Question: Suppose that the world can be described using two states and two stocks Y and Z are available. We assume the stocks' future prices have the following distributions:
State | Future Prices Stock Y | Future Prices Stock Z
1 | $10 | $15
2 | $20 | $11
The initial prices for the stocks are: Y (1) = $13, Z(1) = $10. Our utility function in (w1, w2) space is U(w1, w2) = w1 * w2, where U represents the utility level. Now we have an initial endowment of $420. How many shares and what positions of Y and Z should we choose to build our portfolio so that we actually maximize our utility function? (Assume fractional shares are permitted.)