6. An economy consists of 2 risky assets, A and B, and a riskless asset. The risk-free rate of return is rf = 3%. The Market portfolio M consists of 50% in stock A and 50% in stock B, and the covariance of the returns of A and B is 0.02 (cov(, B) =0.02). The following table summarizes information about the risky assets and about the Market portfolio, composed of these two assets (A and B). Expected Volatility of returns Return Stock A 7% 20% Stock B ? ? Market (M) 11% ? i) Find the expected return of B. ii) Find the cov(r, r) (3 marks) [Hint: note that we know the composition of the Market portfolio] (4 marks) iii) Assuming the assumptions of CAPM hold, compute: The risk premia of stocks A and B The betas of A and B with respect to the market. Hence find, the standard deviation of M, and the Sharpe ratio of M. The standard deviation of B iv) Using your answers above, show that the assumptions of the Single- Factor model (with the Market as the single factor) could not hold in this market. [Hint: use the covariance of A and B, the betas, and the variance of the market to get a contradiction] (4 marks) v) Consider an investor with the following "utility score" function: 1 U (ri) = E(ri) A where E(r) and of denote the expected value and the variance of the return r for a generic asset i. Discuss how would a financial advisor estimate investor's risk aversion? Assume that the investor's A equals 1 and that she optimally decides to put y* of her wealth in the Market portfolio M and 1-y* in the risk-free asset. Find y* and explain how the investor can achieve her optimal allocation if she starts with a wealth of 1,000. Then use an appropriate graph to draw the Capital Market Line and discuss the qualitative relationship between the risk aversion coefficient and the optimal allocation, y*, to the market portfolio. (12 marks) vi) Assuming that all of the parameters computed in parts i) to iv) remain the same, briefly discuss how would the optimal y* change if the investor could only borrow using a higher rate of 5%.