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2. With the data on AAPL, TM, SBUX, FB and S&P 500 index optimize the portfoio in the following ways and find the percentage investment on each asset a. Global minimum variance portfolio b. Minimum variance portfolio when expected return is 0.15% c. Tangency portfolio when risk free rate is 0.025% estment on each asset sbux aapl TM 0.009353235 0.000168633 -0.012086183 0.002373145 0.007669583 0.002051588 0.010597561 0.007137535 -0.005004841 -0.007139669 -0.008420889 0.003963027 -0.002022474 0.006642572 0.003492043 0.026570583 0.019211451 0.003252841 -0.00427723 0.023438784 0.005702121 0.011455015 0.012652164 0.005443007 -0.002722423 0.004902753 0.000751925 0.004913699 0.005901796 0.011720495 0.010540052 0.00696237 0.002524848 0.001827947 -0.002097613 -0.002074067 0.003649289 0.008174413 0.002078377 0.00074856 0.02702703 -0.004148133 -0.001389235 -0.006240617 0.004091067 0.008667791 -0.025573162 -0.006296807 0.003076624 0.012656298 -0.006336708 -0.011211053 -0.015028301 -0.002325733 0.007915341 0.004904168 -0.005639946 -0.002440877 0.002091593 0.005066914 -0.010000017 -0.006338958 -0.01572608 0.00612506 -0.016570632 -0.010396766 -0.015059217 0.001503005 0.003476223 0.00889176 0.004265406 0.009699846 -0.009243343 -0.020685831 0.013952432 -0.008244754 -0.018231504 -0.002631822 0.021439491 0.018079179 0.001960155 -0.000963762 -0.006910409 -0.03288183 0.008146676 0.011004134 0.012370622 0.003615058 0.016726717 -0.010451891 0.015361764 0.011256306 -0.008465339 0.02003345 -0.007550413 0.000783262 -0.003068778 -0.012549005 -0.008374423 -0.000923416 0.010405063 0.006156322 0.005648513 -0.004087709 0.002431738 -0.021956716 -0.026126801 0.021676164 -0.007204715 0.006970339 0.010033678 -0.000105186 -0.007968428 -0.00068246 0.009571918 0.025314422 -0.009181909 -0.013336172 -0.015351769 0.005744045 -0.017740241 -0.001446592 0.006929553 0.014728059 0.008611664 -0.009075074 0.001377228 0.016198518 0.005418652 -0.004760861 -0.010522151 0.004858054 0.012331268 -0.003253736 -0.000982059 0.007245568 0.007643305 0.018223093 0.004378641 0.004266754 -0.001782311 0.00685076 -0.001966953 -0.004240381 -0.004123721 -0.004335797 0.014867313 -0.003312629 0.003800447 -0.015459298 0.00228501 -0.00481149 -0.00433678 -0.013057011 -0.011254646 0.001652155 0.007349902 0.022845682 0.000899648 0.008338502 -0.005407487 0.003745318 -0.000620206 0.013474054 0.008209 0.022548624 0.008163601 0.007993982 0.048755812 0.004704254 -0.002496674 -0.018711439 0.018191551 -0.00154587 -0.005111032 -0.01575572 0.013418801 0.000790367 -0.014705868 0.011422387 -0.021125354 -0.027129959 0.046899646 0.014320265 0.030363527 -0.015322215 0.003181547 -0.001938734 -0.002093385 -0.017498522 -0.022532978 -0.004055675 FB S&P 500 -0.00981419 0.014439495 -0.004711951 -0.004156046 0.0151008 0.010291407 0.006352533 -0.003418172 0.000878945 -0.004247195 -0.001596711 0.010675561 -0.001439317 -2.9034E-005 0.000160194 0.009644506 -0.000160168 0.004074739 -0.007847494 0.001597575 -0.004842607 -0.000314309 0.008678021 -0.001062058 -0.003698633 0.006126534 -0.002824679 -0.000303339 0.004775041 0.002758771 0.001772058 -0.000765724 -0.007156066 -0.001476028 0.003320343 -0.002956304 0.008636694 0.006124919 0.012644062 -0.004538542 -0.005531887 -0.004388503 0.002225103 0.00119608 0.000396408 -0.014173946 0.002694809 0.003944421 0.025452486 -0.01696133 0.010175033 -0.00191768 -0.005951919 0.01260144 -0.024334121 -0.006074711 0.012509866 0.013533671 -0.011500528 -0.003320174 0.004402154 0.012158422 0.004539477 -0.004872579 0.005609669 0.009012755 -0.003254149 -0.001745731 -7.7691E-005 -0.006139422 0.010105745 -0.014558906 0.00107742 -0.0023775 -0.016297686 0.002368562 -0.00507972 0.012236645 0.010839714 -0.008795775 0.004196084 -0.003965372 -0.008821481 0.003529667 0.001405324 0.006608815 0.003898027 -0.002061904 -0.00450417 0.002682533 0.00218425 0.004457481 0.002101689 0.005202865 0.001941898 -0.004581281 0.009690673 0.001629759 -0.01044226 0.005148196 0.001319041 -0.000778444 -0.009531212 -0.011311245 0.000469387 0.009235131 -0.002658711 -0.001480605 0.008075945 0.00508748 0.011977864 0.002357716 -0.000845446 0.0022528 0.015923131 -0.004141314 0.009161747 0.002769232 -0.007428016 -0.003740336 -0.009448938 -0.010128907 -0.01030213 0.010923002 0.012337042 0.002940749 -0.002284927 -0.011837384