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W1 W2 W3 Portfolio S Expected Return
-0.4482 0.5702 0.8780 0.314 0.50
-0.3474 0.5194 0.8280 0.285 0.48
-0.2467 0.4687 0.7780 0.259 0.46
-0.1459 0.4179 0.7280 0.236 0.44
-0.0452 0.3672 0.6780 0.219 0.42
0.0556 0.3164 0.6280 0.207 0.400.1563 0.2657 0.5780 0.203 0.38
0.2571 0.2149 0.5280 0.206 0.36
0.3578 0.1641 0.4780 0.216 0.34
0.4586 0.1134 0.4280 0.233 0.32
0.5593 0.0626 0.3780 0.254 0.30
0.6601 0.0119 0.3280 0.280 0.28
0.7608 -0.0389 0.2780 0.308 0.26
0.8616 -0.0896 0.2281 0.339 0.24
0.9623 -0.1404 0.1781 0.371 0.22
0.0631 -0.1911 0.1281 0.405 0.20
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.000 0.050 0.100 0.150
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Microsoft Excel 12.0 Answer Report
Worksheet: [Markov's Trilemma - TN.xlsx]Sheet1
Report Created: 11/27/2008 4:06:48 PM
Target Cell (Max)
Cell Name Original Value Final Value$E$79 AOL Weight 10% 100%
Adjustable Cells
Cell Name Original Value Final Value
$E$78 INTC Weight 10% 0%
$E$79 AOL Weight 10% 100%
$E$80 IBM Weight 10% 0%
$E$81 GM Weight 10% 0%
$E$82 AA Weight 10% 0%
$E$83 GE Weight 10% 0%
$E$84 IP Weight 20% 0%
$E$85 MRK Weight 20% 0%
Constraints
Cell Name Cell Value Formula Status Slack
$E$86 Weight 100% $E$86=1 Not Binding 0
$E$78 INTC Weight 0% $E$78>=0 Binding 0%
$E$79 AOL Weight 100% $E$79>=0 Not Binding 100%
$E$80 IBM Weight 0% $E$80>=0 Binding 0%$E$81 GM Weight 0% $E$81>=0 Binding 0%
$E$82 AA Weight 0% $E$82>=0 Binding 0%
$E$83 GE Weight 0% $E$83>=0 Binding 0%
$E$84 IP Weight 0% $E$84>=0 Binding 0%
$E$85 MRK Weight 0% $E$85>=0 Binding 0%
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Microsoft Excel 12.0 Sensitivity Report
Worksheet: [Markov's Trilemma - TN.xlsx]Sheet1
Report Created: 11/27/2008 4:06:48 PM
Adjustable Cells
Final ReducedCell Name Value Gradient
$E$78 INTC Weight 0% -100%
$E$79 AOL Weight 100% 0%
$E$80 IBM Weight 0% -100%
$E$81 GM Weight 0% -100%
$E$82 AA Weight 0% -100%
$E$83 GE Weight 0% -100%
$E$84 IP Weight 0% -100%
$E$85 MRK Weight 0% -100%
Constraints
Final Lagrange
Cell Name Value Multiplier
$E$86 Weight 100% 100%
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Microsoft Excel 12.0 Limits Report
Worksheet: [Markov's Trilemma - TN.xlsx]Limits Report 1
Report Created: 11/27/2008 4:06:49 PM
Target
Cell Name Value$E$79 AOL Weight 100%
Adjustable Lower Target Upper Target
Cell Name Value Limit Result Limit Result
$E$78 INTC Weight 0% 0% 100% 0% 100%
$E$79 AOL Weight 100% 100% 100% 100% 100%
$E$80 IBM Weight 0% 0% 100% 0% 100%
$E$81 GM Weight 0% 0% 100% 0% 100%
$E$82 AA Weight 0% 0% 100% 0% 100%
$E$83 GE Weight 0% 0% 100% 0% 100%
$E$84 IP Weight 0% 0% 100% 0% 100%
$E$85 MRK Weight 0% 0% 100% 0% 100%
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INTC AOL IBM GM AA GE IP MRK INTC AOL IBM
Dec-97 35.05 5.66 51.99 47.51 34.15 71.46 41.38 51.40
Jan-98 40.41 5.98 49.07 45.31 37.06 75.47 43.84 56.91 15.29% 0.05654 -0.056
Feb-98 44.75 7.59 51.89 54.34 35.78 75.72 44.97 61.85 10.74% 0.26923 0.0575
Mar-98 38.95 8.54 51.61 53.40 33.56 84.27 45.21 62.38 -12.96% 0.12516 -0.005
Apr-98 40.32 9.99 57.58 53.11 37.79 83.29 50.34 58.63 3.52% 0.16979 0.1157
May-98 35.64 10.41 58.38 57.06 33.94 81.52 44.58 56.93 -11.61% 0.04204 0.0139
Jun-98 36.98 13.14 57.05 53.04 32.26 88.85 41.68 65.34 3.76% 0.26225 -0.023
Jul-98 42.13 14.64 65.84 57.40 33.91 87.73 43.25 60.36 13.93% 0.11416 0.1541
Aug-98 35.52 10.24 55.96 46.47 29.41 78.47 36.07 56.64 -15.69% -0.3005 -0.15Sep-98 42.78 13.95 63.85 43.87 34.87 78.33 45.45 63.57 20.44% 0.3623 0.141
Oct-98 44.50 15.92 73.79 50.51 38.92 86.14 45.27 66.27 4.02% 0.14122 0.1557
Nov-98 53.72 21.89 82.17 56.28 36.58 88.97 42.58 76.12 20.72% 0.375 0.1136
Dec-98 59.18 38.78 91.75 57.64 36.74 100.77 43.93 72.62 10.16% 0.77159 0.1166
5.19% 19.91% 5.28%
RETURNS 68.8% 585.6% 76.5% 21.3% 7.6% 41.0% 6.2% 41.3%Sd 12.65% 25.33% 9.72%
AnnualisedSD 0.438349848 0.87745 0.3368
GeometricMean 0.688445078 5.85159 0.7648
Correlation
INTC AOL IBM GM AA GE IP MRK
SD 0.4383 0.87744539 0.3368 0.3762 0.3487 0.24 0.382750252 0.301336048
INTC 0.43835 1.00 0.59 0.61 0.36 0.60 0.20 0.62 0.52
AOL 0.87745 0.59 1.00 0.62 0.36 0.27 0.64 0.43 0.25
IBM 0.33682 0.61 0.62 1.00 0.65 0.62 0.29 0.58 0.00
GM 0.37623 0.36 0.36 0.65 1.00 0.10 0.26 0.07 0.12
AA 0.34873 0.60 0.27 0.62 0.10 1.00 0.17 0.88 0.13
GE 0.24 0.20 0.64 0.29 0.26 0.17 1.00 0.16 0.30
IP 0.38275 0.62 0.43 0.58 0.07 0.88 0.16 1.00 0.19
MRK 0.30134 0.52 0.25 0.00 0.12 0.13 0.30 0.19 1
Covarinace Matrix INTC AOL IBM GM AA GE IP MRK
INTC 0.1922 0.22596566 0.0899 0.0586 0.0913 0.0207 0.103330696 0.068734565
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AOL 0.226 0.76991041 0.1833 0.1201 0.0836 0.1339 0.145741408 0.06592451
IBM 0.0899 0.18333833 0.1134 0.082 0.0729 0.0233 0.074472563 0.000494603
GM 0.0586 0.12009992 0.082 0.1415 0.0138 0.0233 0.009369196 0.013539101
AA 0.0913 0.08363793 0.0729 0.0138 0.1216 0.0143 0.116927916 0.013416477
GE 0.0207 0.13386423 0.0233 0.0233 0.0143 0.0576 0.015097232 0.021747476
IP 0.1033 0.14574141 0.0745 0.0094 0.1169 0.0151 0.146497755 0.022041715
MRK 0.0687 0.06592451 0.0005 0.0135 0.0134 0.0217 0.022041715 0.090803414
Weight_Covariance ###### 232764147% ###### ###### ###### ###### -368386787% 254890915%INTC AOL IBM GM AA GE IP MRK
########## INTC 1E+12 -1.4633E+12 3E+11 -9E+10 -1E+12 2E+11 1.05906E+12 -4.87435E+11 -4E+11
########## AOL -1E+12 4.1713E+12 -5E+11 2E+11 1E+12 -1E+12 -1.24969E+12 3.91127E+11 1.6E+12
########## IBM 3E+11 -4.552E+11 1E+11 -5E+10 -4E+11 9E+10 2.92637E+11 -1344745858 -2E+11
56833004% GM -9E+10 1.5888E+11 -5E+10 5E+10 4E+10 -5E+10 -19615843028 19613035369 6E+10
########## AA -1E+12 1.082E+12 -4E+11 4E+10 4E+12 -3E+11 -2.39409E+12 1.90069E+11 5.6E+11
########## GE 2E+11 -1.0813E+12 9E+10 -5E+10 -3E+11 7E+11 1.92996E+11 -1.92358E+11 -4E+11
########## IP 1E+12 -1.2497E+12 3E+11 -2E+10 -2E+12 2E+11 1.9881E+12 -2.06968E+11 -3E+11
########## MRK -5E+11 3.9113E+11 -1E+09 2E+10 2E+11 -2E+11 -2.06968E+11 5.89944E+11 3E+11
SUM ###### ########### ###### ###### ###### ###### ############# ############## #######
Variance #######
SD 1052936
INTC AOL IBM GM AA GE IP MRK
15.29% 0.0565 -0.05616465 -0.0463 0.0852 0.0561 0.0594 0.107198444
10.74% 0.2692 0.05746892 0.1993 -0.0345 0.0033 0.0258 0.086803725
-12.96% 0.1252 -0.00539603 -0.0173 -0.062 0.1129 0.0053 0.008569119
3.52% 0.1698 0.11567526 -0.0054 0.126 -0.0116 0.1135 -0.060115422
-11.61% 0.042 0.01389371 0.0744 -0.1019 -0.0213 -0.1144 -0.028995395
3.76% 0.2622 -0.02278177 -0.0705 -0.0495 0.0899 -0.0651 0.147725277
13.93% 0.1142 0.15407537 0.0822 0.0511 -0.0126 0.0377 -0.076216713
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-15.69% -0.3005 -0.15006075 -0.1904 -0.1327 -0.1056 -0.166 -0.061630219
20.44% 0.3623 0.14099357 -0.056 0.1857 -0.0018 0.26 0.122351695
4.02% 0.1412 0.15567737 0.1514 0.1161 0.0997 -0.004 0.042472865
20.72% 0.375 0.11356552 0.1142 -0.0601 0.0329 -0.0594 0.148634375
10.16% 0.7716 0.11658756 0.0242 0.0044 0.1326 0.0317 -0.045980032
Return 68.8% 585.6% 76.5% 21.3% 7.6% 41.0% 6.2% 41.3%
Portfolio Return Sd Weight WxR Weight 12% 15%INTC 68.8% 2.3833 ########### -2E+06 Implied Return 0.10976 0.2319
AOL 585.6% 20.286 232764147% 1E+07 0.19215 0.226
IBM 76.5% 2.65 ########### -816000 0.22597 0.7699
GM 21.3% 0.7379 56833004% 121054 0.08993 0.1833
AA 7.6% 0.2633 555798702% 422407 0.05858 0.1201
GE 41.0% 1.4203 ########### -1E+06 0.09128 0.0836
IP 6.2% 0.2148 ########### -228400 0.02075 0.1339
MRK 41.3% 1.4307 254890915% 1E+06 0.10333 0.1457
1 0.06873 0.0659
Portfolio Return 1E+07
PortfolioSD 1E+06
Return/Risk 10.3
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GM AA GE IP MRK INTC AOL IBM
0.000% 100.000% 0.000%
-0.04631 0.0852 0.0561 0.0594 0.1072 5.7%
0.199294 -0.035 0.0033 0.0258 0.0868 26.9%
-0.0173 -0.062 0.1129 0.0053 0.0086 12.5%
-0.00543 0.126 -0.012 0.1135 -0.06 17.0%
0.074374 -0.102 -0.021 -0.114 -0.029 4.2%
-0.07045 -0.049 0.0899 -0.065 0.1477 26.2%
0.082202 0.0511 -0.013 0.0377 -0.076 11.4%
-0.19042 -0.133 -0.106 -0.166 -0.062 -30.1%-0.05595 0.1857 -0.002 0.26 0.1224 36.2%
0.151356 0.1161 0.0997 -0.004 0.0425 14.1%
0.114235 -0.06 0.0329 -0.059 0.1486 37.5%
0.024165 0.0044 0.1326 0.0317 -0.046 77.2%
2.16% 1.06% 3.12% 1.04% 3.26% 19.91%
10.86% 10.07% 6.93% 11.05% 8.70% 25.33%
0.376227 0.3487 0.24 0.3828 0.3013 0.877445
0.213218 0.0758 0.4102 0.0616 0.4128 585.159%
6.589116757
0.016013 0.0188 0.0075 0.0049 0.0076 0.001729156 0.008610891 0.00572788
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0.01883 0.0642 0.0153 0.01 0.007 0.011155353 0.012145117 0.005493709
0.007494 0.0153 0.0095 0.0068 0.0061 0.001938491 0.006206047 4.1217E-05
0.004882 0.01 0.0068 0.0118 0.0011 0.001941645 0.000780766 0.001128258
0.007606 0.007 0.0061 0.0011 0.0101 0.00119427 0.009743993 0.00111804
0.001729 0.0112 0.0019 0.0019 0.0012 0.004800047 0.001258103 0.00181229
0.008611 0.0121 0.0062 0.0008 0.0097 0.001258103 0.012208146 0.00183681
0.005728 0.0055 4E-05 0.0011 0.0011 0.00181229 0.00183681 0.007566951
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12% 12% 12% 12% 12% 12%0.082934 0.0596 0.0665 0.0415 0.0811 0.037911641 1
0.089932 0.0586 0.0913 0.0207 0.1033 0.068734565
0.183338 0.1201 0.0836 0.1339 0.1457 0.06592451
0.113448 0.082 0.0729 0.0233 0.0745 0.000494603
0.081979 0.1415 0.0138 0.0233 0.0094 0.013539101
0.07292 0.0138 0.1216 0.0143 0.1169 0.013416477
0.023262 0.0233 0.0143 0.0576 0.0151 0.021747476
0.074473 0.0094 0.1169 0.0151 0.1465 0.022041715
0.000495 0.0135 0.0134 0.0217 0.022 0.090803414
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Demonstration of the Portfolio Standard Deviation Calculation RiskFreeRa 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.688Esd3 0.438
W1 -0.05704 W2 0.431444 W3 0.625601 1.00000
Expected Return 0.596449
Correlation12 0.12
Correlation23 0.52
Correlation13 0.35
Covar_12_23_13 0.0136 0.0686 0.0576
Portfolio SD 0.353
Sharpe Ratio 1.491
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Demonstration of the Portfolio Standard Deviation C RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.3
W1 0.023592 W2 0.492837 W3 0.48357 1.00000
Expected 0.406831
Correlatio 0.12
Correlatio 0.3
Correlatio 0.26
Covar_12_ 0.0136 0.0271 0.0293
Portfolio S 0.239
Sharpe Rat 1.410
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Demonstration of the Portfolio Standard Deviation C RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.3Esd3 0.24
W1 0.052848 W2 0.493583 W3 0.453568 1.00000
Expected 0.351177
Correlatio 0.12
Correlatio 0.3
Correlatio 0.26
Covar_12_ 0.0136 0.0217 0.0235
Portfolio S 0.214
Sharpe Rat 1.313
0.141376
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Demonstration of the Portfolio Standard Deviation C RiskFreeR 0.05
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0.003085 W2 0.345454 W3 0.65146 1.00000
Expected 0.410428
Correlatio 0.12
Correlatio 0.3
Correlatio 0.26
Covar_12_ 0.0136 0.0217 0.0235
Portfolio S 0.212
Sharpe Rat 1.696
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Demonstration of the Portfolio Standard Deviation Calcul RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0.359557 W2 0 W3 0.640442 1.00000
Expected Retur 0.339167
Correlation12 0.12
Correlation23 0.30
Correlation13 -0.8
Covar_12_23_1 0.0136 0.0217 -0.0722
Portfolio SD 0.093
Sharpe Ratio 2.893
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Demonstration of the Portfolio Standard Deviation C RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0 W2 0.346437 W3 0.653562 1.00000
Expected 0.411039
Correlatio 0.12
Correlatio 0.30
Correlatio 0.8
Covar_12_ 0.0136 0.0217 0.0722
Portfolio S 0.213
Sharpe Rat 1.602
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Demonstration of the Portfolio Standard Deviation C RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0.052357 W2 0.447643 W3 0.5 1.00000
Expected 0.401029
Correlatio 0.12
Correlatio 0.3
Correlatio 0.26
Covar_12_ 0.0136 0.0217 0.0235
Portfolio S 0.211
Sharpe Rat 1.569
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Demonstration of the Portfolio Standard Deviation C RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0 W2 0.346437 W3 0.653562 1.00000
Expected 0.411039
Correlatio 0.12
Correlatio 0.3
Correlatio 0.26
Covar_12_ 0.0136 0.0217 0.0235
Portfolio S 0.213
Sharpe Rat 1.602
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Demonstration of the Portfolio Standard Deviation Calculation RiskFreeRa 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0.408901789 W2 -0.13116 W3 0.722254 1.00000
Expected Return 0.329052881
Correlation12 0.12
Correlation23 0.3
Correlation13 -0.8
Covar_12_23_1 0.0136 0.0217 -0.0722
Portfolio SD 0.084
Sharpe Ratio 3.087
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Demonstration of the Portfolio Standard Deviation Calcula RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0.541535 W2 0 W3 0.458464 1.00000
Expected Return 0.303317
Correlation12 0.12
Correlation23 0.30
Correlation13 -0.8
Covar_12_23_13 0.0136 0.0217 -0.0722
Portfolio SD 0.000
Sharpe Ratio 1240.111
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Demonstration of the Portfolio Standard Deviation Calculation RiskFreeR 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 -0.61359992 W2 0.213351 W3 1.400249 1.00000
Expected Return 0.53151924
Correlation12 0.12
Correlation23 0.3
Correlation13 0.8
Covar_12_23_13 0.0136 0.0217 0.0722
Portfolio SD 0.236
Sharpe Ratio 1.957
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Demonstration of the Portfolio Standard Deviation Calculation RiskFreeRa 0.07
equal risk return - changing correlation
Er1 0.213
Esd1 0.376
Er2 0.413
Esd2 0.301
Er3 0.41Esd3 0.24
W1 0 W2 1 W3 0 1.00000
Expected Return 0.413
Correlation12 0.12
Correlation23 0.3
Correlation13 0.8
Covar_12_23_13 0.0136 0.0217 0.0722
Portfolio SD 0.232
Sharpe Ratio 1.479
When shorting is not allowed
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3 Asset Allocation Model
Expecte
d Standard Sharpe
Return Deviation Ratios GM MRK GE
GM 33.0% 21.3% 37.6% 0.38 1.00 0.12 0.26
MRK 34.0% 41.3% 30.1% 1.14 0.12 1.00 0.30GE 33.0% 41.0% 24.0% 1.42 0.26 0.30 1.00
100.0%
7% Risk-free rate
34.6% Expected Return
21.3% Expected standard deviation
1.30 Sharpe Ratio
Asset
Weighting
Correlation Coefficient with:
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Demonstration of the Portfolio Standard Deviation Calculation RiskFreeR 0.07
equal risk return - changing correlation
GM 0.213
Esd1 0.376 0.566489
MRK 0.413
Esd2 0.301 1.372093
GE 0.41Esd3 0.24 1.708333
GM 0.33 MRK 0.33 GE 0.34 1.00000
Expected Return 0.34598
Correlation12 0.12
Correlation23 0.30
Correlation13 0.26
Covar_12_23_13 0.0136 0.0217 0.0235
Portfolio SD 0.21215
Sharpe Ratio 1.301
Maximising Sharpe RatioDemonstration of the Portfolio Standard Deviation Calculation RiskFreeR 0.07 10
equal risk return - changing correlation 20
Er1 0.213 10
Esd1 0.376 0.566489 20
Er2 0.413 10
Esd2 0.301 1.372093 20
Er3 0.41 10
Esd3 0.24 1.708333 -1
W1 0.04 W2 0.348443 W3 0.659561 1.04800
Expected Return 0.422847088 -10
Correlation12 0.12 10Correlation23 0.30 -10
Correlation13 0.26 10
Covar_12_23_13 0.0136 0.0217 0.0235 -10
Portfolio SD 0.219 10
Sharpe Ratio 1.613 -10
10
-10
-1
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20
10
20
10
20
10
20
10
-1010
-10
10
-10
10
-10
10