Finance homework need by 5-17-2015 by 12:00 midnight EASTERN TIME!
illmaticallday· All work must be shown on Microsoft excel meaning calculations or not accepted!!
Question #1: Capital Allocation:
1. What is the expected return on the mutual fund?
2. What is the standard deviation of returns for the mutual fund?
Now, assume the correlation between stock and bond returns is 0.35 and the correlations between stock and risk-free returns and between the bond and risk-free returns are 0 (by construction, correlations with the risk-free asset are always zero).
3. What is the standard deviation of returns for the mutual fund? Is it higher or lower than the standard deviation found in part 2? Why?
Now, assume that the standard deviation of the mutual fund portfolio is exactly 23.50% per year and a potential customer has a risk-aversion coefficient of 3.15.
4. What correlation between the stock and bond returns is consistent with this portfolio standard deviation?
5. What is the optimal allocation to the risky mutual fund (the fund with exactly 23.50% standard deviation) for this investor?
6. What is the expected return on the complete portfolio?
7. What is the standard deviation of the complete portfolio?
8. What is the Sharpe ratio of the complete portfolio?
Question #2: Markowitz Optimization:
Open the associated Excel file named QPS2 Data Spring 2015 Problem 2 in My Course Content: Problem Set Spreadsheets. The data file includes 60 months of returns for 11 exchange traded funds; their names and ticker symbols follow:
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Ticker |
Name of Exchange Traded Fund |
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1 |
SPY |
SPDR S&P 500 ETF |
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2 |
MDY |
SPDR S&P MidCap 400 ETF |
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3 |
IWM |
iShares Russell 2000 ETF |
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4 |
QQQ |
Power Shares QQQ ETF |
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5 |
EFA |
iShares MSCI EAFE ETF |
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6 |
VWO |
Vanguard FTSE Emerging Markets Stock Index ETF |
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7 |
VNQ |
Vanguard REIT Index ETF |
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8 |
BND |
Vanguard Total Bond Market ETF |
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9 |
PFF |
iShares US Preferred Stock ETF |
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10 |
GLD |
SPDR Gold Shares ETF |
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11 |
JNK |
SPDR Barclays High Yield Bond ETF |
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All students will do problem 2 using 9 of the above ETFs; all students will include the first 8 ETFs listed above: SPY, MDY, IWM, QQQ, EFA, VWO, VNQ, and BND. All students will include one of the last 3 ETFs: PFF, GLD, and JNK as instructed on your version.
Version C: Include JNK and exclude PFF and GLD.
Use the data on your 9 ETFs to answer the following questions:
1. What is the average return for each of the nine indexes?
2. Show the covariance matrix of returns. Briefly describe how you constructed the covariance matrix.
Consider the simple case where short sales are allowed, but short positions must be greater than or equal to –50% and long positions must be less than or equal to 50%. Use Excel Solver to find the Minimum Variance Portfolio (MVP).
3. What is the expected portfolio return for the MVP portfolio?
4. What is the portfolio standard deviation for the MVP portfolio?
5. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?
Consider the simple case where short sales are allowed, but short positions must be greater than or equal to –75% and long positions must be less than or equal to 75%. Use Excel Solver to find the Maximum return portfolio with a standard deviation of exactly 3.25%.
6. What is the expected portfolio return for this portfolio?
7. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?
Consider the more realistic case where short sales are NOT allowed and no more than 35% of the portfolio and no less than 5% is invested in any ETF. Use Excel Solver to find the Minimum Variance Portfolio (MVP).
8. What is the expected portfolio return for the MVP portfolio?
9. What is the portfolio standard deviation for the MVP portfolio?
10. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?
Consider the simple case where short sales are NOT allowed and no more than 25% and no less than 4% of the portfolio is invested in any ETF. Use Excel Solver to find the Market Portfolio if the risk-free rate is 0.1250%/month (1.50%/year).
11. What is the expected portfolio return for this portfolio?
12. What is the portfolio standard deviation for this portfolio?
13. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?
14. What is the maximum Sharpe ratio?