9
50% 50% AT&T Best Buy AT&T(T) Best Buy(B) Portfolio Date Adj Close Adj Close Returns Returns Return 12/1/2014 33.12 38.98 -5.07% -0.59% -2.83% 11/3/2014 34.89 39.21 1.57% 15.46% 8.52% 10/1/2014 34.35 33.96 0.17% 1.62% 0.90% 9/2/2014 34.29 33.42 0.79% 5.96% 3.38% 8/1/2014 34.02 31.54 -1.79% 7.28% 2.74% 7/1/2014 34.64 29.4 1.97% -4.14% -1.08% 6/2/2014 33.97 30.67 -0.32% 12.80% 6.24% 5/1/2014 34.08 27.19 -0.64% 6.67% 3.01% 4/1/2014 34.3 25.49 3.13% -1.81% 0.66% 3/3/2014 33.26 25.96 9.84% -0.19% 4.82% 2/3/2014 30.28 26.01 -4.18% 13.14% 4.48% 1/2/2014 31.6 22.99 Mean 0.50% 5.11% 2.80% 2.80% Variance 0.001435 0.00404319 0.0009708 0.0009708 Std Devn 0.037879 0.06358609 0.03115771 Covariance -0.0008 Correlation -0.33107 Portfolio risk and return % AT&T 50% % BestBuy 50% Exp Portfolio return 2.80% Exp Portfolio varian 0.000971 = _ ^2 ( _ )+ _ _^ (_,

Minimum Variance Portfolio VIDEO DILAN

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Page 1: Minimum Variance Portfolio VIDEO DILAN

50% 50%AT&T Best Buy AT&T(T) Best Buy(B) Portfolio AT&T Best Buy

Date Adj Close Adj Close Returns Returns Return 0% 100.00%12/1/2014 33.12 38.98 -5.07% -0.59% -2.83% 10% 90.00%11/3/2014 34.89 39.21 1.57% 15.46% 8.52% 20% 80.00%10/1/2014 34.35 33.96 0.17% 1.62% 0.90% 30% 70.00%

9/2/2014 34.29 33.42 0.79% 5.96% 3.38% 40% 60.00%8/1/2014 34.02 31.54 -1.79% 7.28% 2.74% 50% 50.00%7/1/2014 34.64 29.4 1.97% -4.14% -1.08% 60% 40.00%6/2/2014 33.97 30.67 -0.32% 12.80% 6.24% 70% 30.00%5/1/2014 34.08 27.19 -0.64% 6.67% 3.01% 80% 20.00%4/1/2014 34.3 25.49 3.13% -1.81% 0.66% 90% 10.00%3/3/2014 33.26 25.96 9.84% -0.19% 4.82% 100% 0.00%2/3/2014 30.28 26.01 -4.18% 13.14% 4.48%1/2/2014 31.6 22.99

Mean 0.50% 5.11% 2.80% 2.80%Variance 0.001435 0.00404319 0.0009708 0.0009708Std Devn 0.037879 0.06358609 0.03115771Covariance -0.000797Correlation -0.331067

Portfolio risk and return% AT&T 50%% BestBuy 50%Exp Portfolio return 2.80%Exp Portfolio variance 0.000971

𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒=𝑋_𝑇^2 𝑉𝑎𝑟(𝑟_𝑇 )+𝑋_𝐵^2 𝑉𝑎𝑟(𝑟_𝐵 )+2𝑋_𝑇^ 𝑋_𝐵^ 𝐶𝑜𝑣𝑎𝑟(𝑟_𝑇,𝑟_𝐵 )

Page 2: Minimum Variance Portfolio VIDEO DILAN

Mean Variance Stdev5.11% 0.004043 6.36%4.65% 0.003146 5.61%4.19% 0.00239 4.89%3.73% 0.001775 4.21%3.26% 0.001302 3.61%2.80% 0.000971 3.12%2.34% 0.000781 2.79%1.88% 0.000732 2.71%1.42% 0.000825 2.87%0.96% 0.001059 3.25%0.50% 0.001435 3.79%

𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒=𝑋_𝑇^2 𝑉𝑎𝑟(𝑟_𝑇 )+𝑋_𝐵^2 𝑉𝑎𝑟(𝑟_𝐵 )+2𝑋_𝑇^ 𝑋_𝐵^ 𝐶𝑜𝑣𝑎𝑟(𝑟_𝑇,𝑟_𝐵 )

2.00% 3.00% 4.00% 5.00% 6.00% 7.00%0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

Column J

Axis Title

Axis Title

Page 3: Minimum Variance Portfolio VIDEO DILAN

2.00% 3.00% 4.00% 5.00% 6.00% 7.00%0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

Column J

Axis Title

Axis Title

Page 4: Minimum Variance Portfolio VIDEO DILAN

50% 50%GT EMC AT&T(T) Best Buy(B) Portfolio AT&T Best Buy

Date Adj CloseAdj Close Returns Returns Return -20% 120.00%12/1/2014 9.5 14.04 0.208651 0.086687 14.77% 0% 100.00%11/3/2014 8.42 14.32 -0.113684 0.019943 -4.69% 20% 80.00%10/1/2014 8.54 13.61 0.014252 -0.049581 -1.77% 40% 60.00%

9/2/2014 8.71 11.16 0.019906 -0.180015 -8.01% 50% 50.00%8/1/2014 8.7 11.24 -0.001148 0.007168 0.30% 60% 40.00%7/1/2014 9.09 11.4 0.044828 0.014235 2.95% 80% 20.00%6/2/2014 10.95 10.97 0.20462 -0.037719 8.35% 100% 0.00%5/1/2014 10.98 10.77 0.00274 -0.018232 -0.77% 120% -20.00%4/1/2014 10.74 11.54 -0.021858 0.071495 2.48%3/3/2014 10.08 12.87 -0.061453 0.115251 2.69%2/3/2014 12.62 13.42 0.251984 0.042735 14.74%1/2/2014 14.66 14.87 0.161648 0.108048 13.48%

15.44 13.1 0.053206 -0.119032 -3.29%14.46 12.66 -0.063471 -0.033588 -4.85%13.35 12.32 -0.076763 -0.026856 -5.18%11.87 13.12 -0.110861 0.064935 -2.30%14.39 14.06 0.2123 0.071646 14.20%

14.9 13.71 0.035441 -0.024893 0.53%17.41 13.69 0.168456 -0.001459 8.35%

16.8 12.86 -0.035037 -0.060628 -4.78%15.59 12.94 -0.072024 0.006221 -3.29%15.64 13.96 0.003207 0.078825 4.10%17.13 13.93 0.095268 -0.002149 4.66%17.38 13.62 0.014594 -0.022254 -0.38%15.64 13.4 -0.100115 -0.016153 -5.81%14.33 14.02 -0.08376 0.046269 -1.87%14.48 13.63 0.010468 -0.027817 -0.87%

14 13.51 -0.033149 -0.008804 -2.10%12.72 12.8 -0.091429 -0.052554 -7.20%

11.1 10.97 -0.127358 -0.142969 -13.52%11 10.15 -0.009009 -0.074749 -4.19%

13.6 11.65 0.236364 0.147783 19.21%14.5 11.98 0.066176 0.028326 4.73%

15.33 12.25 0.057241 0.022538 3.99%16.85 13.11 0.099152 0.070204 8.47%20.99 13.2 0.245697 0.006865 12.63%24.69 13.99 0.176274 0.059848 11.81%24.62 13.96 -0.002835 -0.002144 -0.25%31.19 13.85 0.266856 -0.00788 12.95%33.26 15.18 0.066367 0.096029 8.12%35.47 16.89 0.066446 0.112648 8.95%34.76 18.1 -0.020017 0.07164 2.58%28.72 18.51 -0.173763 0.022652 -7.56%27.66 19.66 -0.036908 0.062129 1.26%30.41 20.8 0.099422 0.057986 7.87%30.15 25.39 -0.00855 0.220673 10.61%28.75 19.27 -0.046434 -0.24104 -14.37%28.22 18.53 -0.018435 -0.038402 -2.84%

25.2 15.83 -0.107016 -0.14571 -12.64%27.1 15.54 0.075397 -0.01832 2.85%25.8 14.34 -0.047971 -0.07722 -6.26%

Page 5: Minimum Variance Portfolio VIDEO DILAN

26.78 15.4 0.037985 0.073919 5.60%25.41 17.44 -0.051158 0.132468 4.07%17.83 14.69 -0.298308 -0.157684 -22.80%19.63 15.01 0.100953 0.021784 6.14%19.61 15.28 -0.001019 0.017988 0.85%15.31 11.96 -0.219276 -0.217277 -21.83%

8.92 11.78 -0.417374 -0.01505 -21.62%6.43 10.57 -0.279148 -0.102716 -19.09%5.97 10.47 -0.07154 -0.009461 -4.05%6.17 11.04 0.033501 0.054441 4.40%4.44 10.5 -0.280389 -0.048913 -16.47%6.26 11.4 0.40991 0.085714 24.78%

10.99 12.53 0.755591 0.099123 42.74%11.45 11.75 0.041856 -0.062251 -1.02%11.26 13.1 -0.016594 0.114894 4.92%17.02 15.06 0.511545 0.149618 33.06%16.49 15.9 -0.03114 0.055777 1.23%17.03 17.04 0.032747 0.071698 5.22%12.88 16.47 -0.243688 -0.033451 -13.86%13.71 16.83 0.064441 0.021858 4.31%

14.1 17.47 0.028446 0.038027 3.32%13.34 16.67 -0.053901 -0.045793 -4.98%12.99 17.49 -0.026237 0.04919 1.15%12.64 18.04 -0.026944 0.031447 0.23%13.43 19.01 0.0625 0.053769 5.81%

11.9 18.62 -0.113924 -0.020515 -6.72%9.94 18.3 -0.164706 -0.017186 -9.09%

10.67 19.79 0.073441 0.081421 7.74%9.24 18.24 -0.134021 -0.078322 -10.62%

10.75 20.31 0.16342 0.113487 13.85%10.22 21.02 -0.049302 0.034958 -0.72%

9.56 21.49 -0.064579 0.02236 -2.11%11.85 22.9 0.23954 0.065612 15.26%11.88 24.89 0.002532 0.0869 4.47%14.18 27.21 0.193603 0.09321 14.34%14.98 26.56 0.056417 -0.023888 1.63%18.15 28.34 0.211616 0.067018 13.93%17.73 28.47 -0.023141 0.004587 -0.93%16.77 27.55 -0.054145 -0.032315 -4.32%16.17 26.08 -0.035778 -0.053358 -4.46%12.46 22.59 -0.229437 -0.133819 -18.16%10.09 20.99 -0.190209 -0.070828 -13.05%14.36 24.51 0.423191 0.167699 29.54%13.99 23.01 -0.025766 -0.0612 -4.35%14.17 21.54 0.012866 -0.063885 -2.55%

13 25.76 -0.082569 0.195915 5.67%12.86 27.69 -0.010769 0.074922 3.21%11.22 29.88 -0.127527 0.07909 -2.42%10.98 28.21 -0.02139 -0.05589 -3.86%10.45 23.85 -0.04827 -0.154555 -10.14%11.81 25.63 0.130144 0.074633 10.24%11.45 26.21 -0.030483 0.02263 -0.39%

12.2 26.29 0.065502 0.003052 3.43%12.19 27.27 -0.00082 0.037277 1.82%

Page 6: Minimum Variance Portfolio VIDEO DILAN

11.41 24.42 -0.063987 -0.10451 -8.42%12.6 24.82 0.104295 0.01638 6.03%

13.81 25.3 0.096032 0.019339 5.77%13.75 24.61 -0.004345 -0.027273 -1.58%

12.985 23.01 -0.055636 -0.065014 -6.03%12.605 23.89 -0.029265 0.038244 0.45%12.495 22.43 -0.008727 -0.061113 -3.49%

15.14 24.76 0.211685 0.103879 15.78%15.299 23.62 0.010502 -0.042003 -1.58%

18.5 26.15 0.209229 0.107113 15.82%20.12 25.78 0.087568 -0.014149 3.67%

22.451 25.56 0.115855 -0.004655 5.56%20.97 24.071 -0.063739 -0.058255 -6.10%22.26 23.85 0.061516 -0.009181 2.62%23.85 25.15 0.071429 0.054507 6.30%

Mean 2.05% 0.90% 1.47% 1.47%Variance 0.024075 0.00649968 0.0106535 0.0106535Std Devn 0.155162 0.0806206 0.1032158Covariance 0.006019Correlation 0.481202

Portfolio risk and return% AT&T 3%% BestBuy 97%Exp Portfolio return 0.93%Exp Portfolio variance 0.006487

𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒=𝑋_𝑇^2 𝑉𝑎𝑟(𝑟_𝑇 )+ _𝑋 𝐵^2 ( _𝑉𝑎𝑟 𝑟 𝐵 )+2 _ ^ _𝑋 𝑇 𝑋 𝐵^ 𝐶𝑜𝑣 ( _𝑎𝑟 𝑟 𝑇, _𝑟 𝐵 )

Page 7: Minimum Variance Portfolio VIDEO DILAN

Mean Variance Stdev0.66% 0.007433 8.62%0.90% 0.0065 8.06%1.13% 0.007049 8.40%1.36% 0.009081 9.53%1.47% 0.010654 10.32%1.59% 0.012596 11.22%1.82% 0.017594 13.26%2.05% 0.024075 15.52%2.29% 0.032039 17.90%

6.00% 8.00% 10.00%12.00%14.00%16.00%18.00%20.00%0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

0.66%0.90%

1.13%1.36%

1.47%1.59%

1.82%2.05%

2.29%

Column J

Risk (Std Dev)

Retu

rn

Page 8: Minimum Variance Portfolio VIDEO DILAN

𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒=𝑋_𝑇^2 𝑉𝑎𝑟(𝑟_𝑇 )+ _𝑋 𝐵^2 ( _𝑉𝑎𝑟 𝑟 𝐵 )+2 _ ^ _𝑋 𝑇 𝑋 𝐵^ 𝐶𝑜𝑣 ( _𝑎𝑟 𝑟 𝑇, _𝑟 𝐵 )