Question

Here are two questions about an economy that has six states,a through f, and six securities, G through L. The securities payoff matrix is X. Some securities may have negative payoffs in some states, you can think of these as forward contracts

G H I J K L
a 18 21 28 5 9 10
b 14 19 8 23 5 -5
Payoff(matrix) X c 8 11 14 -3 27 20
d 6 23 19 -1 26 14
e 19 -4 25 25 20 -10
f 1 -10 22 18 -1 7

1) Is the market complete?
Yes or No?
2)Sam wants a guaranteed income of 25$.Can you create a portfolio from the six securities to do that? If so how many units of securities H must you include in the portfolio?
a) -0.498 b) 0.200 c)4.39 d)4.57207

Answer 1

G H I J K L
a 18 21 28 5 9 10
b 14 19 8 23 5 -5
c 8 11 14 -3 27 20
d 6 23 19 -1 26 14
e 19 -4 25 25 20 -10
f 1 -10 22 18 -1 7
1) The market is complete.
2) If Sam wants a guaranteed income of 25$. We can create a portfolio
from the six securities to do that. The guaranteed income is possible in
state a. In this case (18+21+28+5+9+10)/21 = 4.39 units of securities H
must you include in the portfolio.
So, the right answer is c) 4.39.