Expected ReturnStandard Deviation

Asset A15%30%

Asset B20%40%

Risk-free Asset5%0%

Correlation between Assets A and B = 0

Assume the minimum variance portfolio consists of 64% A and 36% B. (It really is.)

1.Find the expected return and standard deviation of the minimum variance portfolio.

2.Graph the Investment Opportunity Set. Only include Asset A, Asset B and the Minimum Variance/Standard Deviation portfolio in your graph, but make sure to show their expected returns and standard deviations labeled on the axes.

3.On the graph from the previous problem, circle the portfolios that are inefficient. Why are they inefficient?

Assume you put 50% of your wealth in the risk-free asset and 50% into the minimum variance portfolio.

4.On a new graph, show where you are in Expected Return/Standard deviation space.

5.What is the expected return and standard deviation of the portfolio you created? Is it an efficient portfolio? If you answered "no," show another portfolio on the graph that clearly dominates it in Expected Return/Standard Deviation space.

Now assume that the correlation between Assets A and B is NEGATIVE 1 instead of 0.

6.Does this present an arbitrage opportunity given all other expected returns and standard deviations are otherwise correct as given? Describe PRECISELY how you would engage in arbitrage.

7.Using Calculus, show how to arrive at the minimum variance portfolio given in question 1. (64% Asset A and 36% Asset B.)