Midterm Exam
Notes: 1. Answer all questions. Explain your answers with short essays. Please type them into your answer sheets. 2. State all assumptions and show your calculation results. 3. Due time: Tuesday next week (07/18) in class.
1.a) Explain the concept of mean-variance analysis for portfolio construction. What are the assumptions and limitation of these analyses? What is an efficient portfolio? Does it mean that every efficient portfolio will generate profits for investors?
- b) How would start your own investment plan & policy for the securities in the capital market? What are the procedures you need to follow? Is assessment of the past performance of the firm(s) and future prospective the so-called “investment”? Why or why not?
- c) What is the purpose of CAPM (Capital Asset Pricing Model)? State the setting of the model and explain its concept.
- You’re given with two firms’ financial information as the following. Perform the security analysis for these two firms to determine whether they are possible candidates for a part of your portfolio. The first firm X is in apparel industry and the second firm Y is of the computer industry.
Balance Sheet (in millions) of Company X
2013 2014 2015
Assets
Cash 230 210 970
Marketable securities 50 100 0
Accounts Receivable 1420 1350 1300
Inventory 1260 1578 1450
Plant, Building, and Equipments (net) 2873 1205 990
Investments in affiliates 0 430 1329
Total Assets 5833 4873 6039
Liabilities
Short-term debts 107 130 1030
Advances from customers 421 326 534
Accounts payable 685 792 657
Interest payable 75 98 62
Tax payable 147 120 128
Other Accrued Expenses 20 15 35
Bonds payable 3025 1976 1450
Stockholders’ Equity
Common stock 1001 1201 1875
Additional paid-in capital 74 156 144
Retained earning 278 59 124
Total liabilities and equities 5833 4873 6039
Income Statement(in millions) of Company X
2013 2014 2015
Net Sales 4629 4418 4983
Cost of Goods Sold 2215 3109 2310
Selling and General Expenses 771 812 759
Depreciation Expense 210 298 284
Interest Expense 97 109 121
Income Tax Expense 175 137 254
Net Income 1161 ( 47) 1255
Balance Sheet (in millions) of Company Y
2013 2014 2015
Assets
Cash 1230 210 970
Marketable securities 50 100 0
Accounts Receivable 1420 1350 1300
Inventory 1260 1508 1450
Plant, Building, and Equipments (net) 2073 205 960
Investments in affiliates 0 430 329
Total Assets 6033 3803 5009
Liabilities
Short-term debts 107 130 1030
Advances from customers 421 326 534
Accounts payable 685 792 657
Interest payable 75 98 62
Tax payable 147 120 128
Other Accrued Expenses 20 15 5
Bonds payable 3225 976 450
Stockholders’ Equity
Common stock 1001 1201 1875
Additional paid-in capital 74 86 144
Retained earning 278 59 124
Total liabilities and equities 6033 3803 5009
Income Statement(in millions) of Company Y
2013 2014 2015
Net Sales 4529 5418 5883
Cost of Goods Sold 2215 3109 3310
Selling and General Expenses 771 812 1059
Depreciation Expense 213 298 284
Interest Expense 97 109 621
Income Tax Expense 175 137 154
Net Income 1058 953 455
- a) How do you verify which firm is better for your investment?
- b) What are the limits of ratio analysis for these firms?
- Suppose you are given the following information. There are four funds in your portfolio. Let , be the rates of return for these four funds and let be the rate of return of market index. Assuming the returns follow the index model such that
Also let be the “beta” for these four funds, and the alpha’s are given as =, respectively. Let the variance and mean of market index return be shown as, . In addition, let the following matrix B represent the variance-covariance matrix of these funds’ idiosyncratic risks, where
Answer the following questions.
- Obtain the variance-covariance matrix of the returns of these four funds.
- Construct two efficient portfolios using the EXCEL spreadsheet. (Send in your Excel spreadsheet on-line)
- Construct the efficient frontier using EXCEL spreadsheet. (Send in your Excel spreadsheet on- line)
- If there exist a risk-free rate as 0.5%, calculate the optimal risky portfolio’s allocations and show its location on efficient frontier. Suppose you form an equally weighted portfolio of the assets, and suppose the number of assets increases to as many as possible. If the equally weighted portfolio have the alpha equal to zero, what will this condition imply on the “beta” of this equally-weighted portfolio?
- Suppose you’re given the following historical rates of return for two mutual funds and S&P 500 index, denoted as , and , respectively. Answer the following questions.
- a) If you fit the index model to the returns, what are the results of the estimation? How do you interpret them? Obtain the estimates of the variances for residuals in regressing , and on , respectively. Apply these for the variances of idiosyncratic risks in each fund.
- b) What are your forecasts for these funds’ rates of return if the historical averages are used? Suppose you want to form some efficient portfolios based on the estimates you obtained from (a) and (b), what are the optimal weights for these two funds in your portfolio?
| Date | Ra | Rb | Rm |
| 01/03/12 | 3.67% | 4.69% | 5.27% |
| 02/01/12 | 2.58% | 3.24% | 0.98% |
| 03/01/12 | 1.78% | 0.04% | 0.09% |
| 04/02/12 | -2.21% | -2.27% | -0.75% |
| 05/01/12 | -4.30% | -7.37% | -7.47% |
| 06/01/12 | 2.71% | 3.46% | 4.88% |
| 07/02/12 | 0.52% | 0.95% | 1.25% |
| 08/01/12 | 1.67% | 3.02% | 1.96% |
| 09/04/12 | 1.79% | 2.87% | 2.39% |
| 10/01/12 | -1.01% | -0.73% | -2.00% |
| 11/01/12 | 0.80% | 0.30% | 0.28% |
| 12/03/12 | 0.42% | 2.16% | 0.70% |
| 01/02/13 | 3.88% | 5.59% | 4.92% |
| 02/01/13 | 0.67% | 0.54% | 2.10% |
| 03/01/13 | 1.68% | 0.24% | 3.54% |
| 04/01/13 | 1.40% | -0.78% | 1.79% |
| 05/01/13 | 0.29% | 5.10% | 2.06% |
| 06/03/13 | -1.57% | -2.02% | -1.51% |
| 07/01/13 | 3.88% | 6.23% | 4.83% |
| 08/01/13 | -1.86% | -1.34% | -3.18% |
| 09/03/13 | 4.93% | 4.27% | 2.93% |
| 10/01/13 | 5.17% | 3.81% | 4.36% |
| 11/01/13 | 6.00% | 6.17% | 2.77% |
| 12/02/13 | 5.89% | 2.55% | 2.33% |
| 01/02/14 | -4.51% | -4.56% | -3.62% |
| 02/03/14 | 3.72% | 6.17% | 4.22% |
| 03/03/14 | -0.22% | 0.09% | 1.69% |
| 04/01/14 | -0.07% | -2.22% | 0.62% |
| 05/01/14 | 1.02% | 2.22% | 2.08% |
| 06/02/14 | 3.06% | 5.88% | 1.89% |
| 07/01/14 | -0.45% | -1.92% | -2.52% |
| 08/01/14 | 3.25% | 4.77% | 3.70% |
| 09/02/14 | -1.07% | -6.19% | -1.56% |
| 10/01/14 | 1.78% | 0.42% | 2.29% |
| 11/03/14 | 1.55% | 1.11% | 2.42% |
| 12/01/14 | -0.30% | 0.89% | -0.42% |
| 01/02/15 | -2.15% | -1.83% | -3.15% |
| 02/02/15 | 3.83% | 5.74% | 5.34% |
| 03/02/15 | -0.47% | -0.21% | -1.75% |
| 04/01/15 | 0.29% | -0.17% | 0.85% |
| 05/01/15 | 1.11% | 5.61% | 1.04% |
| 06/01/15 | -1.28% | -0.71% | -2.12% |
| 07/01/15 | 0.99% | 1.33% | 1.95% |
| 08/03/15 | -4.51% | -5.14% | -6.46% |
| 09/01/15 | -2.63% | -3.13% | -2.68% |
| 10/01/15 | 5.28% | 6.67% | 7.97% |
| 11/02/15 | 0.51% | 0.68% | 0.05% |
| 12/01/15 | -1.55% | -2.14% | -1.77% |
| 01/04/16 | -4.69% | -4.94% | -8.21% |
| 02/01/16 | -3.54% | -6.05% | -3.15% |
- c) Suppose your friend Tom forms his portfolio as (1/4, 3/4) in using the above two funds. Is his portfolio efficient? How would you verify the performance of his portfolio based on the historical information? What about the benchmark return for his portfolio?