PS1_Solutions.pdf - 14.07 Fall 2018 Problem Set 1 Due on...

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14.07, Fall 2018: Problem Set 1 Due on September 20 in class. The assignment will not be accepted after 2:45pm on September 20. Exercise 1 is worth 40 points, 10 per sub-question 1. Revised version. There are two companies, A and S, whose stocks are selling at $ 9 and $ 7 respectively. Company A decided to sue company S over patent infringements. When the outcome of the lawsuit is announced, if A wins, its stock will rise to $ 15, and S’s stock will decrease to $ 5. If A loses, its stock will be worth $ 6 and S’s stock will jump to $ 10. Suppose stocks pay no dividends between now and the announcement. a) Suppose whether company A wins or loses the lawsuit represents the two states of the world. i.) Using only company A’s stock and company S’s stock, construct a portfolio that pays $ 1.00 tomorrow if A wins the case, and $ 0.00 if A loses. (You may express resulting portfolio shares as fractions). Purchase shares of A: 1 12 , Short-sell shares of B: - 1 20 ii.) Using only company A’s stock and company S’s stock, construct a portfolio that pays $ 1.00 tomorrow if A loses the case, and $ 0.00 if A wins. (You may express resulting portfolio shares as fractions). Short-sell shares of A: - 1 24 , Purchase shares of B: 1 8 iii.) Calculate the prices of Arrow-Debreu securities in this economy, assuming no arbitrage. b) For simplicity, first assume there is a riskless asset in the economy that pays $ 1 in both states. Calculate the price of such an asset, assuming no-arbitrage. c) For this question only, suppose a riskless bond (say T-bills) yields an interest rate of 5% in the next period when the dispute is solved. Is there an arbitrage opportunity? 1

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