FM+HW+10-Ch.9+Eff+portfolio.xlsm - 1 A B C D E F G 1 The following table shows the var-covar matrix and the mean return for six stocks a compute the

FM+HW+10-Ch.9+Eff+portfolio.xlsm - 1 A B C D E F G 1 The...

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KR 0.0052 0.0033 0.0015 0.0039 0.0068 0.0010 F 0.0033 0.0120 0.0034 0.0072 0.0063 0.0015 TGT 0.0015 0.0034 0.0046 0.0058 0.0039 0.0015 JNPR 0.0039 0.0072 0.0058 0.0379 0.0073 0.0023 AHO 0.0068 0.0063 0.0039 0.0073 0.0389 0.0023 KEY 0.0010 0.0015 0.0015 0.0023 0.0023 0.0018 Global mean variance portfolio (GMVP) KR <-- F TGT JNPR AHO KEY Sum <-- Mean <-- Variance <-- Sigma <-- Efficient portfolio Risk-free 0.45% KR <-- F TGT JNPR AHO KEY Sum <-- Mean <-- Variance <-- Sigma <-- Covar <-- , covariance between GMVP & efficient portfolio Proportion of GMVP 0.3 1. The following table shows the var-covar matrix and the mean return for six stocks: a) compute the variance portfolio(GMVP), b) compute the efficient portfolio aasuming a monthly trisk-free rate of 0.4 frontier as the expected return and standard deviation. Kroger KR Ford F Target TGT Juniper Networks JNPR Ahold AHO KeyCorp KEY Note that the book for vector; here we want a Transpose . Drawing the efficient frontier: By Proposition 2 of Chapter 9, the efficient frontier is the conv any two frontier portfolios. Thus combining the GMVP and the efficient portfolio will give us We do this below. 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 43 44
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Proportion of efficient <-- <-- Portfolio sigma <-- Data table: varying proportion of GMVP Sigma Mean 0.00% 0.00% <-- =B47, data table header -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Expected portfolio return 0% 5% -3% -2% -1% 0% 1% 2% 3% 4% 5% Expected return A B C D E F G 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
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0.24% 1 -0.89% 1 0.48% 1 0.44% 1 -1.46% 1 1.04% 1 combination of GMVP and the eficient portfolio. e global minmum 45%, c) show the Mean returns rmula for the GMVP is for a row a column vector, hence vex combination of s the whole frontier. H I J K L M N O 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 43 44
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10% 15% 20% 25% Portfolio Returns & Sigma Standard deviation H I J K L M N O 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
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SHRINKAGE: VAR-COV AS COMBINATION OF SAMPLE VAR-CO 0.5 KR F TGT JNPR AHO KEY Contains formula: Global mean variance portfolio KR <-- F TGT JNPR AHO KEY Sum <-- Mean <-- Variance <-- Sigma <-- Efficient portfolio Risk-free 0.45% KR <-- F TGT JNPR AHO KEY Sum <-- Mean <-- Variance <-- Sigma <-- Weight on sample var-cov 2. Repeat exercise 4 when the var-covar ma combination of sample matrix in exercise 4 a only the variances. Kroger KR Ford F Target TGT Juniper Networks JNPR Ahold AHO KeyCorp KEY Note that the book formula for the vector; here we want a column ve Transpose . Drawing the efficient frontier: By Proposition 2 of Chapter 9, the efficient frontier is the conve combination of any two frontier portfolios. Thus combining the GMVP and the efficient portfo give us the whole frontier. We do this below.
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