Minimum variance portfolio and the efficient set

Consider two stocks, A and B, with the following expected returns and standard deviations.

     Expected    Standard
       Return      Deviation
A     8.00%    20.00%
B    12.00%    30.00%

The correlation coefficient between the returns of A and B is 0.3. Short selling is allowed.

Q1. Consider a portfolio, P, that comprises 45% invested in stock A and 55% invested in stock B. What is the expected return, standard deviation and coefficient of variation of P?

Q2. Plot A and B in expected return-standard deviation space and draw (approximately) the feasible set for P. On this diagram, mark the minimum variance portfolio and the efficient set.

Q3. Draw (approximately) the feasible set, minimum-variance portfolio and efficient set when the correlation coefficient between A and B is (a) -1 and (b) +1.

Q4. Suppose that the correlation coefficient between A and B was -1. What are the weights of the minimum variance portfolio?

Q5. What would the risk free rate be if the correlation coefficient between A and B is -1?

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