Suppose two securities A and B that have the following payoffs in the future:

State      A         B    Probability

1. 1            $10     $30   0.5
2. 2           $20    $10    0.5

Their current prices are $12 per share of A and $18 per share of B. Both states are equally likely.

a) Construct a completely risk-free portfolio with securities A and B.

b) Based on a), what is the risk-free return (interest rate)?

c) Suppose your initial wealth is W0 = $1, 320, draw your future budget line in both states of the world when you fully invest your initial wealth.

d) Based on c), what is your investment strategy to maximize your future wealth in State 2?

e) Based on c), what is your investment strategy to ensure the stability of your future wealth? (Hint: You want to invest in a risk-free portfolio in this case.)