18 099 305 181 178 094 144 049 090 225 239 150 031

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1.18% 0.99% -3.05% -1.81% 1.78% 0.94% 1.44% 0.49% 0.90% 2.25% -2.39% -1.50% 0.31% 7.96% -1.21% -1.02% -3.47% -0.41% 3.56% 1.60% 1.32% 2.00% -1.03% -0.64% 3.69% 0.30% -0.98% 4.57% 1.44% -0.85% -4.45% -1.00% -0.70% 1.73% 0.97% 0.60% 0.71% -1.71% -1.52% 2.65% 2.24% 6.75% 5.57% 0.16% -0.16% -0.72% -0.99% 0.85% 2.18% 1.71% 0.16% 1.43% 5.24% 2.62% -1.08% 6.14% 0.10% -2.45% 1.25% 1.16% -0.56% -1.13% -1.22% 1.73% 0.37% 2.18% 3.30% 9.96% 6.62% 14.83% 2.40% 3.21% 5.64% 5.37% -0.04% 0.74% 2.00% -2.59% 2.26% -0.46% 1.82% 0.06% 0.95% 1.69% -3.00% 1.45% 3.23% -0.10% 1.58% 1.57% -0.73% 0.54% 6.00% 3.60% 1.07% 5.86% -6.92% 0.69% 5.93% 3.79% -6.97% 2.23% 5.16% 2.24% -2.72% -3.96% -2.79% -3.16% -3.53% 1.54% 9.57% -0.26% 1.81% -0.53% -3.83% -2.79% 10.68% -4.27% -2.67% -1.80% 2.51% -1.76% -2.31% -3.22% 2.37% 0.85% 4.77% -2.53% 2.86% -1.26% 0.70% 3.71% 2.20% -0.14% -2.90% -12.75% -0.37% -0.76% 2.57% 3.25% 4.18% 2.15% 7.31% 5.11% 1.48% -0.96% 5.13% 2.91% -0.78% -0.06% 3.75% -4.19% 1.57% -4.48% 0.67% -3.34% -3.92% -0.23% -2.85% -0.53% -3.63% -2.70% -1.05% 0.21% 0.97% 2.18% -1.78% 2.81% -2.07% -0.24% 1.82% 1.02% 2.81% -0.77% -4.02% -1.04% 2.71% -3.07% -0.70% 3.24% 6.46% -3.79% 2.35% 1.54% 4.00% -2.42% 0.66% 2.14% 0.64% 5.38% 5.21% 7.56% 1.26% 4.95% 0.19% 6.57% 6.61% -2.14% 0.37%
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1.24% 3.35% -9.58% -4.71% 1.43% 0.89% 0.31% 1.55% 6.59% 2.62% -1.41% 0.31% -4.50% -4.22% -5.10% -2.01% 1.27% -4.26% 3.33% 4.63% -0.49% 0.75% 4.03% -1.57% 3.88% -2.09% 0.14% 2.73% -4.62% 1.06% 3.09% 0.18% 0.29% 3.13% 3.65% 0.81% 1.51% -4.62% 0.12% 1.88% 0.86% -0.90% -2.05% 0.12% 0.00% 0.95% 1.66% -2.59% 1.19% -0.34% 1.25% -1.37% 4.60% -1.16% 3.59% 2.87% 0.18% 3.08% -6.92% -1.85% 6.75% 2.29% -12.81% 4.27% 1.59% -4.91% 1.55% -3.98% 1.55% 1.88% 0.27% 0.34% -1.28% 3.34% 1.55% 5.28% 0.71% 3.36% 5.54% 6.85% -2.21% -3.33% -1.89% -4.68% -2.91% 1.93% 2.36% 1.85% 3.05% 2.62% 2.56% 1.31% -4.50% -1.62% 3.91% -2.05% -0.60% -9.31% 0.48% 2.90% 4.45% -3.98% 2.38% 4.95% 1.69% 3.16% 5.17% 7.98% 6.30% 4.81% -2.42% -8.35% -3.15% -0.48% -1.45% 0.437% 0.462% 0.350% 0.616% 0.695% =$'Return Data '.K264 3.21% 3.11% 3.54% 3.82% 3.79% =$'Return Data '.K265 0.0010278 0.000968 0.0012566 0.0014612 0.0014367 =$'Return Data '.K266 GOOG MSFT AAPL AMZN LUV 4.94E-005 5.38E-005 3.33E-005 2.75E-005 1.67E-005 7.98E-005 7.70E-005 5.81E-005 9.79E-005 8.10E-005 5.91E-005 6.59E-005 4.28E-005 5.97E-005 3.38E-005 6.19E-005 5.91E-005 2.89E-005 5.36E-005 5.58E-005 8.76E-005 7.42E-005 6.13E-005 6.64E-005 9.65E-005 0.0010239 0.0001506 0.000112 0.0001917 0.0001167 0.0001506 0.0009643 9.37E-005 0.0001161 9.22E-005 0.000112 9.37E-005 0.0012518 0.0001118 8.74E-005 0.0001917 0.0001161 0.0001118 0.0014556 0.0001152 0.0001167 9.22E-005 8.74E-005 0.0001152 0.0014312 covariance matrix
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GOOG MSFT AAPL AMZN LUV 0.0001647 0.0001795 0.0001111 9.18E-005 5.58E-005 0.0002661 0.0002566 0.0001938 0.0003262 0.00027 0.0001968 0.0002196 0.0001426 0.000199 0.0001127 0.0002065 0.000197 9.63E-005 0.0001786 0.0001861 0.0002919 0.0002473 0.0002042 0.0002215 0.0003216 0.0010239 0.0005021 0.0003733 0.0006391 0.0003892 0.0005021 0.0009643 0.0003123 0.0003871 0.0003074 0.0003733 0.0003123 0.0012518 0.0003727 0.0002915 0.0006391 0.0003871 0.0003727 0.0014556 0.000384 0.0003892 0.0003074 0.0002915 0.000384 0.0014312 GOOG MSFT AAPL AMZN LUV 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0010239 0 0 0 0 0 0.0009643 0 0 0 0 0 0.0012518 0 0 0 0 0 0.0014556 0 0 0 0 0 0.0014312 B265:K265,B319:B328)} MMULT(TRANSPOSE(B319:B328),B274:K283),B319:B328)} 20) 261} to compute the mbda. diagonal and zeros
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4 5 6
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COMPARING THE GM Sample Covariance PG HD KO JNJ WFC PG 0.000343014 0.000149 0.000183463 0.000154212 8.15722E-005 HD 0.000148976 0.0005443 0.000157852 0.000188293 0.000262213 KO 0.000183463 0.0001579 0.000383497 0.000144786 9.90745E-005 JNJ 0.000154212 0.0001883 0.000144786 0.000322635 0.000174418 WFC 8.15722E-005 0.0002622 9.90745E-005 0.000174418 0.000617889 GOOG 0.000164683 0.0002661 0.000196846 0.000206453 0.000291898 MSFT 0.000179471 0.0002566 0.000219556 0.000197025 0.000247268 AAPL 0.000111133 0.0001938 0.000142576 9.62763E-005 0.000204245 AMZN 9.18327E-005 0.0003262 0.00019902 0.000178578 0.000221488 LUV 5.58041E-005 0.00027 0.000112714 0.000186113 0.000321643 Single index model PG HD KO JNJ WFC PG 0.000344333 0.0001292 8.62891E-005 9.99121E-005 0.000143284 HD 0.000129216 0.0005464 0.000149411 0.000173 0.000248099 KO 8.62891E-005 0.0001494 0.000384972 0.000115528 0.000165678 JNJ 9.99121E-005 0.000173 0.000115528 0.000323876 0.000191835 WFC 0.000143284 0.0002481 0.000165678 0.000191835 0.000620266 GOOG 0.000168666 0.000292 0.000195028 0.000225819 0.000323846 MSFT 0.000156252 0.0002706 0.000180674 0.000209198 0.000300011 AAPL 0.000145833 0.0002525 0.000168626 0.000195248 0.000280004 AMZN 0.000159188 0.0002756 0.000184068 0.000213128 0.000305646 LUV 0.000149998 0.0002597 0.000173442 0.000200824 0.000288002 Constant Correlation PG HD KO JNJ WFC PG 0.996168582 0.343457 0.503900284 0.461784665 0.176507794 HD 0.343456989 0.9961686 0.344175809 0.447600381 0.450411904 KO 0.503900284 0.3441758 0.996168582 0.410036528 0.202748798 JNJ 0.461784665 0.4476004 0.410036528 0.996168582 0.389146184 WFC 0.176507794 0.4504119 0.202748798 0.389146184 0.996168582 GOOG 0.276824757 0.3550338 0.312938065 0.357830776 0.365584416 MSFT 0.310863558 0.352873 0.359661696 0.351882179 0.3191124 AAPL 0.168949365 0.2338808 0.204991586 0.150915698 0.231348754 AMZN 0.1294639 0.3650649 0.2653528 0.259585609 0.232649421 LUV 0.079341455 0.3047283 0.15156118 0.272842171 0.340728205 Shrinkage PG HD KO JNJ WFC PG 0.000343014 4.47E-005 5.50389E-005 4.62636E-005 2.44717E-005 HD 4.46928E-005 0.0005443 4.73556E-005 5.64879E-005 7.86638E-005 KO 5.50389E-005 4.74E-005 0.000383497 4.34358E-005 2.97224E-005 JNJ 4.62636E-005 5.65E-005 4.34358E-005 0.000322635 5.23254E-005 WFC 2.44717E-005 7.87E-005 2.97224E-005 5.23254E-005 0.000617889 GOOG 4.94048E-005 7.98E-005 5.90539E-005 6.19359E-005 8.75693E-005
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MSFT 5.38414E-005 7.70E-005 6.58667E-005 5.91076E-005 7.41805E-005 AAPL 3.33398E-005 5.81E-005 4.27728E-005 2.88829E-005 6.12735E-005 AMZN 2.75498E-005 9.79E-005 5.97061E-005 5.35735E-005 6.64464E-005 LUV 1.67412E-005 8.10E-005 3.38143E-005 0.000055834 9.64928E-005
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MVP GOOG MSFT AAPL AMZN LUV PG 0.0001647 0.0001795 0.000111133 9.18E-005 5.58E-005 HD 0.0002661 0.0002566 0.000193796 0.0003262 0.00027 KO 0.0001968 0.0002196 0.000142576 0.000199 0.0001127 JNJ 0.0002065 0.000197 9.62763E-005 0.0001786 0.0001861 WFC 0.0002919 0.0002473 0.000204245 0.0002215 0.0003216 GOOG 0.0010239 0.0005021 0.000373346 0.0006391 0.0003892 MSFT 0.0005021 0.0009643 0.000312287 0.0003871 0.0003074 AAPL 0.0003733 0.0003123 0.001251769 0.0003727 0.0002915 AMZN 0.0006391 0.0003871 0.000372679 0.0014556 0.000384 LUV 0.0003892 0.0003074 0.000291466 0.000384 0.0014312 GOOG MSFT AAPL AMZN LUV PG 0.0001687 0.0001563 0.000145833 0.0001592 0.00015 HD 0.000292 0.0002706 0.000252512 0.0002756 0.0002597 KO 0.000195 0.0001807 0.000168626 0.0001841 0.0001734 JNJ 0.0002258 0.0002092 0.000195248 0.0002131 0.0002008 WFC 0.0003238 0.0003 0.000280004 0.0003056 0.000288 GOOG 0.0010278 0.0003532 0.000329607 0.0003598 0.000339 MSFT 0.0003532 0.000968 0.000305348 0.0003333 0.0003141 AAPL 0.0003296 0.0003053 0.001256583 0.0003111 0.0002931 AMZN 0.0003598 0.0003333 0.000311084 0.0014612 0.00032 LUV 0.000339 0.0003141 0.000293125 0.00032 0.0014367 GOOG MSFT AAPL AMZN LUV PG 0.2768248 0.3108636 0.168949365 0.1294639 0.0793415 HD 0.3550338 0.352873 0.233880761 0.3650649 0.3047283 KO 0.3129381 0.3596617 0.204991586 0.2653528 0.1515612 JNJ 0.3578308 0.3518822 0.150915698 0.2595856 0.2728422 WFC 0.3655844 0.3191124 0.231348754 0.2326494 0.3407282 GOOG 0.9961686 0.5033541 0.328520006 0.5214861 0.3202513 MSFT 0.5033541 0.9961686 0.283153564 0.3254794 0.2606486 AAPL 0.32852 0.2831536 0.996168582 0.2750303 0.2169282 AMZN 0.5214861 0.3254794 0.275030298 0.9961686 0.2650351 LUV 0.3202513 0.2606486 0.216928208 0.2650351 0.9961686 GOOG MSFT AAPL AMZN LUV PG 4.94E-005 5.38E-005 3.33398E-005 2.75E-005 1.67E-005 HD 7.98E-005 7.70E-005 5.81388E-005 9.79E-005 8.10E-005 KO 5.91E-005 6.59E-005 4.27728E-005 5.97E-005 3.38E-005 JNJ 6.19E-005 5.91E-005 2.88829E-005 5.36E-005 5.58E-005 WFC 8.76E-005 7.42E-005 6.12735E-005 6.64E-005 9.65E-005 GOOG 0.0010239 0.0001506 0.000112004 0.0001917 0.0001167 MSFT
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0.0001506 0.0009643 0.000093686 0.0001161 9.22E-005 AAPL 0.000112 9.37E-005 0.001251769 0.0001118 8.74E-005 AMZN 0.0001917 0.0001161 0.000111804 0.0014556 0.0001152 LUV 0.0001167 9.22E-005 8.74399E-005 0.0001152 0.0014312
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28.89% GMVP statistics 3.98% Mean return 0.25% =$SampleVARCOV.F284 20.76% Variance 0.02% =$SampleVARCOV.F285 26.75% Sigma 1.40% =$SampleVARCOV.F286 13.37% -3.75% -1.62% 6.01% 2.33% 3.28% 33.79% GMVP Statistics 8.17%
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