Problem 1. [Finding tangency portfolio] Suppose we have two risky assets with the same variance 2=1. The correlation of these two assets is =0.5. The expected return for asset 1 is R1=1.3 and for asset 2 is R2=1.1. Assume the risk-free return is Rf=1.05. (a) Plot the minimum variance set. (b) Use the fact that the Sharpe ratio is maximized at the tangency portfolio to show that the tangency portfolio has the following form: 12=(1)(R1Rf+R2Rf)(R1R2)+(1)(R2Rf)=11 (c) Find the numerical value of tangency portfolio (1,2). Does short-selling happen? Explain your results. If no short-selling is allowed, what is the tangency portfolio? (d) Suppose Rf=1.25. What is the tangency portfolio? Does it make any sense? Explain. (e) Now, suppose that there is a new project with an expected payoff E(X)=10, and covariance Cov(X,R1)=4,Cov(X,R2)=2. Using the tangency portfolio as the market portfolio, what is the price of this project according to CAPM? [Hint: you need to calculate the covariance of the project and the tangency portfolio using the weight 1 and 2 from (b)]