Essentials of Investments (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
10th Edition
ISBN: 9780077835422
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 6, Problem 4WM
a
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.
a
Expert Solution
Explanation of Solution
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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See the chart below. The top line shows the 90 day yield on corporate bonds and
the bottom line is the US Treasury bill (TB) rate for similar maturity. The yield is
shown on the y-axis. Notice that the gap between the two curves got wider during
the recession years of 2008-2009.
Which of the following reasons can possibly explain this widening?
FRED
6
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5
4
3
2
1
0
-1
2006
·
1950
2008
2010
2012
2014
Shaded areas indicate US recessions - 2014 research.stlouisfed.org
A) During the recession, the government decided to cut the tax rate on interest
earned from corporate bonds but not on interest earned on TB.
B) During the recession, the relative risk on corporate bonds increased.
C) During the recession, the relative liquidity of corporate bonds increased.
D) Two of the first three options can explain this.
E) All of the first three options can explain this.
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Chapter 6 Solutions
Essentials of Investments (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
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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