Question: Problem 1: You have the choice between two risky assets. Asset 1 has expected return 4% and standard deviation 2%. Asset 2 has expected return

Problem 1:

You have the choice between two risky assets. Asset 1 has expected return 4% and standard deviation 2%. Asset 2 has expected return 5% and standard deviation 3%. Both asset returns are correlated with correlation coefficient 0.1.

Q1: What is the expected return of the portfolio?

Q2: What is the variance of the portfolio return?

Q3: Formulate the problem of minimizing portfolio variance. Fractions invested must sum to 1. Short sales are allowed. There is no constraint on the expected return.

Q4: Reformulate the problem you found in Q3 as a function of one variable only.

Q5: Solve the problem you found in Q4. What is the smallest amount of risk, measured by the portfolio standard deviation, that you are able to achieve?

Q6: Formulate the problem of minimizing portfolio variance subject to the expected return between at least m. Short sales are allowed.

Q7: Reformulate the problem you found in Q7 as a function of one variable only.

Q8: Find the optimal solution to the problem you found in Q7 as a function of m.

Q9: Plot the shape of the efficient frontier, that is, m as a function of the optimal standard deviation. (You dont have to be very specific on the function values. I care about the shape of the function only.)

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