7. Assume that the following two-factor model describes the returns of asset i R; = a: + 8 Fi + 3F+ei. where Fi and Fare two independent factors and the e;'s have zero means and variances ? and are uncorrelated with F and F2. The model parameters of portfolios A, B and C are given below: Portfolio Expected return (in %) Bir Residual variance 14 A B 34 1.0 0.5 3.0 0.2 3.0 -0.5 30 71 50 31 15% and 02 Given that the two factors Fi and Fy are uncorrelated and have risks o 10% respectively, and that the risk-free rate for borrowing and lending is 4%. (a) Estimate the variance-covariance matrix of returns of A, B and C. (b) Determine the efficient frontier with a portfolio of A, B and C. (c) If a portfolio D with an expected return of 20%, 80i = 2 and 8p2 = 0 were observed, illustrate the arbitrage opportunities that would exist. 7. Assume that the following two-factor model describes the returns of asset i R; = a: + 8 Fi + 3F+ei. where Fi and Fare two independent factors and the e;'s have zero means and variances ? and are uncorrelated with F and F2. The model parameters of portfolios A, B and C are given below: Portfolio Expected return (in %) Bir Residual variance 14 A B 34 1.0 0.5 3.0 0.2 3.0 -0.5 30 71 50 31 15% and 02 Given that the two factors Fi and Fy are uncorrelated and have risks o 10% respectively, and that the risk-free rate for borrowing and lending is 4%. (a) Estimate the variance-covariance matrix of returns of A, B and C. (b) Determine the efficient frontier with a portfolio of A, B and C. (c) If a portfolio D with an expected return of 20%, 80i = 2 and 8p2 = 0 were observed, illustrate the arbitrage opportunities that would exist