IPO Underpricing. In $1980,$ a certain assistant professor of finance bought $12$ initial public offerings of common stock. He held each of these for approximately one month and then sold. The investment rule he followed was to submit a purchase order for every firm commitment initial public offering of oil and gas exploration companies. There were $22$ of these offerings, and he submitted a purchase order for approximately $$1,000$ in stock for each of these companies. With $10$ of these, no shares were allocated to the assistant professor. With $5$ of the $12$ offerings that were purchased, fewer than the requested number of shares were allocated.

The year $1980$ was very good for oil and gas exploration company owners:

On average, for the $22$ companies that went public, the stocks were selling for $80$ percent above the offering price a month after the initial offering date. The assistant professor looked at this performance record and found that the $$8,400$ invested in the $12$ companies has grown to $$10,000,$ representing a return of only about $20$ percent $($commissions were negligible$).$ Did he have bad luck, or should he have expected to do worse than the average initial public offering investor? Explain