solution
The following tables shows the mean returns and closing share prices yesterday of 2 stocks, Unley and Hess, and their variance-covariance matrix.
| Variance-Covariance Matrix | |||||
| Assets | Mean Return | Closing Price | Unley | Hess | |
| Unley | 10% | $20 | Unley | 0.04 | |
| Hess | 20% | $60 | Hess | –0.006 | 0.09 |
The risk free borrowing rate is 4% and risk free lending rate is 2.5% respectively.
Using Excel Solver, the T1 and T2 tangential portfolios using investments in Unley and Hess are as follows:
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| Unley | 0.511475 | 0.484756 |
| Hess | 0.488525 | 0.515244 |
| Mean Return | 0.148852 | 0.151524 |
| Standard Deviation | 0.170132 | 0.174055 |
a) Using investments in Unley and Hess only, show how you can construct portfolio A that has the lowest risk. What are the weights of Unley and Hess in portfolio A? How many stocks each of Unley and Hess should be purchased to construct a $100,000 portfolio A? What is the expected return and standard deviation of portfolio A?
b) Using investments in Unley and Hess only, show how you can construct portfolio B that generates an expected return of 23%. What are the weights of Unley and Hess in portfolio B? What is the standard deviation of portfolio B?
c) Allowing risk free borrowing and/or lending, and investments in Unley and Hess, show how you can construct portfolio C that also generates an expected return of 23% but has lower risks than portfolio B. What are the weights of each investment that make up portfolio C? Show the amount invested in each asset to produce a $100,000 portfolio C. What is the standard deviation of portfolio C?
(Leave your answers to 4 decimal places)
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