Economics 1723: Problem Set 1 Solutions
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.
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.
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
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:
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.
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
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.