Question 2 a. A mean-variance investor has access to four risky portfolios but can only invest in one of them. She can, however, combine the chosen risky portfolio with the risk-free asset. The risk-free rate is 2% per annum and the four portfolios have the following characteristics; i. Identify the risky portfolio with the highest Sharpe ratio. (15 marks) ii. For each of the portfolios, construct a combination of the riskfree asset and the portfolio you identified in part (i). Show that the portfolio with the highest Sharpe ratio dominates all the other portfolios from the perspective of a greedy and riskaverse investor. (25 marks) iii. What is the efficient way to build a position which has return standard deviation of 50% ? Compute the portfolio weights and the expected return on this position. Comment on the size and sign of the weights. (10 marks) b. Using similar arguments to those you used in part (a), describe how an investor should optimally identify the tangency porffolio in a setting where she has access to N risky assets and a single risk-free asset. Then proceed to describe how the investor should form her optimal portfolio of the tangency portfolio and the risk-free asset. (30 marks) c. Is there a portfolio in part (a) that is a mean-preserving spread of another portfolio? How does the notion of mean-preserving spread relate to second order dominance and help us understand the choice of a greedy and risk-averse investor