# 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 Ă˘â‚¬â€ś0.006 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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 T1 T2 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? 