1. John Alejandro Bedoya Villegas
Estudiante de Ingeniería Administrativa
Universidad Nacional de Colombia sede Medellín
Marzo de 2011
Fecha COLCAP HelmBank (P) Ln(ri) COLCAP Ln(ri) HelmBank (P)
1/4/2010 1,374.28 444
1/5/2010 1,380.62 445 0.004603 0.002250
1/6/2010 1,381.35 440 0.000529 -0.011300
1/7/2010 1,368.91 440 -0.009046 0.000000
1/8/2010 1,374.72 440 0.004235 0.000000
1/12/2010 1,369.53 440 -0.003782 0.000000
1/13/2010 1,379.91 440 0.007551 0.000000
1/14/2010 1,386.91 440 0.005060 0.000000
1/15/2010 1,382.66 440 -0.003069 0.000000
1/18/2010 1,382.07 440 -0.000427 0.000000
1/19/2010 1,386.01 440 0.002847 0.000000
1/20/2010 1,381.80 440 -0.003042 0.000000
1/21/2010 1,355.28 438 -0.019379 -0.004556
1/22/2010 1,364.33 438 0.006655 0.000000
1/25/2010 1,345.21 438 -0.014113 0.000000
1/26/2010 1,357.80 438 0.009316 0.000000
1/27/2010 1,355.80 438 -0.001474 0.000000
1/28/2010 1,353.57 439 -0.001646 0.002281
1/29/2010 1,363.67 440 0.007434 0.002275
2/1/2010 1,358.49 440 -0.003806 0.000000
2/2/2010 1,363.85 440 0.003938 0.000000
2/3/2010 1,359.43 440 -0.003246 0.000000
2/4/2010 1,334.80 440 -0.018284 0.000000
2/5/2010 1,326.08 440 -0.006554 0.000000
2/8/2010 1,327.03 439 0.000716 -0.002275
2/9/2010 1,345.54 439 0.013852 0.000000
2/10/2010 1,353.70 440 0.006046 0.002275
2/11/2010 1,358.21 440 0.003326 0.000000
2/12/2010 1,355.84 445 -0.001746 0.011300
2/15/2010 1,357.59 442 0.001290 -0.006764
2/16/2010 1,364.53 442 0.005099 0.000000
2/17/2010 1,366.11 445 0.001157 0.006764
2/18/2010 1,359.64 440 -0.004747 -0.011300
2/19/2010 1,372.51 440 0.009421 0.000000
2/22/2010 1,372.84 440 0.000240 0.000000
2/23/2010 1,379.75 440 0.005021 0.000000
2/24/2010 1,398.47 441 0.013476 0.002270
2/25/2010 1,385.85 441 -0.009065 0.000000
2/26/2010 1,391.02 442 0.003724 0.002265
3/1/2010 1,392.91 442 0.001358 0.000000
3/2/2010 1,391.36 442 -0.001113 0.000000
3/3/2010 1,401.53 445 0.007283 0.006764
3/4/2010 1,398.81 445 -0.001943 0.000000
3/5/2010 1,399.63 441 0.000586 -0.009029
3/8/2010 1,408.35 445 0.006211 0.009029
3/9/2010 1,403.17 444 -0.003685 -0.002250
3/10/2010 1,403.82 441 0.000463 -0.006780
3/11/2010 1,405.26 438 0.001025 -0.006826

2. 3/12/2010 1,406.49 435 0.000875 -0.006873
3/15/2010 1,404.42 435 -0.001473 0.000000
3/16/2010 1,411.71 435 0.005177 0.000000
3/17/2010 1,429.40 436 0.012453 0.002296
3/18/2010 1,432.30 436 0.002027 0.000000
3/19/2010 1,414.10 438 -0.012788 0.004577
3/23/2010 1,426.74 438 0.008899 0.000000
3/24/2010 1,422.69 438 -0.002843 0.000000
3/25/2010 1,427.24 440 0.003193 0.004556
3/26/2010 1,423.02 435 -0.002961 -0.011429
3/29/2010 1,429.29 435 0.004396 0.000000
3/30/2010 1,430.71 435 0.000993 0.000000
3/31/2010 1,440.58 435 0.006875 0.000000
4/5/2010 1,450.93 435 0.007159 0.000000
4/6/2010 1,460.30 435 0.006437 0.000000
4/7/2010 1,472.19 435 0.008109 0.000000
4/8/2010 1,472.76 435 0.000387 0.000000
4/9/2010 1,468.95 439 -0.002590 0.009153
4/12/2010 1,470.70 438 0.001191 -0.002281
4/13/2010 1,470.91 438 0.000143 0.000000
4/14/2010 1,478.40 435 0.005079 -0.006873
4/15/2010 1,481.14 440 0.001852 0.011429
4/16/2010 1,463.27 440 -0.012138 0.000000
4/19/2010 1,453.14 442 -0.006947 0.004535
4/20/2010 1,467.76 442 0.010011 0.000000
4/21/2010 1,475.06 442 0.004961 0.000000
4/22/2010 1,478.51 435 0.002336 -0.015964
4/23/2010 1,488.05 436 0.006432 0.002296
4/26/2010 1,484.44 440 -0.002429 0.009132
4/27/2010 1,472.11 435 -0.008341 -0.011429
4/28/2010 1,457.28 442 -0.010125 0.015964
4/29/2010 1,469.22 440 0.008160 -0.004535
4/30/2010 1,467.26 440 -0.001335 0.000000
5/3/2010 1,490.16 440 0.015487 0.000000
5/4/2010 1,481.63 440 -0.005741 0.000000
5/5/2010 1,446.55 435 -0.023961 -0.011429
5/6/2010 1,403.06 435 -0.030526 0.000000
5/7/2010 1,412.80 435 0.006918 0.000000
5/10/2010 1,438.18 424 0.017805 -0.025613
5/11/2010 1,442.63 424 0.003089 0.000000
5/12/2010 1,451.06 434 0.005826 0.023311
5/13/2010 1,454.93 435 0.002663 0.002301
5/14/2010 1,444.27 434 -0.007354 -0.002301
5/18/2010 1,429.49 434 -0.010286 0.000000
5/19/2010 1,406.37 434 -0.016306 0.000000
5/20/2010 1,395.99 434 -0.007408 0.000000
5/21/2010 1,397.39 434 0.001002 0.000000
5/24/2010 1,410.93 438 0.009643 0.009174
5/25/2010 1,399.25 438 -0.008313 0.000000
5/26/2010 1,432.82 438 0.023708 0.000000
5/27/2010 1,428.47 437 -0.003041 -0.002286
5/28/2010 1,446.48 437 0.012529 0.000000
5/31/2010 1,444.54 441 -0.001342 0.009112
6/1/2010 1,447.26 441 0.001881 0.000000
6/2/2010 1,451.91 441 0.003208 0.000000

3. 6/3/2010 1,453.36 430 0.000998 -0.025260
6/4/2010 1,430.30 430 -0.015994 0.000000
6/8/2010 1,433.27 430 0.002074 0.000000
6/9/2010 1,445.53 430 0.008517 0.000000
6/10/2010 1,446.34 435 0.000560 0.011561
6/11/2010 1,448.08 434 0.001202 -0.002301
6/15/2010 1,450.71 430 0.001815 -0.009259
6/16/2010 1,461.39 429 0.007335 -0.002328
6/17/2010 1,460.56 429 -0.000568 0.000000
6/18/2010 1,472.41 420 0.008081 -0.021202
6/21/2010 1,466.78 425 -0.003831 0.011834
6/22/2010 1,467.67 420 0.000607 -0.011834
6/23/2010 1,471.95 420 0.002912 0.000000
6/24/2010 1,468.73 415 -0.002190 -0.011976
6/25/2010 1,475.04 420 0.004287 0.011976
6/28/2010 1,472.02 420 -0.002050 0.000000
6/29/2010 1,453.60 415 -0.012592 -0.011976
6/30/2010 1,466.78 425 0.009026 0.023811
7/1/2010 1,459.01 420 -0.005311 -0.011834
7/2/2010 1,455.04 420 -0.002725 0.000000
7/6/2010 1,463.82 420 0.006016 0.000000
7/7/2010 1,462.31 420 -0.001032 0.000000
7/8/2010 1,474.59 415 0.008363 -0.011976
7/9/2010 1,478.49 415 0.002641 0.000000
7/12/2010 1,496.79 415 0.012302 0.000000
7/13/2010 1,507.16 413 0.006904 -0.004831
7/14/2010 1,521.17 411 0.009253 -0.004854
7/15/2010 1,532.45 411 0.007388 0.000000
7/16/2010 1,526.67 411 -0.003779 0.000000
7/19/2010 1,528.75 408 0.001362 -0.007326
7/21/2010 1,565.50 413 0.023755 0.012180
7/22/2010 1,566.33 413 0.000530 0.000000
7/23/2010 1,569.86 410 0.002251 -0.007290
7/26/2010 1,596.49 410 0.016821 0.000000
7/27/2010 1,602.61 408 0.003826 -0.004890
7/28/2010 1,591.33 410 -0.007063 0.004890
7/29/2010 1,562.05 410 -0.018571 0.000000
7/30/2010 1,571.62 415 0.006108 0.012121
8/2/2010 1,575.01 410 0.002155 -0.012121
8/3/2010 1,586.92 414 0.007533 0.009709
8/4/2010 1,595.41 412 0.005336 -0.004843
8/5/2010 1,601.01 415 0.003504 0.007255
8/6/2010 1,580.41 410 -0.012950 -0.012121
8/9/2010 1,582.51 443 0.001328 0.077413
8/10/2010 1,577.34 464 -0.003272 0.046315
8/11/2010 1,558.12 456 -0.012260 -0.017392
8/12/2010 1,557.42 441 -0.000449 -0.033448
8/13/2010 1,567.78 447 0.006630 0.013514
8/17/2010 1,575.02 439 0.004607 -0.018059
8/18/2010 1,581.48 445 0.004093 0.013575
8/19/2010 1,586.73 442 0.003314 -0.006764
8/20/2010 1,585.60 448 -0.000712 0.013483
8/23/2010 1,606.82 441 0.013294 -0.015748
8/24/2010 1,605.58 454 -0.000772 0.029052
8/25/2010 1,602.95 454 -0.001639 0.000000

4. 8/26/2010 1,616.93 451 0.008684 -0.006630
8/27/2010 1,639.89 456 0.014100 0.011025
8/30/2010 1,642.91 459 0.001840 0.006557
8/31/2010 1,664.18 466 0.012863 0.015135
9/1/2010 1,713.81 480 0.029386 0.029600
9/2/2010 1,681.03 480 -0.019312 0.000000
9/3/2010 1,687.24 475 0.003687 -0.010471
9/6/2010 1,719.62 486 0.019009 0.022894
9/7/2010 1,715.27 487 -0.002533 0.002055
9/8/2010 1,735.68 504 0.011829 0.034312
9/9/2010 1,730.15 495 -0.003191 -0.018019
9/10/2010 1,699.91 500 -0.017633 0.010050
9/13/2010 1,695.47 507 -0.002615 0.013903
9/14/2010 1,703.11 502 0.004496 -0.009911
9/15/2010 1,693.44 499 -0.005694 -0.005994
9/16/2010 1,691.32 490 -0.001253 -0.018201
9/17/2010 1,691.24 485 -0.000047 -0.010257
9/20/2010 1,709.46 487 0.010716 0.004115
9/21/2010 1,716.15 494 0.003906 0.014271
9/22/2010 1,707.34 488 -0.005147 -0.012220
9/23/2010 1,693.47 480 -0.008157 -0.016529
9/24/2010 1,697.26 476 0.002236 -0.008368
9/27/2010 1,711.46 481 0.008332 0.010449
9/28/2010 1,744.84 477 0.019316 -0.008351
9/29/2010 1,766.22 489 0.012179 0.024846
9/30/2010 1,769.50 485 0.001855 -0.008214
10/1/2010 1,766.79 490 -0.001533 0.010257
10/4/2010 1,766.42 483 -0.000209 -0.014389
10/5/2010 1,794.73 495 0.015900 0.024541
10/6/2010 1,825.05 500 0.016753 0.010050
10/7/2010 1,808.89 499 -0.008894 -0.002002
10/8/2010 1,826.38 490 0.009622 -0.018201
10/11/2010 1,845.91 494 0.010637 0.008130
10/12/2010 1,842.54 495 -0.001827 0.002022
10/13/2010 1,873.50 500 0.016663 0.010050
10/14/2010 1,855.43 499 -0.009692 -0.002002
10/15/2010 1,833.59 494 -0.011841 -0.010071
10/19/2010 1,857.75 496 0.013090 0.004040
10/20/2010 1,860.52 498 0.001490 0.004024
10/21/2010 1,877.98 485 0.009341 -0.026451
10/22/2010 1,906.66 490 0.015156 0.010257
10/25/2010 1,900.10 489 -0.003447 -0.002043
10/26/2010 1,870.75 480 -0.015567 -0.018576
10/27/2010 1,862.84 475 -0.004237 -0.010471
10/28/2010 1,871.21 470 0.004483 -0.010582
10/29/2010 1,901.83 478 0.016231 0.016878
11/2/2010 1,913.88 475 0.006316 -0.006296
11/3/2010 1,923.28 484 0.004899 0.018770
11/4/2010 1,942.37 488 0.009877 0.008230
11/5/2010 1,940.38 480 -0.001025 -0.016529
11/8/2010 1,939.96 475 -0.000216 -0.010471
11/9/2010 1,938.49 468 -0.000758 -0.014847
11/10/2010 1,889.62 449 -0.025534 -0.041445
11/11/2010 1,841.69 440 -0.025692 -0.020248
11/12/2010 1,795.09 448 -0.025628 0.018019

5. 11/16/2010 1,729.16 435 -0.037419 -0.029447
11/17/2010 1,786.89 440 0.032841 0.011429
11/18/2010 1,814.13 440 0.015129 0.000000
11/19/2010 1,778.83 436 -0.019650 -0.009132
11/22/2010 1,775.45 428 -0.001902 -0.018519
11/23/2010 1,750.36 428 -0.014232 0.000000
11/24/2010 1,790.15 435 0.022478 0.016223
11/25/2010 1,784.80 435 -0.002993 0.000000
11/26/2010 1,770.59 432 -0.007994 -0.006920
11/29/2010 1,762.11 427 -0.004801 -0.011642
11/30/2010 1,779.94 430 0.010068 0.007001
12/1/2010 1,793.55 427 0.007617 -0.007001
12/2/2010 1,825.55 438 0.017684 0.025435
12/3/2010 1,830.26 440 0.002577 0.004556
12/6/2010 1,841.85 440 0.006312 0.000000
12/7/2010 1,837.18 440 -0.002539 0.000000
12/9/2010 1,826.70 440 -0.005721 0.000000
12/10/2010 1,830.86 440 0.002275 0.000000
12/13/2010 1,841.24 436 0.005653 -0.009132
12/14/2010 1,845.71 442 0.002425 0.013668
12/15/2010 1,823.61 447 -0.012046 0.011249
12/16/2010 1,826.74 455 0.001715 0.017739
12/17/2010 1,823.10 461 -0.001995 0.013101
12/20/2010 1,815.55 458 -0.004150 -0.006529
12/21/2010 1,824.82 455 0.005093 -0.006572
12/22/2010 1,839.59 465 0.008061 0.021740
12/23/2010 1,846.50 470 0.003749 0.010695
12/24/2010 1,853.24 465 0.003644 -0.010695
12/27/2010 1,866.12 464 0.006926 -0.002153
12/28/2010 1,849.51 458 -0.008941 -0.013015
12/29/2010 1,839.72 457 -0.005307 -0.002186
12/30/2010 1,823.70 458 -0.008746 0.002186
1/3/2011 1,803.00 458 -0.011415 0.000000
1/4/2011 1,810.27 451 0.004024 -0.015402
1/5/2011 1,790.57 445 -0.010942 -0.013393
1/6/2011 1,766.77 445 -0.013381 0.000000
1/7/2011 1,781.71 450 0.008421 0.011173
1/11/2011 1,763.08 450 -0.010511 0.000000
1/12/2011 1,784.10 445 0.011852 -0.011173
1/13/2011 1,801.86 443 0.009905 -0.004505
1/14/2011 1,796.05 450 -0.003230 0.015678
1/17/2011 1,801.66 445 0.003119 -0.011173
1/18/2011 1,790.41 446 -0.006264 0.002245
1/19/2011 1,766.21 444 -0.013609 -0.004494
1/20/2011 1,741.61 435 -0.014026 -0.020479
1/21/2011 1,756.48 435 0.008502 0.000000
1/24/2011 1,759.99 437 0.001996 0.004587
1/25/2011 1,754.92 437 -0.002885 0.000000
1/26/2011 1,771.55 440 0.009432 0.006842
1/27/2011 1,773.04 453 0.000841 0.029117
1/28/2011 1,768.13 446 -0.002773 -0.015573
1/31/2011 1,762.43 446 -0.003229 0.000000
2/1/2011 1,759.61 446 -0.001601 0.000000
2/2/2011 1,745.24 450 -0.008200 0.008929
2/3/2011 1,735.96 448 -0.005332 -0.004454

6. 2/4/2011 1,709.06 440 -0.015617 -0.018019
2/7/2011 1,691.87 440 -0.010109 0.000000
2/8/2011 1,710.54 430 0.010975 -0.022990
2/9/2011 1,696.85 427 -0.008036 -0.007001
2/10/2011 1,687.92 425 -0.005277 -0.004695
2/11/2011 1,694.51 417 0.003897 -0.019003
2/14/2011 1,701.65 415 0.004205 -0.004808
2/15/2011 1,692.43 415 -0.005433 0.000000
2/16/2011 1,689.95 411 -0.001466 -0.009685
2/17/2011 1,666.93 408 -0.013715 -0.007326
2/18/2011 1,644.66 406 -0.013450 -0.004914
2/21/2011 1,658.33 422 0.008277 0.038652
2/22/2011 1,661.43 421 0.001868 -0.002372
2/23/2011 1,698.63 418 0.022143 -0.007151
2/24/2011 1,699.17 420 0.000318 0.004773
2/25/2011 1,713.40 420 0.008340 0.000000
2/28/2011 1,750.97 416 0.021690 -0.009569

7. dministrativa
olombia sede Medellín
285
Indice-Accion Media Varianza Desv. Estandar
(1) COLCAP 0.00085 0.000095 0.009737
(2) HelmBank (P) -0.00023 0.000149 0.012202
Matriz de Covarianza
Ln(ri) COLCAP Ln(ri) HelmBank (P)
(1) Ln(ri) COLCAP 0 0
(2) Ln(ri) HelmBank (P) 0 0
Matriz de Correlacion
Ln(ri) COLCAP Ln(ri) HelmBank (P)
(1) Ln(ri) COLCAP 1 0.26
(2) Ln(ri) HelmBank (P) 0.26 1
Datos tomados de
http://www.grupoaval.com/portal/page?_pageid=33,54994&_dad=portal&_schema=PORTAL
Resultados
W* Optimo
W* = (W1) (1-W*) = (W2)
Ecuacion 10 0.649 0.351
Ecuacion 12 0.649 0.351
Varianza y volatilidad optima del portafolio
Varianza Volatilidad
Ecuacion 13 - 17 7.3E-05 8.5E-03
Ecuacion 13 - 17 7.3E-05 8.5E-03
Rendimiento medio del Portafolio
Up
Ecuacion 16 0.000473
Variasiones w no optimos Rentabilidad
W1 W2 esperada
1 0 0.00085
0.9 0.1 0.00074
0.8 0.2 0.00064
0.7 0.3 0.00053
0.6 0.4 0.00042
0.5 0.5 0.00031
0.4 0.6 0.00020
0.3 0.7 0.00010
0.2 0.8 -0.00001
0.1 0.9 -0.00012
0 1 -0.00023
Puntos optimos 0.000473

8. Combinacion portafolios
Portafolio optimo
Frontera de portafolios
0.001000
0.00085
0.000800
0.00074
0.00064 Combinacion porta
0.000600
0.00053
0.000473
0.000400 0.00042
0.00031
Rentabilidad
0.000200 0.00020
media
0.00010
0.000000 -0.00001
-0.0
-0.000200
-0.000400
reduccion0.00700 0.00800 0.13 0.00900 Volatilidad
0.01000 0.01100

13. &_schema=PORTAL
Desviación
estandar
0.00974
0.00916
0.00875
0.00854
0.00854
0.00875
0.00915
0.00973
0.01044
0.01128
0.01220
0.00852

14. de portafolios
Combinacion portafolios Portafolio optimo
-0.00001
-0.00012
-0.00023
0 0.01100 0.01200 0.01300 0.01400