Question

Your brother Joe is a surgeon who suffers badly from the overconfidence bias. He loves to trade stocks and believes his predictions with 100% confidence. In fact, he is uninformed like most investors. Rumors are that Vital Signs (a startup that makes warning labels in the medical industry) will receive a takeover offer at $0.62 per share. Absent the takeover offer, the stock will trade at $15.05 per share. The uncertainty will be resolved in the next few hours. Your brother believes that the takeover will occur with certainty and has instructed his broker to buy the stock at any price less than $20.62. In fact, the true probability of a takeover is 50%, but a few people are informed and know whether the takeover will actually occur. They also have submitted orders. Nobody else is trading in the stock.

a. Describe what will happen to the market price once these orders are submitted if in fact the takeover will occur in a few hours. What will your brother's profits be: positive, negative or zero?

b. What range of possible prices could result once these orders are submitted if the takeover will not occur. What will your brother's profits be: positive, negative or zero?

c. What are your brother's expected profits?

Answer 1

a) In this case, the informed traders and Joe will both submit buy orders for any price less than $20.62, so the only market clearing price is $20.62, and nobody trades. Since there is no trade happening, Joe earns Zero profits.

b) If the informed traders expect the takeover to not happen, they will submit sell orders for any price above $15.05. Jow will submit his buy order for any price below $20.62. Trade will occur at some price in between, and Joe will make losses.

c) Joes expected profit = P(successful takeover) * Profits + P(failed take over)*losses

since in the event of successful takeover, joe earns zero profits and in the event of failed take over Joe earns losses, the overall expected profit for joe is negative.