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LOS a, (Part 2): Calculate the expected return and the standard deviation of return for a portfolio of two or three assets.
Q1. Andy Green, CFA, and Sue Hutchinson, CFA, are considering adding alternative investments to the portfolio they manage for a private client. They have found that it is recommended that a large, well-diversified portfolio like the one that they manage should include a 5 to 10% allocation in alternative investments such as commodities, distressed companies, emerging markets, etc.. After much discussion, Green and Hutchinson have decided that they will not choose individual assets themselves. Instead of choosing individual alternative investments, they will add a hedge fund to the portfolio. They decide to divide up their research by having each of them take a different focus. In their research of hedge funds, Green focuses on hedge funds that have the highest returns. Hutchinson focuses on finding hedge funds that can allow the client’s portfolio to lower risk while, with the use of leverage, maintain the same level of return.
After completing their research into finding appropriate hedge funds, Green proposes two hedge funds: the New Horizon Emerging Market Fund, which takes long-term positions in emerging markets, and the Hi Rise Real Estate Fund, which holds a highly leveraged real estate portfolio. Hutchinson proposes two hedge funds: the Quality Commodity Fund, which takes conservative long-term positions in commodities, and the Beta Naught Fund, which manages an equity long/short portfolio that has the goal of targeting the portfolio’s market risk to zero. The Beta Naught Fund engages in short-term pair trading to capture additional returns while keeping the beta of the fund equal to zero. The table below lists the statistics for the client’s portfolio without any alternative investments and for the four hedge funds based upon recent data. The expected return, standard deviation and beta of the client portfolio and the hedge funds are expected to have the same values in the near future. The historical data shows that estimating a covariance between two portfolios with their respective betas and market variance produces fairly reliable and accurate estimates. The variance of the market return is 324(%2).
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Current Client Portfolio |
New Horizon |
Hi Rise Real Estate |
Quality Commodity |
Beta Naught |
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Average |
10% |
20% |
10% |
6% |
4% |
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Std. Dev. |
16% |
50% |
16% |
16% |
25% |
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Beta |
0.8 |
0.9 |
0.4 |
-0.2 |
0 |
Green and Hutchinson have decided to sell off 10% of the current client portfolio and replace it with one of the four hedge funds. They have agreed to select the hedge fund that will provide the highest Sharpe Ratio when 10% of the client’s portfolio is allocated to that hedge fund.
As an alternative to investing 10% in one hedge fund, Green and Hutchinson have discussed investing 5% in the Beta Naught Fund and 5% in one of the other three hedge funds. This new 50/50 hedge fund portfolio would then serve as the 10% allocation in alternative investments for the client’s portfolio.
Green and Hutchinson divided up their research into return enhancement and diversification benefits. Based upon the stated goals of their research, which of the two approaches is more likely to lead to an appropriate choice? The focus of:
A) Hutchinson’s research.
B) neither manager is appropriate and will not achieve a meaningful result.
C) Green’s research.
Q2. Of the proposed hedge funds, which is most likely to introduce active risk into the client’s portfolio?
A) Hi Rise Real Estate Fund.
B) New Horizon Emerging Market Fund.
C) The Beta Naught Fund.
Q3. Which of the following is closest to the expected return of the client’s portfolio if 10% of the portfolio is invested in the New Horizon Emerging Market Fund?
A) 11.0%.
B) 10.2%.
C) 11.8%.
Q4. Which of the following is closest to the expected standard deviation of the client’s portfolio if 10% of the portfolio is invested in the Quality Commodity Fund?
A) 9.6%.
B) 14.2%.
C) 16.0%.
Q5. Which of the following is closest to the expected return of a portfolio that consists of 90% of the original client’s portfolio, 5% of the Hi Rise Real Estate Fund and 5% in the Beta Naught Fund?
A) 9.7%.
B) 9.0%.
C) 10.4%.
Q6. There was a discussion of allocating 5% each in Beta Naught and one of the other funds. When combined with Beta Naught in a 50/50 portfolio, which of the other three funds will produce a portfolio that has the lowest standard deviation?
A) New Horizon only.
B) Quality Commodity only.
C) Either Hi Rise or Quality Commodity.
Q6. Joe Janikowski owns a portfolio consisting of 2 stocks. Janikowski has compiled the following information:
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Stock |
Topper Manufacturing |
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Base Construction |
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Expected Return (percent |
12 |
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11 |
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Standard Deviation (percent) |
10 |
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15 |
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Portfolio Weighting (percent) |
75 |
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25 |
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Correlation |
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0.22 |
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The expected return for the portfolio is:
A) 11.75%.
B) 11.50%.
C) 12.00%.
Q7. The standard deviation of the portfolio is closest to:
A) 0.0839.
B) 0.0070.
C) 0.0909.
Q8. Which of the following statements is least accurate regarding modern portfolio theory?
A) All portfolios on the capital allocation line are perfectly negatively correlated.
B) The capital market line is developed under the assumption that investors can borrow or lend at the risk-free rate.
C) For a portfolio made up of the risk-free asset and a risky asset, the standard deviation is the weighted proportion of the standard deviation of the risky asset.
Q9. Given the following information, what is the expected return on the portfolio of the two funds?
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The Washington Fund |
The Jefferson Fund |
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Expected Return |
30% |
36% |
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Variance |
0.0576 |
0.1024 |
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Investment |
$2,000,000 |
$6,000,000 |
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Correlation |
0.40 |
A) 33.0%.
B) 31.5%.
C) 34.5%.
Q10. An analyst has estimated the returns on a specific real estate asset for three economic scenarios: contraction, expansion, and normal. The probability distribution for the state of the economy and the real estate returns are in the accompanying table.
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State of the Economy |
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Contraction |
Normal |
Expansion |
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Probability |
20% |
65% |
15% |
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Scenario return |
-5% |
15% |
25% |
The expected return on this real estate investment is approximately:
A) 12.50%.
B) 15.00%.
C) 14.50%.
[此贴子已经被作者于2009-4-2 10:39:30编辑过] | 
发表于 2009-4-2 10:37
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