ECON 1723 Fall 2013 Problem Set Solution 1 - Economics 1723...

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1 Economics 1723: Problem Set 1 Solutions Problem 1: a) Buy 3 units of asset 1 and sell 1 unit of asset 2. This strategy will have 0.5 dollars of cash flow today and zero cash flow tomorrow. There is an arbitrage opportunity because there is a violation of LOOP (Law of One Price), which states that assets with the same payoffs in all states of the world must have the same price. b) Buy 3 units of asset 1 and sell 1 unit of asset 2. This strategy will break even today and have a payoff of 0.5 dollars if state 1 occurs tomorrow. This arbitrage opportunity arises because of a violation of the positivity of state prices. In particular, the strategy replicates the payoff of half a unit of A-D security for state 1 at no cost. No arbitrage requires that A-D security prices for all states must be strictly positive, which is not true here. c) Buy 1 unit of asset 3, sell 8 units of asset 1 and 0.75 unit of asset 2. This will generate 0.35 dollar of cash flow today and zero cash flow in the future no matter which state happens (There are other ways to arbitrage as well!). Again, LOOP is violated here. Problem 2: Within the context of a corporate spin-off, the stub value represents the implied stand- alone value of the parent company’s assets without the subsidiary. In other words, the stub value is a projection of what the company will be worth after it distributes shares of the subsidiary to its existing shareholders. A negative stub value implies that the parent company’s assets have a negative value after the subsidiary is divorced from it. It is anomalous because stock prices (the per share value of the company’s assets) can never fall below zero. The following three factors may allow negative stub value anomalies such as the 3Com/Palm anomaly to persist: (1) In some cases, stocks are hard to short because most investors are individuals who do not know they can (or choose not to) profit by lending their shares. (2) If the parent company issues debt using its shareholdings as collateral and then defaults, the shareholders of the parent company lose their shares. As a result, the link between the parent and its subsidiary could be severed before the mispricing is corrected. (3) The risk arbitrageurs face that stub values become more negative before they turn positive. If this happens, the arbitrageur will have to put up more collateral or otherwise be forced to close the position at a loss.
2 (Please note that this suggested solution is merely an outline. Other factors may also be relevant.) Problem 3:
3 Problem 4: a)

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