 0.994699677 165106.856 15 1345510.963 594671.69 63 16 1943 0.25 0.00 0.03 1.094815558 41 1.058248488 184724.0808 16 1256885.12 669702.70 69 17 1944 0.19 0.00 0.02 1.0724005 42 1.143877415 221301.704 17 705552.2802 744733.71 71 18 1945 0.36 0.00 0.02 1.155049259 43 1.114463687 256632.713 18 998608.8526 819764.72 94 19 1946 -0.08 0.00 0.18 0.812443143 44 1.248893855 330507.0183 19 602285.19 894795.73 85 20 1947 0.05 0.01 0.09 0.945299412 45 1.031681386 350977.9389 20 971409.6126 969826.74 75 21 1948 0.06 0.01 0.03 1.003612772 46 0.978931668 353583.419 21 927183.3237 1044857.75 75 22 1949 0.18 0.01 -0.02 1.12027075 47 0.877597556 320303.9444 22 910843.5425 1119888.76 59 23 1950 0.31 0.01 0.06 1.094936344 48 0.944458317 312513.7241 23 580754.3669 1194919.77 51 24 1951 0.24 0.01 0.06 1.062056429 49 0.999810696 322454.564 24 766034.0317 1269950.78 49 25 1952 0.18 0.02 0.01 1.090884354 50 0.951430276 316793.035 25 545628.3812 1344981.79 40 26 1953 -0.01 0.02 0.01 0.995961094 51 1.03626685 338282.1205 26 1382783.113 1420012.80 34 27 1954 0.53 0.01 -0.01 1.277124455 52 0.981563841 342045.4977 27 988516.9629 1495043.81 24 28 1955 0.33 0.02 0.00 1.166916187 53 1.008248907 354866.9993 28 1160994.873 1570074.82 19 29 1956 0.07 0.03 0.03 1.019538572 54 0.933740063 341353.5343 29 1411536.638 1645105.83 13 30 1957 -0.10 0.03 0.03 0.936712123 55 1.143987522 400504.1839 30 998961.7526 1720136.84 17 31 1958 0.44 0.02 0.02 1.206250471 56 0.941768337 387182.1591 31 638363.8046 1795167.85 17 32 1959 0.12 0.03 0.02 1.058248488 57 1.149931152 455232.8264 32 832276.5303 1870198.86 16 33 1960 0.00 0.03 0.01 1.003257909 58 1.031681386 479655.2335 33 1183208.388 1945229.87 9 34 1961 0.27 0.02 0.01 1.136895891 59 1.059208489 518054.8952 34 588808.3075 2020260.88 6 35 1962 -0.09 0.03 0.01 0.957069274 60 0.801916944 425436.9982 35 1047981.524 2095291.89 9 36 1963 0.23 0.03 0.02 1.110347344 61 1.079644689 469320.7955 36 567104.7964 2170322.90 5 37 1964 0.16 0.04 0.01 1.089029181 62 1.110456242 531160.2071 37 671615.9069 2245353.91 5 38 1965 0.12 0.04 0.02 1.061102888 63 1.019538572 551538.3191 38 1579291.266 2320384.92 5 39 1966 -0.10 0.05 0.03 0.941768337 64 1.059208489 594194.0698 39 830991.4341 2395415.93 2 40 1967 0.24 0.04 0.03 1.107029034 65 1.079644689 651518.4716 40 710925.4404 2470446.94 6 41 1968 0.11 0.05 0.05 1.031681386 41 1217704.551 2545477.95 0 42 1969 -0.08 0.07 0.06 0.933740063 42 414814.6991 2620508.96 0 43 1970 0.04 0.07 0.06 0.995763777 43 988645.2384 2695539.97 4 44 1971 0.14 0.05 0.03 1.059208489 44 1134451.457 2770570.98 1 45 1972 0.19 0.04 0.03 1.07685802 45 1179794.326 2845601.99 1 46 1973 -0.14 0.07 0.09 0.885034684 46 1122653.991 2920633.00 3 47 1974 -0.26 0.08 0.12 0.809504624 47 904876.2679 2995664.01 1 48 1975 0.37 0.06 0.07 1.136119695 48 753989.7358 3070695.02 1 49 1976 0.24 0.05 0.05 1.090932598 49 648878.2373 3145726.03 0 50 1977 -0.07 0.05 0.07 0.928518657 50 1206112.412 3220757.04 1 51 1978 0.07 0.07 0.09 0.978931668 51 770017.4287 3295788.05 0 52 1979 0.19 0.10 0.13 1.008248907 52 887458.5356 3370819.06 0 53 1980 0.32 0.11 0.13 1.079644689 53 1911078.593 3445850.07 0 54 1981 -0.05 0.14 0.09 0.962142219 54 1186425.443 3520881.08 1 55 1982 0.20 0.11 0.04 1.114463687 55 564067.0817 3595912.09 0 56 1983 0.22 0.08 0.04 1.111776032 56 1549403.26 3670943.10 0 57 1984 0.06 0.10 0.04 1.037813411 57 557850.3735 3745974.11 0 58 1985 0.31 0.07 0.04 1.149931152 58 679834.2007 3821005.12 0 59 1986 0.18 0.06 0.01 1.110456242 59 1009785.27 3896036.13 0 60 1987 0.06 0.06 0.04 1.012766117 60 1712234.588 3971067.14 0 61 1988 0.17 0.06 0.04 1.067747803 61 973997.9836 4046098.15 1 62 1989 0.31 0.08 0.05 1.144726988 62 1183749.299 63 1990 -0.03 0.08 0.06 0.963588477 63 1151459.719 64 1991 0.30 0.06 0.03 1.144163887 64 736845.2665 65 1992 0.07 0.03 0.03 1.024768661 65 884120.1794 66 1993 0.10 0.03 0.03 1.03626685 66 930690.9888 67 1994 0.01 0.04 0.03 0.999810696 67 1305056.503 68 1995 0.37 0.06 0.03 1.18350869 68 1109077.372 69 1996 0.23 0.05 0.03 1.101906748 69 1617940.674 70 1997 0.33 0.05 0.02 1.170848291 70 973478.2 71 1998 0.28 0.05 0.02 1.146841294 71 981968.0299 72 1999 0.21 0.05 0.03 1.09751331 72 2462492.767 73 2000 -0.09 0.06 0.03 0.951430276 73 468164.5481 74 2001 -0.12 0.04 0.02 0.944458317 74 1437801.448 75 2002 -0.22 0.02 0.02 0.877597556 75 734180.9486 76 2003 0.28 0.01 0.02 1.125770245 76 1318611.825 77 2004 0.11 0.01 0.03 1.026435151 77 476618.4264 78 2005 0.05 0.03 0.03 1.004898477 78 1169585.403 79 2006 0.16 0.05 0.03 1.074159648 79 1283905.287 80 2007 0.05 0.05 0.04 1.009438289 80 766295.2463 81 2008 -0.37 0.02 0.00 0.824409663 81 1264827.484 82 2009 0.26 0.00 0.03 1.100405492 82 1248216.157 83 2010 0.15 0.00 0.01 1.058916991 83 891415.9742 84 2011 0.02 0.00 0.03 0.981563841 84 878752.3674 85 2012 0.16 0.00 0.02 1.061226731 85 1832758.58 86 2013 0.32 0.00 0.02 1.143877415 86 1091737.308 87 1275543.751 88 1252194.43 89 1532584.034 90 889025.0794 91 1275776.469 92 2071229.871 93 508088.7998 94 982845.1729 95 504306.8934 96 1956888.34 97 1360493.811 98 792089.8259 99 780117.7815 100 486697.1041 101 1155584.388 102 645589.4014 103 409185.8308 104 717824.1239 105 1003966.021 106 669187.3911 107 395466.644 108 2207787.775 109 589469.116 110 1464995.612 111 936215.7884 112 1031149.937 113 1039557.283 114 875534.5258 115 1284507.771 116 993517.3008 117 665123.8448 118 2398423.451 119 614310.919 120 449989.7159 121 1268586.179 122 1824862.854 123 1724988.889 124 811532.5648 125 1269585.565 126 1172343.6 127 1345016.372 128 790434.5021 129 996800.5469 130 574818.7105 131 796960.2371 132 1864681.378 133 526642.6776 134 942627.5368 135 827390.617 136 838198.7113 137 1727894.818 138 1450059.619 139 2031945.118 140 1302050.395 141 860514.7887 142 1875403.536 143 1022132.675 144 743830.672 145 2092854.97 146 1476449.857 147 1226910.733 148 812341.9713 149 1006410.762 150 774983.6827 151 1126375.296 152 1287517.296 153 1034532.901 154 851907.1972 155 1376424.831 156 1103230.162 157 993881.5262 158 684926.5035 159 474880.7572 160 1079818.97 161 1354059.421 162 1086622.175 163 1722299.147 164 809266.5205 165 680833.5359 166 482170.0195 167 871546.8781 168 1573698.821 169 467588.527 170 812232.9823 171 1622706.363 172 1258874.145 173 964146.9635 174 868235.4751 175 771352.1879 176 810891.4651 177 975230.0789 178 569915.1123 179 768465.5409 180 407761.0577 181 1358879.113 182 776285.7288 183 665268.0033 184 713733.0359 185 1744341.311 186 490549.011 187 559522.2088 188 780744.6139 189 1156852.218 190 878864.8179 191 1545087.11 192 857132.5445 193 885249.074 194 2027628.582 195 2260566.824 196 656343.1049 197 629622.4681 198 949852.9295 199 2240904.212 200 1106359.849 201 1711152.784 202 948934.7381 203 952760.5658 204 1105826.363 205 875043.8507 206 1181130.245 207 401210.5857 208 1543510.894 209 310176.5252 210 666873.1104 211 623663.3726 212 2031656.405 213 728895.4199 214 1114061.383 215 2685538.98 216 1504418.421 217 581027.03 218 743558.6484 219 971833.0385 220 488958.3044 221 826099.2395 222 768894.7573 223 800972.815 224 643961.0448 225 554886.9462 226 1667945.786 227 2305862.232 228 639869.8254 229 761680.4805 230 695803.6746 231 1700207.032 232 637003.0802 233 1131796.627 234 1673173.438 235 1055379.375 236 1748273.817 237 747972.0262 238 1034877.673 239 836961.9598 240 984782.3499 241 781165.4955 242 1139252.421 243 1142436.375 244 815250.7284 245 837576.8125 246 626850.7432 247 856278.5555 248 1359766.151 249 763967.7481 250 1646618.89 251 2050067.341 252 1436843.511 253 1244988.989 254 550226.9875 255 732648.868 256 670961.9113 257 656647.8793 258 1021500.254 259 1005664.562 260 706816.6649 261 938174.9692 262 807092.1545 263 1410243.075 264 1729841.096 265 1129032.064 266 522638.4357 267 1003739.821 268 1708556.403 269 816315.6241 270 787255.9394 271 1888943.893 272 887658.6283 273 827975.6384 274 1159450.934 275 909551.0349 276 1402652.305 277 1597515.696 278 875591.9398 279 1476795.237 280 1407616.182 281 1929826.31 282 633911.7592 283 1896917.577 284 981963.1171 285 444140.4343 286 434678.8922 287 1158424.805 288 1797985.325 289 1727897.929 290 2730901.349 291 890015.9799 292 1271232.623 293 617230.2488 294 1293341.943 295 1211582.057 296 1739499.804 297 1463242.212 298 700942.3291 299 822433.0224 300 980025.2409 301 646106.516 302 1375024.328 303 1011330.988 304 609772.7169 305 1099215.481 306 985995.027 307 815309.0305 308 1207355.037 309 1410300.678 310 831002.9789 311 709313.9156 312 662747.7067 313 766018.2165 314 739370.9027 315 904412.5808 316 822546.2183 317 1248422.028 318 1721811.362 319 1121230.939 320 768114.7626 321 1025032.622 322 841204.8168 323 1215524.915 324 933568.8255 325 1139035.029 326 877987.9351 327 596091.518 328 619337.126 329 413335.6682 330 405334.0684 331 939418.2043 332 1164414.664 333 1022358.826 334 871616.1806 335 491853.3509 336 529891.8024 337 1233179.075 338 458943.1592 339 634351.8491 340 803373.1377 341 1359481.857 342 729047.9678 343 1204733.071 344 587846.6626 345 1500453.034 346 700205.3158 347 1068669.08 348 1385931.207 349 643653.9853 350 1112456.578 351 1083107.48 352 1096253.818 353 1490044.642 354 628677.8818 355 1834189.204 356 682866.2079 357 833290.8466 358 1154773.276 359 710635.2542 360 760515.2243 361 1753986.371 362 901369.0397 363 1668222.329 364 520289.5072 365 1767401.289 366 1161743.419 367 967494.5523 368 828670.7433 369 1221277.397 370 421853.6463 371 980467.8404 372 493328.0708 373 2339556.616 374 1294592.693 375 1252413.86 376 1836251.583 377 910703.5933 378 1001151.83 379 1090788.955 380 454340.9153 381 1020491.004 382 663242.8575 383 1519078.135 384 1146970.2 385 1425493.96 386 1047874.171 387 899901.5076 388 615042.0658 389 2866297.299 390 634442.6374 391 946200.507 392 754369.7593 393 1067609.024 394 444936.045 395 898255.891 396 722350.5788 397 583428.9843 398 558165.2934 399 614726.416 400 925276.8355 401 880709.555 402 1566388.32 403 1015490.336 404 796787.0242 405 842831.2288 406 968887.6543 407 563744.398 408 646194.6206 409 1426277.295 410 1193126.99 411 863433.8127 412 916390.3497 413 814396.7823 414 1105987.841 415 1322576.986 416 1014588.916 417 1087379.664 418 906377.3316 419 969342.4409 420 765099.1826 421 980681.1661 422 1375494.305 423 749234.3173 424 548196.9766 425 1258410.106 426 600445.1499 427 1125034.011 428 1053159.182 429 587405.422 430 2424154.324 431 938341.9882 432 482821.0112 433 816170.3697 434 940749.908 435 611761.9346 436 1256715.85 437 595906.6058 438 1222227.365 439 742148.8469 440 1027796.104 441 1175285.036 442 1055717.828 443 828846.7265 444 1545721.503 445 1799596.985 446 804992.5029 447 1583271.643 448 1212678.451 449 968531.1567 450 4046098.153 451 1235374.605 452 830220.4236 453 1024841.027 454 2684786.05 455 922700.5274 456 725402.6187 457 781135.3561 458 1227763.553 459 690031.2427 460 673465.6208 461 981231.0151 462 1238682.833 463 2434594.278 464 1028041.076 465 555235.9229 466 1282050.078 467 556091.7406 468 1799341.283 469 857458.1471 470 814391.9338 471 942795.4006 472 1465543.305 473 1857984.291 474 895717.9977 475 860991.696 476 653109.3993 477 922141.8045 478 1187816.209 479 413854.5245 480 524691.4272 481 1431996.538 482 552709.089 483 1172394.867 484 595697.5576 485 791618.6286 486 1186695.794 487 512300.5454 488 903840.7893 489 1120419.123 490 1338907.63 491 2000550.118 492 1472124.84 493 570298.544 494 2000344.855 495 1470271.946 496 586712.323 497 1349494.132 498 2974755.036 499 827362.9133 500 963604.5702 501 2205533.978 502 880799.3079 503 1253675.1 504 932940.8157 505 1591145.913 506 1775678.341 507 958980.029 508 2001200.529 509 602020.4444 510 578114.9929 511 673931.14 512 541523.2832 513 545913.6878 514 2232572.689 515 1098758.485 516 1605385.283 517 864141.4047 518 526657.8723 519 1073923.8 520 1206052.101 521 765452.6577 522 527326.7017 523 465624.4672 524 1505895.339 525 438763.3549 526 549733.9604 527 1112719.179 528 1164436.096 529 1150851.867 530 1671817.678 531 1394324.119 532 805449.5798 533 797516.7078 534 1768496.803 535 1338487.738 536 812845.5677 537 840147.7659 538 2666535.268 539 1122969.802 540 1134566.947 541 1318521.511 542 2190737.254 543 604087.3196 544 440507.7661 545 878444.8752 546 1267081.775 547 661972.1155 548 1663711.3 549 462004.6288 550 797682.0396 551 1050053.283 552 777827.0506 553 796781.8614 554 692837.1197 555 952737.9279 556 1210121.384 557 1384404.198 558 784478.7719 559 1109191.67 560 831535.4469 561 815722.5947 562 937723.7978 563 1236267.598 564 501360.1328 565 1277346.307 566 1058087.517 567 1336014.142 568 3007702.544 569 1238741.277 570 956407.6131 571 610592.1366 572 696000.1886 573 529819.9801 574 3184413.907 575 579727.0711 576 382031.4997 577 1320052.833 578 500318.9482 579 615828.3562 580 945686.6863 581 2848268.842 582 1900146.123 583 711000.8279 584 1010039.421 585 699927.0188 586 959919.8736 587 1443640.319 588 2253550.841 589 584036.3315 590 464573.432 591 1930029.879 592 846549.9412 593 666499.7547 594 1077001.355 595 988559.76 596 728433.9527 597 849357.5375 598 749936.8215 599 1134622.373 600 1888864.77 601 1257875.987 602 1077524.47 603 831235.1783 604 2113252.399 605 746953.1446 606 968288.9795 607 955626.2478 608 713161.0129 609 708045.0342 610 692012.76 611 550942.1083 612 856598.9359 613 1311777.066 614 811389.7908 615 433906.1898 616 751766.453 617 1393267.374 618 997681.3121 619 500077.1371 620 1780402.804 621 1812730.461 622 909562.8632 623 832854.9636 624 560137.349 625 1186369.123 626 1116317.808 627 692302.9506 628 1332004.707 629 759091.6383 630 669618.0702 631 1092756.879 632 984780.894 633 1347945.874 634 1796519.8 635 511993.0693 636 892788.1219 637 695554.7356 638 562298.0017 639 1472233.018 640 1827935.796 641 843613.3608 642 1005456.763 643 917027.8045 644 923565.5706 645 701165.3406 646 771686.3891 647 1000485.59 648 611100.1491 649 975766.603 650 1375288.255 651 1089644.692 652 710294.9579 653 462483.8551 654 630209.8459 655 1108931.072 656 1348305.621 657 1008728.383 658 706622.5486 659 913719.9739 660 768976.5246 661 539116.2948 662 1782476.03 663 923836.9453 664 2010847.078 665 1668282.724 666 2432894.919 667 424480.6602 668 732355.994 669 836065.9466 670 549711.9498 671 1039554.812 672 831334.2313 673 843706.7807 674 586538.9846 675 1283410.344 676 1337557.843 677 439130.7464 678 1247900.649 679 1111109.381 680 552823.3804 681 877735.3609 682 857951.1986 683 1395877.511 684 1869514.182 685 916261.0211 686 782345.1963 687 1310164.791 688 980022.0133 689 854267.0509 690 628470.391 691 1003575.384 692 506723.4875 693 1109386.825 694 538680.7612 695 415704.1657 696 1313460.92 697 1020456.262 698 1134228.483 699 992161.0059 700 638929.7535 701 560183.5786 702 953809.8699 703 2075717.899 704 1280210.884 705 1056997.916 706 1331649.148 707 426388.1874 708 1110630.887 709 1204640.326 710 539249.0686 711 946918.076 712 483623.8421 713 758275.6061 714 1181279.728 715 875225.6305 716 432962.2064 717 716356.3975 718 1216267.292 719 1070049.398 720 1947755.404 721 788143.5069 722 1113729.632 723 1415888.45 724 563640.7458 725 631078.1924 726 878424.1836 727 943952.6352 728 702967.1554 729 840932.9519 730 1437613.464 731 382918.0861 732 1117624.131 733 2790284.15 734 294547.6521 735 1226684.354 736 1533700.805 737 1333108.147 738 1062663.981 739 1645135.415 740 701688.183 741 996731.1537 742 546975.9216 743 422429.6528 744 1522953.581 745 1476011.092 746 956608.9249 747 1252572.862 748 715788.1023 749 961052.9446 750 364012.9509 751 1511810.631 752 1155554.754 753 1008208.145 754 2103949.766 755 1297437.858 756 1048237.535 757 753104.5891 758 726136.3304 759 555708.0221 760 985174.6243 761 935496.0304 762 706917.9339 763 940544.6201 764 1080066.576 765 1642815.736 766 2081476.597 767 879196.96 768 665464.8748 769 869572.8819 770 744160.0526 771 1229370.517 772 1637708.688 773 648975.5823 774 1700752.397 775 809230.9663 776 1066966.369 777 793488.1554 778 1200671.783 779 962315.4528 780 578778.7108 781 749938.1109 782 882599.5853 783 764214.6495 784 646079.3859 785 410384.9601 786 752261.6828 787 811338.1252 788 1865927.236 789 940076.0891 790 684221.9941 791 686439.676 792 556168.6848 793 895004.7305 794 763577.259 795 1139171.879 796 537009.4297 797 496136.7458 798 1084853.621 799 1508869.709 800 1177171.708 801 623232.1433 802 561464.6409 803 1008918.744 804 1252043.562 805 747961.462 806 1838283.145 807 588249.0464 808 645222.8581 809 1220676.882 810 1527942.614 811 990240.0682 812 2688990.876 813 1129705.274 814 486527.7862 815 1188748.82 816 450175.4224 817 1301391.379 818 1108182.291 819 2037353.23 820 1445185.849 821 690139.0737 822 1342995.57 823 953983.722 824 1338188.638 825 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2891635.742 951 1001111.136 952 838171.6541 953 1647115.751 954 623043.3742 955 1062549.758 956 1054012.112 957 1291274.841 958 1561021.928 959 1651410.779 960 860988.8747 961 1002217.647 962 643335.1168 963 1041639.757 964 797486.368 965 852231.9686 966 842389.1072 967 1040629.784 968 601791.7156 969 789370.4706 970 1349570.559 971 627100.7709 972 1417912.638 973 3446086.568 974 887742.1208 975 773716.1707 976 2153143.364 977 1186236.767 978 1479286.658 979 846633.6205 980 1002811.897 981 849423.3916 982 1090694.266 983 958742.2427 984 1023873.352 985 2102643.053 986 1062463.448 987 659416.2673 988 664922.7953 989 1413854.509 990 1134120.551 991 1409603.034 992 976690.3445 993 723989.6796 994 1903395.875 995 1008171.165 996 989707.3081 997 1611405.328 998 662211.2375 999 1511585.713 1000 619692.009

Assignment 1

Due: Wednesday, 01.24.17 at 11:59 pm

In this assignment you will use a Monte Carlo simulation to investigate the effect of randomness in returns on an individual's future retirement wealth.

Saving for Retirement

Assume an investor begins saving for retirement at age 25 and retires at age 65. Each year, she contributes $5,000 to her retirement account and her employer matches this contribution for a total of $10,000 in annual savings. To keep things simple, assume that each of the 40 annual payments is added to the account at the end the year.^[1]Savings are invested as follows: 50% in a broad stock market index and 50% in T-Bills.

Your task is to compute the accumulated real retirement savings (at age 65) for different return realizations. As explained below, you will generate returns using a Monte Carlo simulation. On Blackboard, you will find an Excel file containing historical net returns on the S&P 500 and 3-month T-bills, as well as the net inflation rate from 1928 to 2013. The return on the CPI serves as a measure of inflation.

STEPS:

1.Compute the annual real return on the 50/50 portfolio for each year in the sample. Theresulting set of 86 portfolio returns represents the empirical distribution. These are the returns investors historically realized when investing in a 50/50 mix of stocks and T-bills over this time period.

2.We will use the historical data to assess what may happen in the future via a Monte Carlosimulation. To generate a possible path of future returns, draw 40 times with replacement from the empirical distribution.^[2][3]Assuming the historical returns are located in the cell range H11:H96, a random draw can be generated with

=INDEX(H11:H96,RANDBETWEEN(1,86))

The set of 40 draws you generated can be viewed as one scenario of what may happen in the next 40 years.

3.Using the simulated return path, compute the investor's wealth at age 65.

4.Repeat steps two and three 1,000 times. The most efficient way of doing so in Excel is to use a data table. An example is contained in the Excel file "Monte Carlo Simulation Example" on Blackboard.

QUESTIONS:

AReport the mean and standard deviation of the portfolio returns computed in step one.

BReport the mean, standard deviation, 25^th and 75^th percentiles, minimum, maximum as well as a histogram of the 1,000 values you generated for the wealth at age 65. Interpret each of these statistics, i.e. explain in words what they tell you in the context of the example.

CAssuming a 50/50 mix of both assets, what amount would the investor need to save annually such that her real retirement wealth at at least $1m with a probability of 75%? Assume that the employer matches the investor's contribution. [Hint: (1) To find this number, create an input cell for the annual savings (sum of the investor's and her employers contributions) and use trial-and-error to determine the required amount. (2) The number you find will only be approximate because of simulation noise - that is ok!.]

Assuming annual savings of $10,000 (including the employer's contribution), what mix of the two assets ensures that the investor's savings amount to $1.5m on average? How do the standard deviation and the minimum savings change in this case relative to the baseline scenario of a 50/50 mix?[Hint: (1) To find the necessary mix, create an input cell for the asset mix and use trial-and-error to determine the required amount. (2) The number you find will only be approximate because of simulation noise - that is ok!.]

[1] The first payment is added on the investor's 25-th birthday and first earns returns during "year 26". The last payment is added on the investor's 64-th birthday and first earns returns during "year 65". The investor retires on her 65-th birthday. Thus, there are 40 total returns and the final retirement wealth is determined on the investor's 65-th birthday.

[2] Recall that this procedure is valid under the assumption that returns are independently and identically distributed (i.i.d.). In other words, we assume that each of the return realizations computed in step one represents an equally likely draw from the same distribution of possible returns.

[3] /2