1. Asset Allocation. This is a comprehensive problem solving question about asset allocation. The ultimate goal is to find the optimal asset allocation in a simplified scenario with TWO risky-assets (stocks) and one risk-free asset. We will break down this huge question into several steps, which may help you understand the important concepts related to the problem. Information about the assets is provided below. There are two stocks available on the market, Stock A and Stock B. There are no restrictions on stock trading, which means you may buy stocks, short-sale stocks, or buy on margin. The expected return and volatility of the two stocks are calculated using historic data, and are provided as follows

Stock A: Expected return E [rA] = 8%, volatility A = 10%

Stock B: Expected return E [rB ] = 10%, volatility B = 15%

The correlation between the returns of the two stocks is given by AB = 0.5 The rate on the risk-free asset is fixed at rf = 5%. You may invest in the risk-free asset and earn the risk-free rate, or you may also borrow from the risk-free asset and pay the same rate. Suppose you have mean-variance preference and your utility function has the following form U = E [r] 1 A^2 where your risk aversion coefficient is A = 5.

a) Suppose you can invest in both Stock A and Stock B, but not the risk-free asset. In risk-return space (volatility on the horizontal axis and return on the vertical axis), draw an approximation of the set of portfolios combining the two stocks. Label the axis and the two stocks. Label the efficient frontier and the global minimum variance portfolio. Label the risk-free asset as well.

b) Among the set of portfolios combining the two stocks as you plotted in (a), the portfolio that has the highest Sharpe ratio is what we call the tangency portfolio. Use the following formula to calculate the weight of Stock A in the tangency portfolio. Also calculate the weight of Stock B (which is 1 wA ).

c) Following (b), what is the expected return and volatility of the tangency portfolio ? What is the Sharpe ratio of the tangency portfolio?

(d) On the graph of (a), draw the best capital allocation line, and label the tangency portfolio.