Loose-Leaf Essentials of Investments
Loose-Leaf Essentials of Investments
10th Edition
ISBN: 9781259604966
Author: Kane, Alex, Marcus Professor, Alan J., Bodie Professor, Zvi
Publisher: McGraw-Hill Education
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Portfolio Management
Portfolio management is the process by which an investor decides that how the person will invest in a variety of assets in order to get a desired return in the future. A portfolio means a pool of assets that includes securities, bonds, and other investme…
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Chapter 6, Problem 4WM

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Summary Introduction

To determine: The efficient frontier is the combination of portfolios that best meets the expectation of optimum risk and return tradeoff thus making the combination efficient. Now to make a efficient frontier we have to choose the time period from 2008 to 2018. For this visit the website www.portfoliovisualizer.com and feed the data by choosing the asset class and weights of them on historical portfolio.

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The efficient frontier:

We have chosen five asset class such as US stock market, European stock market, short term treasuries, REIT and Gold.

The Result is hereunder:

    Efficient Frontier
    Start Year 2008
    End Year 2018
    Geometric Returns No
    Efficient Frontier Assets
    # Asset CAGR Expected Return (*) Standard Deviation Sharpe Ratio (*) Min. Weight Max. Weight
    1 US Stock Market 8.28% 9.56% 15.31% 0.598 0.00% 100.00%
    2 European Stocks 0.42% 2.50% 20.14% 0.104 0.00% 100.00%
    3 Intermediate Term Treasury 3.19% 3.29% 4.41% 0.653 0.00% 100.00%
    4 REIT 7.05% 10.33% 24.23% 0.409 0.00% 100.00%
    5 Gold 3.14% 4.86% 18.31% 0.243 0.00% 100.00%
    Tangency Portfolio
    Asset Class Allocation
    US Stock Market 21.06%
    Intermediate Term Treasury 78.94%
    Asset Correlations
    Asset US Stock Market European Stocks Intermediate Term Treasury REIT Gold
    US Stock Market 1 0.88 -0.22 0.74 0.03
    European Stocks 0.88 1 -0.13 0.67 0.12
    Intermediate Term Treasury -0.22 -0.13 1 0.05 0.41
    REIT 0.74 0.67 0.05 1 0.08
    Gold 0.03 0.12 0.41 0.08 1
    Based on monthly returns from Jan 2008 to Nov 2018
    Efficient Frontier Points
    # US Stock Market European Stocks Intermediate Term Treasury REIT Gold Expected Return (*) Standard Deviation (*) Sharpe Ratio (*)
    1 0.00% 100.00% 0.00% 0.00% 0.00% 2.50% 20.14% 0.104
    2 0.00% 90.30% 9.70% 0.00% 0.00% 2.58% 18.14% 0.119
    3 0.00% 80.60% 19.40% 0.00% 0.00% 2.66% 16.14% 0.139
    4 0.00% 70.89% 29.11% 0.00% 0.00% 2.73% 14.16% 0.164
    5 0.00% 61.19% 38.81% 0.00% 0.00% 2.81% 12.21% 0.196
    6 0.00% 51.49% 48.51% 0.00% 0.00% 2.89% 10.30% 0.24
    7 0.00% 41.79% 58.21% 0.00% 0.00% 2.96% 8.46% 0.301
    8 0.00% 32.09% 67.91% 0.00% 0.00% 3.04% 6.75% 0.389
    9 0.00% 22.39% 77.61% 0.00% 0.00% 3.12% 5.28% 0.512
    10 0.00% 12.68% 87.32% 0.00% 0.00% 3.19% 4.33% 0.643
    11 0.52% 6.96% 92.52% 0.00% 0.00% 3.27% 4.14% 0.69
    12 1.67% 6.13% 92.20% 0.00% 0.00% 3.35% 4.11% 0.714
    13 2.82% 5.29% 91.88% 0.00% 0.00% 3.42% 4.08% 0.738
    14 3.98% 4.46% 91.56% 0.00% 0.00% 3.50% 4.05% 0.763
    15 5.13% 3.63% 91.25% 0.00% 0.00% 3.58% 4.02% 0.787
    16 6.28% 2.79% 90.93% 0.00% 0.00% 3.65% 3.99% 0.812
    17 7.43% 1.96% 90.61% 0.00% 0.00% 3.73% 3.97% 0.836
    18 8.59% 1.12% 90.29% 0.00% 0.00% 3.81% 3.95% 0.86
    19 9.74% 0.29% 89.97% 0.00% 0.00% 3.89% 3.93% 0.884
    20 10.96% 0.00% 89.04% 0.00% 0.00% 3.96% 3.91% 0.908
    21 12.23% 0.00% 87.77% 0.00% 0.00% 4.04% 3.91% 0.929
    22 13.49% 0.00% 86.51% 0.00% 0.00% 4.12% 3.91% 0.947
    23 14.75% 0.00% 85.25% 0.00% 0.00% 4.20% 3.93% 0.963
    24 16.01% 0.00% 83.99% 0.00% 0.00% 4.27% 3.96% 0.975
    25 17.27% 0.00% 82.73% 0.00% 0.00% 4.35% 4.00% 0.985
    26 18.53% 0.00% 81.47% 0.00% 0.00% 4.43% 4.05% 0.992
    27 19.79% 0.00% 80.21% 0.00% 0.00% 4.51% 4.11% 0.996
    28 21.06% 0.00% 78.94% 0.00% 0.00% 4.58% 4.18% 0.998
    29 22.32% 0.00% 77.68% 0.00% 0.00% 4.66% 4.26% 0.997
    30 23.58% 0.00% 76.42% 0.00% 0.00% 4.74% 4.35% 0.994
    31 24.84% 0.00% 75.16% 0.00% 0.00% 4.82% 4.45% 0.99
    32 26.10% 0.00% 73.90% 0.00% 0.00% 4.90% 4.56% 0.984
    33 27.36% 0.00% 72.64% 0.00% 0.00% 4.97% 4.67% 0.977
    34 28.62% 0.00% 71.38% 0.00% 0.00% 5.05% 4.79% 0.969
    35 29.88% 0.00% 70.12% 0.00% 0.00% 5.13% 4.91% 0.96
    36 31.15% 0.00% 68.85% 0.00% 0.00% 5.21% 5.05% 0.95
    37 32.41% 0.00% 67.59% 0.00% 0.00% 5.29% 5.18% 0.94
    38 33.67% 0.00% 66.33% 0.00% 0.00% 5.37% 5.33% 0.93
    39 34.93% 0.00% 65.07% 0.00% 0.00% 5.44% 5.47% 0.919
    40 36.16% 0.00% 63.72% 0.00% 0.12% 5.52% 5.62% 0.909
    41 37.35% 0.00% 62.26% 0.00% 0.39% 5.60% 5.78% 0.898
    42 38.55% 0.00% 60.80% 0.00% 0.65% 5.68% 5.94% 0.887
    43 39.74% 0.00% 59.34% 0.00% 0.92% 5.76% 6.10% 0.877
    44 40.93% 0.00% 57.88% 0.00% 1.19% 5.84% 6.26% 0.866
    45 42.13% 0.00% 56.42% 0.00% 1.45% 5.92% 6.43% 0.856
    46 43.32% 0.00% 54.96% 0.00% 1.72% 5.99% 6.59% 0.846
    47 44.51% 0.00% 53.50% 0.00% 1.99% 6.07% 6.77% 0.837
    48 45.71% 0.00% 52.04% 0.00% 2.25% 6.15% 6.94% 0.827
    49 46.90% 0.00% 50.58% 0.00% 2.52% 6.23% 7.11% 0.818
    50 48.09% 0.00% 49.12% 0.00% 2.79% 6.31% 7.29% 0.809
    51 49.29% 0.00% 47.66% 0.00% 3.05% 6.39% 7.47% 0.8
    52 50.48% 0.00% 46.20% 0.00% 3.32% 6.47% 7.65% 0.792
    53 51.67% 0.00% 44.74% 0.00% 3.59% 6.55% 7.83% 0.784
    54 52.87% 0.00% 43.28% 0.00% 3.85% 6.63% 8.01% 0.776
    55 54.06% 0.00% 41.82% 0.00% 4.12% 6.71% 8.19% 0.768
    56 55.25% 0.00% 40.36% 0.00% 4.39% 6.78% 8.38% 0.761
    57 56.44% 0.00% 38.90% 0.00% 4.66% 6.86% 8.56% 0.754
    58 57.64% 0.00% 37.44% 0.00% 4.92% 6.94% 8.75% 0.747
    59 58.83% 0.00% 35.98% 0.00% 5.19% 7.02% 8.94% 0.74
    60 60.02% 0.00% 34.52% 0.00% 5.46% 7.10% 9.12% 0.733
    61 61.22% 0.00% 33.06% 0.00% 5.72% 7.18% 9.31% 0.727
    62 62.41% 0.00% 31.60% 0.00% 5.99% 7.26% 9.50% 0.721
    63 63.60% 0.00% 30.14% 0.00% 6.26% 7.34% 9.69% 0.715
    64 64.80% 0.00% 28.68% 0.00% 6.52% 7.42% 9.88% 0.709
    65 65.99% 0.00% 27.22% 0.00% 6.79% 7.50% 10.08% 0.704
    66 67.18% 0.00% 25.76% 0.00% 7.06% 7.58% 10.27% 0.698
    67 68.38% 0.00% 24.30% 0.00% 7.32% 7.66% 10.46% 0.693
    68 69.57% 0.00% 22.84% 0.00% 7.59% 7.74% 10.65% 0.688
    69 70.76% 0.00% 21.38% 0.00% 7.86% 7.82% 10.85% 0.683
    70 71.96% 0.00% 19.92% 0.00% 8.12% 7.90% 11.04% 0.678
    71 73.15% 0.00% 18.46% 0.00% 8.39% 7.98% 11.24% 0.673
    72 74.34% 0.00% 17.00% 0.00% 8.66% 8.06% 11.43% 0.669
    73 75.53% 0.00% 15.54% 0.00% 8.92% 8.14% 11.63% 0.665
    74 76.73% 0.00% 14.08% 0.00% 9.19% 8.22% 11.83% 0.66
    75 77.92% 0.00% 12.62% 0.00% 9.46% 8.30% 12.02% 0.656
    76 79.11% 0.00% 11.16% 0.00% 9.72% 8.38% 12.22% 0.652
    77 80.31% 0.00% 9.70% 0.00% 9.99% 8.46% 12.42% 0.648
    78 81.50% 0.00% 8.24% 0.00% 10.26% 8.54% 12.62% 0.644
    79 82.69% 0.00% 6.78% 0.00% 10.53% 8.62% 12.81% 0.641
    80 83.89% 0.00% 5.32% 0.00% 10.79% 8.70% 13.01% 0.637
    81 85.08% 0.00% 3.86% 0.00% 11.06% 8.78% 13.21% 0.634
    82 86.27% 0.00% 2.40% 0.00% 11.33% 8.87% 13.41% 0.63
    83 87.47% 0.00% 0.94% 0.00% 11.59% 8.95% 13.61% 0.627
    84 88.84% 0.00% 0.00% 0.00% 11.16% 9.03% 13.81% 0.624
    85 90.53% 0.00% 0.00% 0.00% 9.47% 9.11% 14.01% 0.62
    86 92.23% 0.00% 0.00% 0.00% 7.77% 9.19% 14.23% 0.617
    87 93.92% 0.00% 0.00% 0.00% 6.08% 9.27% 14.45% 0.613
    88 95.62% 0.00% 0.00% 0.00% 4.38% 9.35% 14.68% 0.609
    89 97.31% 0.00% 0.00% 0.00% 2.69% 9.43% 14.92% 0.605
    90 99.00% 0.00% 0.00% 0.00% 1.00% 9.51% 15.16% 0.6
    91 95.62% 0.00% 0.00% 4.38% 0.00% 9.59% 15.44% 0.595
    92 84.99% 0.00% 0.00% 15.01% 0.00% 9.68% 15.88% 0.583
    93 74.37% 0.00% 0.00% 25.63% 0.00% 9.76% 16.50% 0.566
    94 63.75% 0.00% 0.00% 36.25% 0.00% 9.84% 17.28% 0.545
    95 53.12% 0.00% 0.00% 46.88% 0.00% 9.92% 18.20% 0.522
    96 42.50% 0.00% 0.00% 57.50% 0.00% 10.00% 19.23% 0.499
    97 31.87% 0.00% 0.00% 68.13% 0.00% 10.08% 20.37% 0.475
    98 21.25% 0.00% 0.00% 78.75% 0.00% 10.16% 21.59% 0.452
    99 10.63% 0.00% 0.00% 89.37% 0.00% 10.25% 22.88% 0.43
    100 0.00% 0.00% 0.00% 100.00% 0.00% 10.33% 24.23% 0.409

Here the tangency portfolio has a Sharpe ratio of 0.998 and the allocation is given hereunder:

    Asset Class Allocation
    US Stock Market 21.06%
    Intermediate Term Treasury 78.94%

Increase in expected return increased the weight of US equity in Tangency portfolio. This shows that weight of any asset in a portfolio having maximum Sharpe ratio have direct proportional relationship with its expected return.

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Chapter 6 Solutions

Loose-Leaf Essentials of Investments

Ch. 6 - Prob. 1PSCh. 6 - When adding a risky asset to a portfolio of many...Ch. 6 - A portfolio’s expected return is 12%, its standard...Ch. 6 - An investor ponders various allocations to the...Ch. 6 - The standard deviation of the market-index...Ch. 6 - Suppose that the returns on the stock fund...Ch. 6 - Use the rate-of-return data for the stock and bond...Ch. 6 - Prob. 8PSCh. 6 - Prob. 9PSCh. 6 - Prob. 10PS
Ch. 6 - Prob. 11PSCh. 6 - Prob. 12PSCh. 6 - Prob. 13PSCh. 6 - Suppose that many stocks are traded in the market...Ch. 6 - You can find a spreadsheet containing annual...Ch. 6 - Assume expected returns and standard deviations...Ch. 6 - Prob. 17PSCh. 6 - Prob. 18PSCh. 6 - A project has a 0.7 chance of doubling your...Ch. 6 - Investors expect the market rate of return this...Ch. 6 - The following figure shows plots of monthly rates...Ch. 6 - Prob. 22PSCh. 6 - Prob. 23PSCh. 6 - Prob. 25CCh. 6 - Prob. 1CPCh. 6 - Prob. 2CPCh. 6 - Abigail Grace has a $900,000 fully diversified...Ch. 6 - Prob. 4CPCh. 6 - Prob. 5CPCh. 6 - Prob. 6CPCh. 6 - Prob. 7CPCh. 6 - Prob. 1WMCh. 6 - Following the procedures in the previous question,...Ch. 6 - Prob. 3WMCh. 6 - Prob. 4WM
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