I have some financial mathematics problems

Problem 3 [Required, 25 marks! The following table shows the expected return up and standard deviation up of 4 portfolios Expected return Standard n deviation op Portfolio 1 Portfolio 2 Portfolio 3 0.13 Portfolio 4 The return rate of riskfree asset is r}- = 0.04. You are given that some of the portfolios are efcient. Suppose that EAPM formula is valid. (a) Which portfolio is efcient? Explain your answer. (bl Suppose that expected return of a portfolio is 0.2, nd the amount of systematic risk {in term of variance] of the portfolio. [C] Is it possible to construct a portfolio with expected return ,up a 0.15 and op. S 0.3? Explain your answer. Problem 4 [Required, 25 marks! We consider a market with 1 riskfree asset and N risky assets. The following tables show the investment goal of three different investors: Investment goals m I Standard deviation of return a'. 5 0.2 I Expected return pp 2 0.15 I Standard deviation of return 0'. S 0.12 Investor C I Expected return pp 2 0.1 I Standard deviation of return 01:. 5 0.15 You are given that - Exactly 1 of the above investment goals is infeasible. - The return rate of riskfree asset is r} = 0.05. - Assuming that the tangency portfolio exists and is efcient (a) Is it possible to construct a portfolio consists of risky assets only which the Sharpe ratio is greater than DJ? Explain your answer. [b] An investor is seeking for the minimum variance portfolio with expected return ,up = 0.1?. He chooses a portfolio consisting of these assets [riskfree and risky assets}. It is found that the expected return and standard deviation of return of this portfolio are pp = 0.1? and (IF = 0.2. Determine if it is the desired portfolio