Table of Contents

Master Data
Tracing Portfolio Frontier
2 Assets -Solver
Correlations
Maximize Returns - 3 Assets
Minimum Variance - 3 Assets
EF 3 Assets
Matrix Algebra - 3 Assets
 Date CAT WMT JPM GM ORCL T PFE YHOO QQQQ
6/1/2001 -0.075885 -0.055715 -0.095177 0.130939 0.24183 -0.069533 -0.066234 0.102649 0.021833
7/2/2001 0.10812 0.145439 -0.018996 -0.011475 -0.048421 0.131105 0.029241 -0.118118 -0.086357
8/1/2001 -0.092631 -0.140468 -0.089884 -0.132463 -0.324668 -0.091568 -0.068073 -0.326901 -0.122777
9/4/2001 -0.103902 0.031844 -0.133376 -0.216487 0.030303 0.151834 0.046785 -0.256324 -0.208831
10/1/2001 0.00557 0.038363 0.045438 -0.036597 0.077901 -0.186652 0.044983 0.23356 0.169884
11/1/2001 0.060423 0.073065 0.066947 0.216841 0.034661 -0.019067 0.036148 0.430147 0.169517
12/3/2001 0.102089 0.044816 -0.036465 -0.022112 -0.015681 0.0479 -0.079893 0.140103 -0.018728
1/2/2002 -0.03059 0.042158 -0.054211 0.052142 0.249819 -0.037761 0.045731 -0.028185 -0.010196
2/1/2002 0.104 0.033916 -0.140952 0.046776 -0.03708 0.010327 -0.013839 -0.161253 -0.122821
3/1/2002 0.024155 -0.010422 0.218632 0.140821 -0.229844 -0.010562 -0.02975 0.276625 0.06745
4/1/2002 -0.033412 -0.088743 -0.005854 0.06119 -0.215625 -0.164256 -0.085334 -0.200433 -0.120169
5/1/2002 -0.0427 -0.031451 0.024247 -0.023943 -0.211155 0.103832 -0.044908 0.085366 -0.053222
6/3/2002 -0.063721 0.018192 -0.056476 -0.140025 0.195707 -0.110489 0.011589 -0.078652 -0.131053
7/1/2002 -0.079401 -0.106052 -0.256272 -0.129071 0.057022 -0.085187 -0.075614 -0.107046 -0.086126
8/1/2002 -0.023657 0.08747 0.057831 0.04012 -0.041958 -0.105963 0.026558 -0.22003 -0.015352
9/3/2002 -0.146896 -0.078063 -0.280638 -0.187352 -0.180396 -0.187276 -0.122801 -0.070039 -0.1178
10/1/2002 0.107101 0.087674 0.112096 -0.144979 0.296438 0.292929 0.095163 0.560669 0.184585
11/1/2002 0.221807 0.006504 0.212984 0.21148 0.192345 0.11084 -0.00395 0.225201 0.1293
12/2/2002 -0.08399 -0.061484 -0.046479 -0.071696 -0.111111 -0.048791 -0.030281 -0.105033 -0.120734
1/2/2003 -0.030564 -0.05362 -0.013786 -0.014439 0.113889 -0.090573 -0.00223 0.112469 0.002922
2/3/2003 0.068473 0.005291 -0.028457 -0.05724 -0.005819 -0.148882 -0.017511 0.146154 0.02913
3/3/2003 0.047026 0.08443 0.045735 -0.004337 -0.093645 -0.035224 0.044748 0.151486 0.003639
4/1/2003 0.076178 0.082508 0.255528 0.072232 0.095941 0.181931 -0.013067 0.03164 0.087429
5/1/2003 -0.008592 -0.065758 0.119374 -0.006432 0.095118 0.090052 0.01324 0.204197 0.085217
6/2/2003 0.067272 0.021796 0.04021 0.01908 -0.076864 0.003842 0.100907 0.095845 0.005121
7/1/2003 0.219258 0.041683 0.035966 0.039786 -0.001665 -0.072249 -0.023079 -0.048318 0.061821
8/1/2003 0.0647 0.058238 -0.023686 0.11254 0.070058 -0.03868 -0.098886 0.072622 0.050224
9/2/2003 -0.041704 -0.056098 0.002991 -0.004046 -0.123149 -0.00912 0.015356 0.059916 -0.029242
10/1/2003 0.06963 0.057175 0.055997 0.042658 0.064 0.095831 0.039838 0.235161 0.085347
11/3/2003 0.03778 -0.05604 -0.013806 0.014194 0.004177 -0.02915 0.0674 -0.016018 0.005493
12/1/2003 0.091851 -0.045043 0.037544 0.248353 0.100666 0.119593 0.052509 0.046977 0.031052
1/2/2004 -0.054886 0.015196 0.068691 -0.069686 0.047619 -0.010455 0.036943 0.043536 0.016732
2/2/2004 -0.030393 0.105949 0.054519 -0.021503 -0.071429 -0.058337 0.004872 -0.056194 -0.013439
3/1/2004 0.043941 0.00457 0.022857 -0.018112 -0.067599 0.021951 -0.043636 0.093369 -0.020017
4/1/2004 -0.012601 -0.045144 -0.096568 0.003689 -0.0625 0.027685 0.020279 0.042079 -0.029787
5/3/2004 -0.030682 -0.019974 -0.020024 -0.031855 0.013333 -0.048305 -0.007143 0.213777 0.05117
6/1/2004 0.054342 -0.057966 0.052284 0.026322 0.046491 0.023426 -0.029715 0.187215 0.032545
7/1/2004 -0.070138 0.009726 -0.028555 -0.073983 -0.119028 0.058655 -0.067698 -0.153846 -0.0757
8/2/2004 -0.010571 -0.004128 0.060259 -0.030892 -0.05138 0.017568 0.027663 -0.074351 -0.024774
9/1/2004 0.106555 0.010067 0.003881 0.028304 0.131394 0.006197 -0.063257 0.189407 0.032875
10/1/2004 0.006263 0.01368 -0.020436 -0.092731 0.12234 -0.015398 -0.054239 0.067237 0.050058
11/1/2004 0.13667 -0.034509 -0.024528 0.014138 0.006319 -0.003575 -0.034941 0.039514 0.060072
12/1/2004 0.065024 0.016973 0.036127 0.038339 0.076923 0.023767 -0.031484 0.001595 0.030413
1/3/2005 -0.082262 -0.007854 -0.034589 -0.081119 0.003644 -0.066141 -0.101585 -0.065552 -0.06332
2/1/2005 0.06676 -0.015041 -0.021092 -0.018569 -0.05955 0.012664 0.096336 -0.083499 -0.004579
3/1/2005 -0.037856 -0.026321 -0.053129 -0.175558 -0.036293 -0.015285 -0.000825 0.050511 -0.017587
4/1/2005 -0.032522 -0.059224 0.035848 -0.092175 -0.073718 0.018344 0.034269 0.017699 -0.043514
5/2/2005 0.068641 0.005045 0.007523 0.200995 0.107266 -0.017552 0.033932 0.078261 0.088684
6/1/2005 0.012758 0.020515 -0.012246 0.07833 0.03125 0.015515 -0.011583 -0.068548 -0.033325
 7/1/2005 0.13662 0.023952 0.004536 0.08288 0.02803 0.043519 -0.039063 -0.037807 0.076334
8/1/2005 0.029429 -0.086048 -0.035521 -0.05792 -0.042741 -0.015084 -0.031707 -0.0006 -0.015252
9/1/2005 0.05866 -0.025366 0.001248 -0.104768 -0.04542 -0.004505 -0.019731 0.015606 0.01239
10/3/2005 -0.100824 0.079484 0.090087 -0.104765 0.022581 0.008597 -0.129336 0.092494 -0.015043
11/1/2005 0.098674 0.026499 0.04461 -0.18591 -0.006309 0.044415 -0.016724 0.08818 0.060834
12/1/2005 -0.000177 -0.03322 0.037503 -0.113462 -0.030952 -0.016753 0.10005 -0.0261 -0.01757
1/3/2006 0.180011 -0.014883 0.010026 0.239154 0.029484 0.073831 0.10141 -0.122511 0.039245
2/1/2006 0.076425 -0.016219 0.035005 -0.146171 -0.011933 0.063059 0.029727 -0.067481 -0.021511
3/1/2006 -0.01747 0.045393 0.012367 0.047155 0.102254 -0.0199 -0.048516 0.006238 0.021006
4/3/2006 0.058179 -0.046878 0.098479 0.075869 0.065741 -0.018352 0.016435 0.016119 -0.001914
5/1/2006 -0.036967 0.079782 -0.060372 0.188353 -0.02536 -0.005967 -0.057214 -0.036303 -0.072387
6/1/2006 0.021078 -0.005877 -0.014976 0.106432 0.018987 0.070428 -0.007916 0.044634 -0.000517
7/3/2006 -0.044293 -0.076014 0.095145 0.082007 0.033126 0.088224 0.10727 -0.177576 -0.043175
8/1/2006 -0.063796 0.008684 0.000896 -0.087304 0.046092 0.038131 0.070456 0.06227 0.047825
9/1/2006 -0.008403 0.102855 0.028412 0.139804 0.132822 0.045665 0.028796 -0.123136 0.046158
10/2/2006 -0.073344 -0.000822 0.017403 0.0498 0.04115 0.062975 -0.060342 0.04193 0.047572
11/1/2006 0.021783 -0.064556 -0.024375 -0.156955 0.031402 -0.010122 0.040619 0.025437 0.034353
12/1/2006 -0.011229 0.005495 0.043612 0.051059 -0.100262 0.054436 -0.057621 -0.054424 -0.018881
1/3/2007 0.049868 0.032568 0.061949 0.068738 0.001167 0.063605 0.013018 0.108457 0.021099
2/1/2007 0.005644 0.013124 -0.030255 -0.021954 -0.042541 -0.02199 -0.038162 0.090074 -0.016803
3/1/2007 0.040374 -0.023611 -0.020392 -0.039519 0.103469 0.071291 0.011741 0.013934 0.005312
4/2/2007 0.088103 0.020758 0.084513 0.019421 0.036955 -0.008958 0.047619 -0.103867 0.055824
5/1/2007 0.082071 -0.002096 -0.005182 -0.031644 0.030851 0.067665 0.050038 0.023538 0.031549
6/1/2007 -0.005599 0.039286 0.001351 0.017006 0.014448 -0.019594 0.006912 0.002787 0.000633

STD 7.51% 5.45% 8.26% 10.42% 10.71% 8.01% 5.47% 14.36% 7.06%
MEAN 1.92% 0.17% 0.75% 0.07% 0.93% 0.61% -0.25% 2.57% 0.36%
 XOM HAL INFY MSFT
-0.015488 -0.236355 -0.043936 0.055275
-0.044048 -0.016159 0.015534 -0.093261
-0.033187 -0.204675 -0.204589 -0.138077
-0.01844 -0.186656 -0.356571 -0.102983
0.001156 0.094727 0.399751 0.136219
-0.046478 -0.126673 0.209075 0.10425
0.050863 -0.389173 0.086093 0.03159
-0.006338 0.050167 0.01355 -0.038015
0.063787 0.208599 -0.125 -0.084523
0.061325 0.035573 0.190985 0.033973
-0.083462 -0.005089 -0.052598 -0.133746
-0.00028 0.092072 -0.087339 -0.025435
0.024944 -0.13466 -0.094214 0.074176
-0.101723 -0.171854 0.005733 -0.122762
-0.029528 0.150327 0.099349 0.022838
-0.100063 -0.143466 -0.042222 -0.108789
0.055071 0.253731 0.322506 0.222281
0.040634 0.329365 0.163158 0.078936
0.004127 -0.124378 -0.164404 -0.10388
-0.022447 0.003409 -0.066185 -0.081642
0.002911 0.079275 -0.048325 0.001965
0.027088 0.029381 -0.007448 0.021078
0.007221 0.03262 -0.33015 0.056169
0.041459 0.115499 0.07943 -0.037273
-0.013469 -0.031858 0.214151 0.041549
-0.009102 -0.035649 -0.00777 0.030372
0.066748 0.090995 0.066562 0.00396
-0.02899 0.007819 0.198972 0.048203
-0.000591 -0.015517 0.243723 -0.054348
-0.003549 -0.016637 -0.017233 -0.016357
0.13268 0.11309 0.148798 0.064719
-0.005241 0.16 -0.074139 0.010131
0.040306 0.06 -0.048987 -0.040535
-0.013674 -0.045543 -0.027241 -0.06054
0.023107 -0.019087 -0.01222 0.048215
0.023087 -0.025712 0.041753 0.003981
0.026735 0.046362 0.12568 0.088987
0.042523 0.04908 0.076484 -0.002832
0.001604 -0.077323 0.039608 -0.038945
0.048501 0.15493 0.085625 0.013086
0.018329 0.1 0.175832 0.011667
0.046925 0.119734 0.083692 0.067957
0.000205 -0.05099 -0.037195 -0.003085
0.006548 0.047992 -0.047184 -0.016634
0.232974 0.069189 0.154441 -0.039732
-0.058533 -0.013966 -0.032976 -0.039328
-0.043082 -0.038244 -0.197117 0.046908
-0.0097 0.030928 0.22203 0.022811
0.022731 0.118571 0.07488 -0.037037
 0.022226 0.171988 -0.082545 0.031017
0.024571 0.108609 -0.005731 0.072202
0.060732 0.105177 0.049568 -0.060232
-0.116461 -0.137563 -0.082647 -0.001194
0.039028 0.079065 0.059563 0.080112
-0.032069 -0.026442 0.122034 -0.054982
0.117152 0.285013 -0.057402 0.076142
-0.048828 -0.14413 -0.071047 -0.04209
0.024978 0.073788 0.09977 0.0125
0.036471 0.07038 0.010196 -0.112233
-0.029512 -0.04349 -0.091356 -0.058576
0.007185 -0.005142 0.082313 0.028648
0.10418 -0.100925 0.075526 0.032637
0.003606 -0.01997 0.09151 0.072061
-0.008383 -0.127817 0.064335 0.064072
0.064463 0.136991 0.093724 0.049871
0.08013 0.045455 0.027537 0.026038
-0.002363 -0.079809 0.019303 0.017147
-0.033035 -0.048544 0.063063 0.033378
-0.028583 0.04898 -0.064511 -0.08385
0.052683 0.026589 -0.073951 -0.010684
0.052043 0.000948 0.041725 0.074154
0.052252 0.134427 -0.059218 0.028485
0.012625 -0.003338 0.011 -0.003258

5.33% 12.06% 12.78% 6.67%

1.21% 1.48% 2.38% 0.26%
 JPM ORCL
MEAN 0.75% 0.93%
STD. DEVIATION 8.26% 10.71%
VARIANCE 0.00683 0.01146
CORRELATION 0.15452
COVARIANCE 0.00137

Weights 0 100%

Expected Return 0.93%

Portfolio Variance 0.011465
Portfolio Std. Deviation 10.71%

JPM Variance Risk Return

Expected Return
0% 0.011465 10.71% 0.93% Risk-Return Tradeoff betwee
5% 0.010494 10.24% 0.92%
10% 0.009601 9.80% 0.91%
1.10%
15% 0.008786 9.37% 0.90%
20% 0.008048 8.97% 0.90%
25% 0.007388 8.60% 0.89%
30% 0.006807 8.25% 0.88%
35% 0.006303 7.94% 0.87%
40% 0.005876 7.67% 0.86% 0.90%
45% 0.005528 7.43% 0.85%
50% 0.005257 7.25% 0.84%
55% 0.005064 7.12% 0.83%
60% 0.004949 7.03% 0.82%
65% 0.004912 7.01% 0.81%
70% 0.004952 7.04% 0.80% 0.70%
75% 0.00507 7.12% 0.79% 6.00% 7.00% 8.00% 9.00%
80% 0.005267 7.26% 0.78%
Risk (Standard De
85% 0.00554 7.44% 0.77%
90% 0.005892 7.68% 0.76%
95% 0.006322 7.95% 0.75%
100% 0.006829 8.26% 0.75%
isk-Return Tradeoff between two stocks

7.00% 8.00% 9.00% 10.00% 11.00% 12.00%

Risk (Standard Deviation)
 Minimum Variance Portfolio for two assets using Solver and calculus method

JPM ORCL
MEAN RETURN 0.75% 0.93%
STD. DEVIATION 8.26% 10.71%
VARIANCE 0.00683 0.01146
CORRELATION 0.15452
=B4*B17+C4*C17
COVARIANCE 0.00137

Two Asset Portfolio

Expected Return 0.81% =B17^2*B6+C17^2*C6+2*B17*C17*B8
Portfolio Variance 0.004912
Portfolio Std. Deviation 7.01%
=SQRT(B12)

Weight in JPM ORCL

64.90% 35.10%
=1-B17

Solver Solution

Using Calculus Method

64.90% 35.10%

=1-B26
= (C6-B8) / (C6+B6-2*B8)
s method
 A B Effect of change in Correlation Co-efficient o
MEAN 3.00% 2.00%
STD. DEVIATION 25.00% 15.00%
VARIANCE 0.06 0.02
CORRELATION 0.54 CORRELATION -1

=SQRT(B17^2*$B$4+(1-B17)^2*$C$4+2*B17*(1-B17)*$B$4*$C$4*$B$5
A B
Weights 50% 50%

Expected Return 2.50%

Portfolio Variance 14.71% =ABS($B17*$B$3-(1-$B17)*$C$3)

Weight of
A Risk Return Risk Return
0% 15.00% 2.00% 15.00% 2.00%
5% 14.33% 2.05% 13.00% 2.05%
10% 13.78% 2.10% 11.00% 2.10%
15% 13.36% 2.15% 9.00% 2.15%
20% 13.09% 2.20% 7.00% 2.20%
25% 12.98% 2.25% 5.00% 2.25%
30% 13.03% 2.30% 3.00% 2.30%
35% 13.23% 2.35% 1.00% 2.35%
40% 13.59% 2.40% 1.00% 2.40%
45% 14.08% 2.45% 3.00% 2.45%
50% 14.71% 2.50% 5.00% 2.50%
55% 15.44% 2.55% 7.00% 2.55%
60% 16.27% 2.60% 9.00% 2.60%
65% 17.18% 2.65% 11.00% 2.65%
70% 18.16% 2.70% 13.00% 2.70%
75% 19.20% 2.75% 15.00% 2.75%
80% 20.28% 2.80% 17.00% 2.80%
85% 21.41% 2.85% 19.00% 2.85%
90% 22.58% 2.90% 21.00% 2.90%
95% 23.78% 2.95% 23.00% 2.95%
100% 25.00% 3.00% 25.00% 3.00%
rrelation Co-efficient on 2-asset portfolio
Expected Returns, monthly

Effect of Correlation Coefficient

CORRELATION 1 on a 2-Asset Portfolio frontier

2*B17*(1-B17)*$B$4*$C$4*$B$5)
3.50%

3.00%
=$B17*$B$3+(1-$B17)*$C$3
2.50%

Risk Return
2.00% 15.00% 2.00%
15.50% 2.05%
16.00% 2.10%
1.50%
16.50% 2.15%
17.00% 2.20%
1.00% 17.50% 2.25%
0.00% 5.00% 18.00%
10.00% 2.30% 15.00% 20.00% 25.00% 30.00%
18.50% 2.35%
Risk (Standard Deviation)
19.00% 2.40%
19.50% 2.45%
20.00% 2.50%
20.50% 2.55%
21.00% 2.60%
21.50% 2.65%
22.00% 2.70%
22.50% 2.75%
23.00% 2.80%
23.50% 2.85%
24.00% 2.90%
24.50% 2.95%
25.00% 3.00%
 3 -Assets Using Solver
JPM ORCL HAL
MEAN RETURN 0.75% 0.93% 1.48% JPM
STD. DEVIATION 8.26% 10.71% 12.06% JPM 0.006829
VARIANCE 0.0068 0.0115 0.0145 ORCL 0.001367
HAL 0.003373

=B3*B17+C3*C17+D3*D17
Three Asset Portfolio
Expected Return 1.16% 100 =B17^2*B5+C17^2*C5+D17^2*D5+2*B17*C17*H5+2*C17*D17*I6+2*D17*
Portfolio Variance 0.00640016
Portfolio Std. Deviation 8.00%
=SQRT(B12)
The variance-covariance mat
Weight in JPM ORCL HAL
created using Tools/Data
23.49% 28.11% 48.40% =1-C17-B17 Analysis/Covariance. For 3-
assets, select a output range
the worksheet where you wa
your variance-covariance ma
(in this example it is $G$3) a
Standard Deviation 8% would create a 3 by 3 matrix.
 ORCL HAL

0.011465
0.002807 0.014542

7*C17*H5+2*C17*D17*I6+2*D17*B17*H6

The variance-covariance matrix is

created using Tools/Data
Analysis/Covariance. For 3-
assets, select a output range in
the worksheet where you want
your variance-covariance matrix
(in this example it is $G$3) and it
would create a 3 by 3 matrix.
 s7

0.423293976 0.416732875

Page 14
 3 -Assets Using Solver
JPM ORCL HAL
MEAN RETURN 0.75% 0.93% 1.48% JPM
STD. DEVIATION 8.26% 10.71% 12.06% JPM 0.006829
VARIANCE 0.0068 0.0115 0.0145 ORCL 0.001367
HAL 0.003373

=B3*B17+C3*C17+D3*D17
Three Asset Portfolio
Expected Return 1.06% 100 =B17^2*B5+C17^2*C5+D17^2*D5+2*B17*C17*H5+2*C17*D17*I6+2*D17*
Portfolio Variance 0.00535761
Portfolio Std. Deviation 7.32%
=SQRT(B12)
The variance-covariance mat
Weight in JPM ORCL HAL
created using Tools/Data
33.00% 33.00% 34.00% =1-C17-B17 Analysis/Covariance. For 3-
assets, select a output range
the worksheet where you wa
your variance-covariance ma
(in this example it is $G$3) a
would create a 3 by 3 matrix.
 ORCL HAL

0.011465
0.002807 0.014542

7*C17*H5+2*C17*D17*I6+2*D17*B17*H6

The variance-covariance matrix is

created using Tools/Data
Analysis/Covariance. For 3-
assets, select a output range in
the worksheet where you want
your variance-covariance matrix
(in this example it is $G$3) and it
would create a 3 by 3 matrix.
Date JPM ORCL HAL Mean Variance
6/1/2001 -0.095177 0.2418 -0.236355 JPM 0.75% 0.00683
7/2/2001 -0.018996 -0.0484 -0.016159 ORCL 0.93% 0.01146
8/1/2001 -0.089884 -0.3247 -0.204675 HAL 1.48% 0.01454
9/4/2001 -0.133376 0.0303 -0.186656 s
10/1/2001 0.045438 0.0779 0.094727 JPM 55.796%
11/1/2001 0.066947 0.0347 -0.126673 ORCL 30.923%
12/3/2001 -0.036465 -0.0157 -0.389173 HAL 13.281%
1/2/2002 -0.054211 0.2498 0.050167 constraint 1
2/1/2002 -0.140952 -0.0371 0.208599 constraint 0.90%
3/1/2002 0.218632 -0.2298 0.035573
4/1/2002 -0.005854 -0.2156 -0.005089 JPM ORCL
5/1/2002 0.024247 -0.2112 0.092072 JPM 0.00682882 0.001367
6/3/2002 -0.056476 0.1957 -0.13466 ORCL 0.00136726 0.011465
7/1/2002 -0.256272 0.0570 -0.171854 HAL 0.0033726 0.002807
8/1/2002 0.057831 -0.0420 0.150327
9/3/2002 -0.280638 -0.1804 -0.143466
10/1/2002 0.112096 0.2964 0.253731
11/1/2002 0.212984 0.1923 0.329365
12/2/2002 -0.046479 -0.1111 -0.124378
1/2/2003 -0.013786 0.1139 0.003409
2/3/2003 -0.028457 -0.0058 0.079275
3/3/2003 0.045735 -0.0936 0.029381
4/1/2003 0.255528 0.0959 0.03262
5/1/2003 0.119374 0.0951 0.115499
6/2/2003 0.04021 -0.0769 -0.031858
7/1/2003 0.035966 -0.0017 -0.035649
8/1/2003 -0.023686 0.0701 0.090995
9/2/2003 0.002991 -0.1231 0.007819
10/1/2003 0.055997 0.0640 -0.015517
11/3/2003 -0.013806 0.0042 -0.016637
12/1/2003 0.037544 0.1007 0.11309
1/2/2004 0.068691 0.0476 0.16
2/2/2004 0.054519 -0.0714 0.06
3/1/2004 0.022857 -0.0676 -0.045543
4/1/2004 -0.096568 -0.0625 -0.019087
5/3/2004 -0.020024 0.0133 -0.025712
6/1/2004 0.052284 0.0465 0.046362
7/1/2004 -0.028555 -0.1190 0.04908
8/2/2004 0.060259 -0.0514 -0.077323
9/1/2004 0.003881 0.1314 0.15493
10/1/2004 -0.020436 0.1223 0.1
11/1/2004 -0.024528 0.0063 0.119734
12/1/2004 0.036127 0.0769 -0.05099
1/3/2005 -0.034589 0.0036 0.047992
2/1/2005 -0.021092 -0.0595 0.069189
3/1/2005 -0.053129 -0.0363 -0.013966
4/1/2005 0.035848 -0.0737 -0.038244
5/2/2005 0.007523 0.1073 0.030928
6/1/2005 -0.012246 0.0312 0.118571
 7/1/2005 0.004536 0.0280 0.171988
8/1/2005 -0.035521 -0.0427 0.108609
9/1/2005 0.001248 -0.0454 0.105177
10/3/2005 0.090087 0.0226 -0.137563
11/1/2005 0.04461 -0.0063 0.079065
12/1/2005 0.037503 -0.0310 -0.026442
1/3/2006 0.010026 0.0295 0.285013
2/1/2006 0.035005 -0.0119 -0.14413
3/1/2006 0.012367 0.1023 0.073788
4/3/2006 0.098479 0.0657 0.07038
5/1/2006 -0.060372 -0.0254 -0.04349
6/1/2006 -0.014976 0.0190 -0.005142
7/3/2006 0.095145 0.0331 -0.100925
8/1/2006 0.000896 0.0461 -0.01997
9/1/2006 0.028412 0.1328 -0.127817
10/2/2006 0.017403 0.0411 0.136991
11/1/2006 -0.024375 0.0314 0.045455
12/1/2006 0.043612 -0.1003 -0.079809
1/3/2007 0.061949 0.0012 -0.048544
2/1/2007 -0.030255 -0.0425 0.04898
3/1/2007 -0.020392 0.1035 0.026589
4/2/2007 0.084513 0.0370 0.000948
5/1/2007 -0.005182 0.0309 0.134427
6/1/2007 0.001351 0.0144 -0.003338

MEAN 0.75% 0.93% 12.06%

SD 8.26% 10.71% 1.48%
VAR 0.0068 0.0115
CORRELATION 0.1545
COVARIANCE 0.0014
Std. Dev
8.264%
10.707%
12.059%
i
1
1
1
0.004681 Portfolio Variance
6.84% Portfolio Standard Deviation

HAL
0.003373
0.002807
0.014542
Date JPM ORCL HAL Mean Variance
6/1/2001 -0.095177 0.2418 -0.236355 JPM 0.75% 0.00683
7/2/2001 -0.018996 -0.0484 -0.016159 ORCL 0.93% 0.01146
8/1/2001 -0.089884 -0.3247 -0.204675 HAL 1.48% 0.01454
9/4/2001 -0.133376 0.0303 -0.186656 s
10/1/2001 0.045438 0.0779 0.094727 JPM 55.796%
11/1/2001 0.066947 0.0347 -0.126673 ORCL 30.923%
12/3/2001 -0.036465 -0.0157 -0.389173 HAL 13.281%
1/2/2002 -0.054211 0.2498 0.050167 constraint 1
2/1/2002 -0.140952 -0.0371 0.208599 constraint 0.90%
3/1/2002 0.218632 -0.2298 0.035573
4/1/2002 -0.005854 -0.2156 -0.005089 JPM ORCL
5/1/2002 0.024247 -0.2112 0.092072 JPM 0.00682882 0.001367260813
6/3/2002 -0.056476 0.1957 -0.13466 ORCL 0.00136726 0.01146483685
7/1/2002 -0.256272 0.0570 -0.171854 HAL 0.0033726 0.002806586611
8/1/2002 0.057831 -0.0420 0.150327
9/3/2002 -0.280638 -0.1804 -0.143466
10/1/2002 0.112096 0.2964 0.253731
11/1/2002 0.212984 0.1923 0.329365
12/2/2002 -0.046479 -0.1111 -0.124378
1/2/2003 -0.013786 0.1139 0.003409
2/3/2003 -0.028457 -0.0058 0.079275 Calculus Solution
3/3/2003 0.045735 -0.0936 0.029381
4/1/2003 0.255528 0.0959 0.03262 A 0.02112574
5/1/2003 0.119374 0.0951 0.115499 B 213.633332
6/2/2003 0.04021 -0.0769 -0.031858 C 1.92562491
7/1/2003 0.035966 -0.0017 -0.035649 D 0.8051
8/1/2003 -0.023686 0.0701 0.090995
9/2/2003 0.002991 -0.1231 0.007819 Std. Dev 6.84% 0.901%
10/1/2003 0.055997 0.0640 -0.015517
11/3/2003 -0.013806 0.0042 -0.016637
12/1/2003 0.037544 0.1007 0.11309 Risk Return
1/2/2004 0.068691 0.0476 0.16 0 10.04% 0.45%
2/2/2004 0.054519 -0.0714 0.06 1 9.26% 0.52%
3/1/2004 0.022857 -0.0676 -0.045543 2 8.56% 0.59%
4/1/2004 -0.096568 -0.0625 -0.019087 3 7.94% 0.65%
5/3/2004 -0.020024 0.0133 -0.025712 4 7.45% 0.72%
6/1/2004 0.052284 0.0465 0.046362 5 7.08% 0.79%
7/1/2004 -0.028555 -0.1190 0.04908 6 6.88% 0.86%
8/2/2004 0.060259 -0.0514 -0.077323 7 6.85% 0.92%
9/1/2004 0.003881 0.1314 0.15493 8 7.00% 0.99%
10/1/2004 -0.020436 0.1223 0.1 9 7.31% 1.06%
11/1/2004 -0.024528 0.0063 0.119734 10 7.76% 1.13%
12/1/2004 0.036127 0.0769 -0.05099 11 8.34% 1.19%
1/3/2005 -0.034589 0.0036 0.047992 12 9.02% 1.26%
2/1/2005 -0.021092 -0.0595 0.069189 13 9.77% 1.33%
3/1/2005 -0.053129 -0.0363 -0.013966 14 10.58% 1.40%
4/1/2005 0.035848 -0.0737 -0.038244 15 11.45% 1.46%
5/2/2005 0.007523 0.1073 0.030928 16 12.35% 1.53%
6/1/2005 -0.012246 0.0312 0.118571 17 13.28% 1.60%
 7/1/2005 0.004536 0.0280 0.171988 18 14.23% 1.67%
8/1/2005 -0.035521 -0.0427 0.108609 19 15.21% 1.74%
9/1/2005 0.001248 -0.0454 0.105177 20 16.20% 1.80%
10/3/2005 0.090087 0.0226 -0.137563
11/1/2005 0.04461 -0.0063 0.079065
12/1/2005 0.037503 -0.0310 -0.026442
1/3/2006 0.010026 0.0295 0.285013
2/1/2006 0.035005 -0.0119 -0.14413
3/1/2006 0.012367 0.1023 0.073788
4/3/2006 0.098479 0.0657 0.07038
5/1/2006 -0.060372 -0.0254 -0.04349
6/1/2006 -0.014976 0.0190 -0.005142
7/3/2006 0.095145 0.0331 -0.100925
8/1/2006 0.000896 0.0461 -0.01997
9/1/2006 0.028412 0.1328 -0.127817
10/2/2006 0.017403 0.0411 0.136991
11/1/2006 -0.024375 0.0314 0.045455
12/1/2006 0.043612 -0.1003 -0.079809
1/3/2007 0.061949 0.0012 -0.048544
2/1/2007 -0.030255 -0.0425 0.04898
3/1/2007 -0.020392 0.1035 0.026589
4/2/2007 0.084513 0.0370 0.000948
5/1/2007 -0.005182 0.0309 0.134427
6/1/2007 0.001351 0.0144 -0.003338

MEAN 0.75% 0.93% 12.06%

SD 8.26% 10.71% 1.48%
VAR 0.0068 0.0115
CORRELATION 0.1545
COVARIANCE 0.0014
Std. Dev
8.264%
10.707%
12.059%
i
1
1
1
0.004681 Portfolio Variance
6.84% Portfolio Standard Deviation

HAL
0.003373
0.002807
0.014542

=MMULT(TRANSPOSE(s),MMULT(Sigma,s))
E xpected Return (m onthly)

Efficient Frontier for 3 Risky Assets

2.00%
1.80%
1.60%
1.40%
1.20%
1.00%
0.80%
0.60%
0.40%
0.20%
0.00%
6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Standard Deviation (Risk)
0.80%
0.60%
0.40%
0.20%
0.00%
6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Standard Deviation (Risk)
scenario 1

1
0
0

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