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fm3_chapter09 - A 1 2 B C D E F G CALCULATING THE EFFICIENT...

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CALCULATING THE EFFICIENT Variance-covariance matrix 0.40 0.03 0.02 0.00 0.06 0.02 0.03 0.20 0.00 -0.06 0.05 0.01 0.02 0.00 0.30 0.03 0.07 0.03 0.00 -0.06 0.03 0.10 0.08 0.04 Constant 0.04 Computing an envelope portfolio with constant = 0 z 0.1019 ### 0.0540 ### 0.5657 0.2998 0.1141 0.0605 1.1052 0.5857 Sum 1.0000 ### Computing an envelope portfolio with constant = 0.04 z 0.0330 ### 0.0423 ### 0.1959 0.2514 0.0468 0.0601 0.5035 0.6462 Sum 1.0000 ### E(x) 0.0693 E(x) 0.0710 ### Var(x) 0.0367 Var(y) 0.0398 ### Sigma(x) 0.1917 Sigma(y) 0.1995 ### Cov(x,y) 0.0376 ### Corr(x,y) 0.9842 ### A single portfolio calculation Proportion of x 0.3 7.05% ### 19.65% ### Data table: we vary the proportion of x to produce a graph of the frontier Proportion of x Sigma Return 0.1965 0.0705 <-- Data table header refers to cells B36 and B Expected returns E(r) Expected minus constant E(r) - c Envelope portfolio x Envelope portfolio y E(r p ) σ p A B C D E F G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
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-1.400 0.2199 0.0734 -1.200 0.2164 0.0730 -1.000 0.2131 0.0727 -0.800 0.2100 0.0724 -0.600 0.2070 0.0720 -0.400 0.2043 0.0717 -0.200 0.2018 0.0713 0.000 0.1995 0.0710 0.100 0.1984 0.0708 0.200 0.1974 0.0707 0.300 0.1965 0.0705 0.400 0.1956 0.0703 0.500 0.1948 0.0702 0.600 0.1941 0.0700 0.700 0.1934 0.0698 0.800 0.1927 0.0697 0.900 0.1922 0.0695 1.000 0.1917 0.0693 1.200 0.1909 0.0690 1.400 0.1903 0.0686 1.600 0.1901 0.0683 1.800 0.1901 0.0680 2.000 0.1903 0.0676 2.200 0.1908 0.0673 2.400 0.1916 0.0670 2.600 0.1927 0.0666 2.800 0.1940 0.0663 3.000 0.1956 0.0659 jumps in x for table 0.2 0.1850 0.1900 0.1950 0.200 0.0620 0.0640 0.0660 0.0680 0.0700 0.0720 0.0740 Portfolio x Portfolio y Proportio Proportio A B C D E F G 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
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T FRONTIER #MACRO? #MACRO? #MACRO? #MACRO? B35 H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
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000 0.2050 0.2100 0.2150 0.2200 0.2250 Proportion of x: -1.0 Proportion of y: 2 on of x: 2.8 on of y: -1.8 Portfolio w: 50% in x, 50% in y H 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
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Variance-covariance matrix 0.40 0.03 0.02 0.00 0.06 0.03 0.20 0.00 -0.06 0.05 0.02 0.00 0.30 0.03 0.07 0.00 -0.06 0.03 0.10 0.08 Computing an envelope portfolio with constant = -0.03 z 0.0502 ### 0.0475 0.2883 0.2730 0.0636 0.0603 0.6539 0.6192 Sum 1.0000 Computing an envelope portfolio with constant = 0.08 z -0.0359 ### 0.1093 -0.1740 0.5293 -0.0205 0.0625 -0.0982 0.2989 Sum 1.0000 Constant 0.01 Computing an envelope portfolio with constant = 0.01 z 0.0846 ### 0.0526 0.4732 0.2940 0.0973 0.0604 0.9548 0.5930 Sum 1.0000 Proportions of x and y which determine w Proportion of x 0.9183 ### Proportion of y 0.0817 ### Check: Multiply the above proportions times portfolios x and y to get w CALCULATING THE ENVELOPE All constants c lead to the same enve Expected returns Envelope portfolio x Envelope portfolio y Additional calculation: Fix another constant, and show that the resulting portfolio is a combination of the two above portfolios Envelope portfolio w A B C D E F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
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0.0526 ### 0.2940 ### 0.0604 0.5930 A B C D E F 41 42 43 44
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#MACRO?
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