Problem 34. IPO
You are going to participate in the purchase of the initial shares of a company. We know that the stock value of the company is a random variable drawn from the uniform distribution \([0,1000]\). Although you are not aware of the value at the IPO, you do have the knowledge of the distribution. You offer a bid \(x\) to the owner of the company. If the value of the company’s shares at the IPO is less than \(x\), you would buy that company’s shares at a value of \(x\) dollars, otherwise you wouldn’t buy anything.
You know that the value of the company’s stock will increase by \(50\) percent after your purchase. What proposal would you make to the owner of the company?
Link to the problem on Twitter: https://twitter.com/Riazi_Cafe/status/1700391308991586677
Your best move is to propose a bid of \(0\) to the owner (which does not load to a purchase).
Suppose you offer a bid of \(x\) to buy the company’s share. Then the probability that you will buy the stock is \(x/1000\) (probability that the stock value is less than \(x\)). Also, in this case, the average share value is equal to \(x/2\), which after a \(50\%\) increase will be equal to \(0.75x\), which is still less than the amount of money paid. Thus, the it is best if you make a bid of \(x=0\).