Your cousin Jess is a surgeon who suffers badly from the overconfidence bias. Jess loves to trade stocks and makes predictions with 100% confidence. In fact, Jess is uninformed like most investors. Rumors are that Vital Signs (a start-up that makes warning labels in the medical industry)

will receive a takeover offer at $20 per share. Absent the takeover offer, the stock will trade at $15 per share. The uncertainty will be resolved in the next few hours. Jess believes that the takeover will occur with certainty and has decided to buy the stock. In fact, the true probability of a takeover is 50%.

a. Suppose all other investors correctly believe there is a 50% chance of a takeover, and as a result the stock is currently trading for $17.50 per share. What is your cousin’s expected profit at this purchase price?

b. Suppose instead there are many overconfident investors like your cousin who expect the takeover will occur with certainty. If these investors also try to buy the stock, how will it affect the price at which your cousin is likely to trade? What are your cousin’s expected profits now?Appendix