Problem 4. Let us consider the financial market with two risky assets with returns R1 and R2. (a) Suppose R1 is an exponential random variable with parameter 1 = 2. Z is a uniform random variable on [0, 1], which is independent of R1. We have the relationship that R2 = 2R1 + 32. Find the minimum variance portfolio and its minimum variance. [10 marks] (b) Suppose that we know oi = 0.04 and o = 0.06 and P12 = 0.8. Find the minimum variance portfolio and its minimum variance with and without short selling. [10 marks] (c) We have the following information of R and R2: Scenario Probability 0.4 W2 0.5 R1 1.2 R2 0.7 1 0.5 1.5 Find the minimum variance portfolio and its minimum variance. [10 marks] Problem 4. Let us consider the financial market with two risky assets with returns R1 and R2. (a) Suppose R1 is an exponential random variable with parameter 1 = 2. Z is a uniform random variable on [0, 1], which is independent of R1. We have the relationship that R2 = 2R1 + 32. Find the minimum variance portfolio and its minimum variance. [10 marks] (b) Suppose that we know oi = 0.04 and o = 0.06 and P12 = 0.8. Find the minimum variance portfolio and its minimum variance with and without short selling. [10 marks] (c) We have the following information of R and R2: Scenario Probability 0.4 W2 0.5 R1 1.2 R2 0.7 1 0.5 1.5 Find the minimum variance portfolio and its minimum variance. [10 marks]