You have 840 to invest in the two securities below. The table shows the initial prices of the two securities and their payoff at time T in each one of the two states of nature.

Answer the following questions (show all the details of your calculations and display the results with four decimal places):

i. Short sales are not allowed. If you decide to invest in security A only, how many shares of security A can you buy?

ii. Suppose that short sales are allowed but you must be able to meet all claims under the occurrence of either state i.e. you cannot default. What is the maximum number of shares of security B you can sell to buy security A?

iii. Considering your answer in (ii), show the outcome of your investment in each state.

iv. Considering your answer in (iii), explain whether there are arbitrage opportunities.

v. If securities A and B are the only securities available in the market, what is the risk

free rate?

Security A Security B Initial Price 10 12 State 1 12.00 18.00 Payoff State 2 16.00 8.00 Security A Security B Initial Price 10 12 State 1 12.00 18.00 Payoff State 2 16.00 8.00