Q3. Consider the following probability distribution for stocks A and B. Scenario Probability Return on Stock A Return on Stock B 1 0.3 2 0.5 3 0.2 7% 11% -16% -9% 14% 26% Assume that the risk-free rate is 3%. The correlation between A and B is -0.5. Please answer the following questions. (6 points.) 1. Suppose the tangency portfolio on the efficient frontier has expected return of 6.9%. Please solve for the optimal weights of the tangency portfolio. 2. Compute the reward-to-volatility ratios of Stock A and Stock B. Explain why tan- gency portfolio is superior to the individual stock A or B. Please provide quantita- tive argument. 4 3. Suppose two investors are making their capital allocation decisions. Investor 1 is more risk-averse than Investor 2. For each of the following choices, determine whether the resulting allocation is NOT consistent with Markowitz portfolio se- lection analysis (note: more than one of the allocations might not be consistent). Please briefly explain your choice(s). A. Both investors choose to invest 25% of their entire wealth in the risk-free asset. B. Investor 2 decides to invest 100% of his wealth in the tangency portfolio, while Investor 1 decides to invest 65% of his wealth in the tangency portfolio and 35% in the risk-free asset. C. Investor 2 decides to go with 100% of his wealth in Stock B. D. Investor 1 decides to invest 58% of his wealth in the tangency portfolio, while Investor 2 decides to invest 78% of his wealth in the tangency portfolio. 5