Question 4: Portfolio Optimization (10p) We're now ready to apply our knowledge towards optimizing investment port- folios. Let's say we want to divide our investments into cryptocurrency, bonds and equities. We want to invest with the following idea: the investments in cryptocurrency will be p% we expect cryptocurrency returns to be 0.1 (10%), return on equity to be 0.08(8%), and return on bonds to be g (100 *q%) the total return should give us a return of r (100 *r%) 2 the natural condition should also hold true, i.e. the proportion of cryp- tocurrency, bonds and equity equals to 1. This implies our portfolio comprises only of these three invesments. 1. Chose a realistic proportion p for the investments in cryptocurreny, the expected return on bonds q, and total return r. Write down the three equations that form a linear system of equations Ax=b. 2. What does the vector x represent? 3. Solve the system of equations using the method that you think is best. 4. Explain why you chose the method above. Question 4: Portfolio Optimization (10p) We're now ready to apply our knowledge towards optimizing investment port- folios. Let's say we want to divide our investments into cryptocurrency, bonds and equities. We want to invest with the following idea: the investments in cryptocurrency will be p% we expect cryptocurrency returns to be 0.1 (10%), return on equity to be 0.08(8%), and return on bonds to be g (100 *q%) the total return should give us a return of r (100 *r%) 2 the natural condition should also hold true, i.e. the proportion of cryp- tocurrency, bonds and equity equals to 1. This implies our portfolio comprises only of these three invesments. 1. Chose a realistic proportion p for the investments in cryptocurreny, the expected return on bonds q, and total return r. Write down the three equations that form a linear system of equations Ax=b. 2. What does the vector x represent? 3. Solve the system of equations using the method that you think is best. 4. Explain why you chose the method above