Suppose that the world can be described using two states and two stocks Y and Z are available. We...

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, w(2) = 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.)

Robert · Accepted Answer

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, 
w(2) = w1 × w2,

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...

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