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There are two possible states of nature, s = 1, and s = 2, over the next period.There are two securities i and j) whose current prices are $10 and $15, respectively.Security i has a payoff of $10 in state s = 1, and $16 in state s = 2, while security j provides $25 in state s = 1 and $8 in state s = 2.
-A third security is introduced.It generates a payoff of $16 in state s = 1 and $24 in state s = 2.How many units of this new security can you buy if your initial wealth is $3,100?
A)200 units
B)162 units
C)154 units
D)127 units
E)More information is needed

Question

Quizplus · Accepted Answer

To determine the number of units of the new security that can be purchased, we need to calculate the price of the security in each state.

In state s = 1, the total payoff from the three securities would be $57 (10 from security i, 25 from security j, and 16 from the new security). In state s = 2, the total payoff would be $48 (16 from security i, 8 from security j, and 24 from the new security).

To find the price of the new security, we need to find the expected payoff in each state and discount it by the risk-free rate of return. Assuming the risk-free rate is 5%, we have:

Expected payoff in state s = 1: (0.5)(16) = 8
Expected payoff in state s = 2: (0.5)(24) = 12
Price of new security = (8/(1+0.05)) + (12/(1+0.05)^2) = $21.36

Therefore, the number of units of the new security that can be purchased with $3,100 is:
3100/21.36 = 145.15

Rounding down, we get 145 units. However, if we purchase 200 units of the security, the total cost would be $4,272, which is greater than the initial wealth of $3,100. Therefore, option A, 200 units, is not feasible. Therefore, the best choice is not to purchase any units of the new security.

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