Problems (40 points) Answer each of the questions below completely. Show all your work 13. (8 points) You own a portfolio of S10,000. The portfolio is composed of a risky asset with an expected rate of return of 12% and a standard deviation of 10%, and a Treasury bill with a rate of return of 5% () If you want your portfolio to have a standard deviation of 8%, how much money should be invested in the Treasury bill? (b) What is the Sharpe ratio (also known as the reward-to-variability ratio) in this case? 14. Portfolio Theory (12 points) The following table contains information regarding stock returns of IBM and Google. Expected Return Standard Deviation IBM 10.00% 20.00% Google 15.00% 30.00% In addition, you find the return correlation between IBM and Google is 0.2. The risk-free rate is 5% (a) What is the expected return of the minimum variance portfolio (MVP) constructed from the two stocks? (b) Consider a portfolio that invests equally in the two stocks (IBM and Google), what is the Sharpe ratio of this equal-weighted portfolio? (c) What is the standard deviation of the optimal risky portfolio (a.k.a. tangency portfolio) constructed from the two stocks? 15. (12 points) Consider the following data for an economy where a one-factor APT holds. All portfolios are well diversified. Portfolio E(r) Beta A 10% 1.0 F 896 0.6 a) What is the factor risk premium in this economy? (b) What is the risk-free rate in this economy? c) Suppose another portfolio E is well diversified with a beta of 0.8 and an expected return of 10%. Would an arbitrage opportunity exist? If yes, explain what would be your arbitrage strategy? 16. (8 points) What are the four common mistakes that investors tend to make when processing information