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Bonus Problem 2 (Optional, 30 marks) (a) We consider an investment problem with 1 riskfree asset (with return r) and N risky assets (N 23). We let Wp, Wo be any two portfolios lies on frontier curve. Show that any portfolio w on the frontier curve can be expressed as W = Bwp + (1 - BWQ, where is some real number. (*Note: This theorem can be regarded as two-fund theorem..) (b) We consider an investment problem with 1 riskfree asset and N risky assets (N 3). The following table shows the expected return and variance of portfolio return of 4 portfolios: Expected return variance of return Portfolio A (WA) 0.04 (0.07) Portfolio B (WB) 0.06 (0.02)2 Portfolio C(w) 0.1 (0.15) Portfolio D (wo) 0.12 (0.3) You are also given that - the return rate of riskfree asset is r = 0.07 and - at least one of the portfolios is efficient. Find the minimum variance portfolio with expected return at least 0.11. Express your answer in terms of w, (riskfree asset) and WA, W. Wc, Wp. Bonus Problem 2 (Optional, 30 marks) (a) We consider an investment problem with 1 riskfree asset (with return r) and N risky assets (N 23). We let Wp, Wo be any two portfolios lies on frontier curve. Show that any portfolio w on the frontier curve can be expressed as W = Bwp + (1 - BWQ, where is some real number. (*Note: This theorem can be regarded as two-fund theorem..) (b) We consider an investment problem with 1 riskfree asset and N risky assets (N 3). The following table shows the expected return and variance of portfolio return of 4 portfolios: Expected return variance of return Portfolio A (WA) 0.04 (0.07) Portfolio B (WB) 0.06 (0.02)2 Portfolio C(w) 0.1 (0.15) Portfolio D (wo) 0.12 (0.3) You are also given that - the return rate of riskfree asset is r = 0.07 and - at least one of the portfolios is efficient. Find the minimum variance portfolio with expected return at least 0.11. Express your answer in terms of w, (riskfree asset) and WA, W. Wc, Wp