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) We can solve the optimal asset allocation problem with two risky-assets and one risk-free asset. We know that the optimal portfolio is a combination of the risk-free asset and the tangency portfolio.

1. Suppose you invest weight wp in the tangency portfolio, and 1 wp in the risk-free asset. Given the expected return and volatility of the tangency portfolio in (f), what is the optimal wp that maximize your utility? (Hint: w = E[r]rf ) A^2

2. Remember that the tangency portfolio is a combination of Stock A and Stock B, with weight wA in Stock A, and 1 wA in Stock B. Given the optimal weight wp, calculate the optimal weight in Stock A and Stock B implied by wp. Also calculate the optimal weight in the risk-free asset.

3. Calculate the expected return and volatility of the optimal portfolio in (2) that combines Stock A, Stock B, and the risk-free asset.

4. Calculate the utility of the optimal portfolio. This is the maximum utility you can get by investing in the two risk-assets and one risk-free asset.