Activos:
Activo A:
AMZN
Inicial:
2019-03-25
Final:
2024-03-22
Anual
r:
19.7552 %
D.E. σ:
35.1125 %
Var. σ2:
0.1233
Activo B:
AAPL
Inicial:
2019-03-25
Final:
2024-03-22
Anual
r:
31.2365 %
D.E. σ:
31.7232 %
Var. σ2:
0.1006
Activo C:
BAC
Inicial:
2019-03-25
Final:
2024-03-22
Anual
r:
12.2377 %
D.E. σ:
35.6448 %
Var. σ2:
0.1271
Activo D:
CCL
Inicial:
2019-03-25
Final:
2024-03-22
Anual
r:
2.0883 %
D.E. σ:
73.1965 %
Var. σ2:
0.5358
Activo E:
GMEXICOB.MX
Inicial:
2019-03-25
Final:
2024-03-22
Anual
r:
20.4727 %
D.E. σ:
38.5020 %
Var. σ2:
0.1482
CovAB :
0.000271
CovAC :
0.000147
CovAD :
0.000292
CovAE :
0.000031
CovBC :
0.000200
CovBD :
0.000325
CovBE :
0.000043
CovCD :
0.000592
CovCE :
0.000049
CovDE :
0.000044
F = X12 σ12 + X22 σ22 + X32 σ32 + X42 σ42 + X52 σ52 + 2X1X2 σ12 + 2X2X3 σ23 + 2X3X4 σ34 + 2X4X5 σ45 + 2X5X1 σ51 + λ1 ( XE1 + XE2 + XE3 + XE4 + XE5 - Ep ) + λ2 ( X1 + X2 + X3 + X4 + X5 - 1 )
σ12 σ12 σ13 σ14 σ15 E1 1
σ21 σ22 σ23 σ24 σ25 E2 1
σ31 σ32 σ32 σ34 σ35 E3 1
σ41 σ42 σ43 σ42 σ45 E4 1
σ51 σ52 σ53 σ54 σ52 E5 1
E 1 E 2 E 3 E 4 E 5 0 0
1 1 1 1 1 0 0
X 1
X 2
X 3
X 4
X 5
λ1 /2
λ2 /2
=
0
0
0
0
0
Ep
1
0.123289
0.000271
0.000147
0.000292
0.000031
19.755234
1.000000
0.000271
0.100636
0.000200
0.000325
0.000043
31.236476
1.000000
0.000147
0.000200
0.127055
0.000592
0.000049
12.237723
1.000000
0.000292
0.000325
0.000592
0.535773
0.000044
2.088268
1.000000
0.000031
0.000043
0.000049
0.000044
0.148241
20.472670
1.000000
19.755234
31.236476
12.237723
2.088268
20.472670
0.000000
0.000000
1.000000
1.000000
1.000000
1.000000
1.000000
0.000000
0.000000
X 1
X 2
X 3
X 4
X 5
λ1 /2
λ2 /2
=
0
0
0
0
0
Ep
1
CX = B => X = C-1 B
Matriz inversa:
| 6.1975 | -2.0500 | -2.0293 | -0.5331 | -1.5851 | -0.0028 | 0.2915 |
| -2.0500 | 2.2008 | 0.7282 | 1.0424 | -1.9214 | 0.0459 | -0.6548 |
| -2.0293 | 0.7282 | 4.2486 | -1.3975 | -1.5500 | -0.0281 | 0.8054 |
| -0.5331 | 1.0424 | -1.3975 | 1.2571 | -0.3688 | -0.0148 | 0.3581 |
| -1.5851 | -1.9214 | -1.5500 | -0.3688 | 5.4253 | -0.0002 | 0.1998 |
| -0.0028 | 0.0459 | -0.0281 | -0.0148 | -0.0002 | -0.0004 | 0.0088 |
| 0.2915 | -0.6548 | 0.8054 | 0.3581 | 0.1998 | 0.0088 | -0.2107 |
Resultados (Pesos de X):
X1 =-0.0028 Ep + 0.2915
X2 =0.0459 Ep + -0.6548
X3 =-0.0281 Ep + 0.8054
X4 =-0.0148 Ep + 0.3581
X5 =-0.0002 Ep + 0.1998
X1 =-0.0028 Ep + 0.2915
X2 =0.0459 Ep + -0.6548
X3 =-0.0281 Ep + 0.8054
X4 =-0.0148 Ep + 0.3581
X5 =-0.0002 Ep + 0.1998
min F = X12 σ12 + X22 σ22 + X32 σ32 + X42 σ42 + X52 σ52 + X62 σ62 + 2X1X2 σ12 + 2X2X3 σ23 + 2X3X4 σ34 + 2X4X5 σ45 + 2X5X6 σ56 + 2X6X1 σ61 + λ ( X1 + X2 + X3 + X4 + X5 + X6 - 1 )
σ12 σ12 σ13 σ14 σ15 σ16 1
σ21 σ22 σ23 σ24 σ25 σ26 1
σ31 σ32 σ32 σ34 σ35 σ36 1
σ41 σ42 σ43 σ42 σ45 σ46 1
σ51 σ52 σ53 σ54 σ52 σ56 1
σ61 σ62 σ63 σ64 σ65 σ62 1
1 1 1 1 1 1 0
X 1
X 2
X 3
X 4
X 5
X 6
λ/2
=
0
0
0
0
0
0
1
Matriz inversa:
| 6.2152 | -2.3443 | -1.8490 | -0.4381 | -1.5839 | 0.2348 |
| -2.3443 | 7.0918 | -2.2692 | -0.5373 | -1.9411 | 0.2877 |
| -1.8490 | -2.2692 | 6.0856 | -0.4295 | -1.5379 | 0.2279 |
| -0.4381 | -0.5373 | -0.4295 | 1.7673 | -0.3625 | 0.0537 |
| -1.5839 | -1.9411 | -1.5379 | -0.3625 | 5.4254 | 0.1960 |
| 0.2348 | 0.2877 | 0.2279 | 0.0537 | 0.1960 | -0.0291 |
Resultados (Pesos de X):
X1 = 23.48
X2 = 28.77
X3 = 22.79
X4 = 5.37
X5 = 19.6
λ6 = -2.91
X1 = 23.48
X2 = 28.77
X3 = 22.79
X4 = 5.37
X5 = 19.6
λ6 = -2.91
Valores eficientes
Ep = 2,053.90%
σp = 17.0587%
σp2 = 2.9100