the price of such an asset, assuming no-arbitrage. What is the riskless interest rate in this
case?
c) Now 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? If the answer is yes,
outline how you would trade to exploit it.
For the last part of this problem, suppose the riskless bond in part c) no longer exists.
d) Suppose investors choose their portfolios to optimize their expected utility over wealth
in each state,
E
[
U
(
W
)]
. Suppose also that the two states of the world are similar for investors
in the sense that they have the same wealth in each state. Given this information, can you
calculate investors±assessment for the probability that A will win the lawsuit? If your answer
is yes, calculate the probability. If your answer is no, explain why not.
2

4. In the Harvard-Yale football game, the possible outcomes are as follows. In the ²rst
half, Harvard can go ahead by 10 points or Yale can go ahead by 10 points. In the second
half, the change in the score can be 10 points in Harvard±s favor or 10 points in Yale±s favor.
Harvard has the better team, so in the ²rst half there is a 70% probability that Harvard
will take the lead. However Harvard±s team is lazy; if it ends the ²rst half in the lead, there
is a 50% probability that the score will move in Yale±s favor in the second half. If Yale±s
team ends the ²rst half in the lead, the probability remains 70% that the score will move in
Harvard±s favor in the second half.
a) Draw the event tree. At each node of the tree, enter the Harvard lead (the number of