Initial public offerings (IPOs) have a reputation for being underpriced. Thus, if you can obtain shares of an underpriced IPO, you might make a large profit on the first day of trading. In contrast to underpriced IPOs, there are overpriced IPOs. An overpriced IPO is one in which the price typically declines on the first day of trading. Thus, obtaining shares of an overpriced IPO may result in negative returns on the first trading day. You decide to start an investment fund that will invest in all new IPOs. You call your new fund the Superior Performance IPO Fund. Assume that the average underpriced IPO makes a 30% return in one day and the probability of obtaining shares in the average underpriced IPO is P_u. Assume that the average overpriced IPO makes a -10% return in one day and the probability of obtaining shares in the average overpriced IPO is P_o . It is four times more likely to obtain shares of an overpriced IPO than an underpriced IPO, and there is a 50 percent chance of not obtaining any shares (in which case you invest in a t-bill with an expected effective annual return of 6 percent).

1. Find P_o and P_u

2. State what the probability is of investing in a t-bill.

3. Find the daily return to the T-bill, assuming 365 days in a year

4. Using the probabilities and daily returns of underpriced IPOs, overpriced IPOs, and T-bills, what is the expected daily return of the Superior Performance IPO fund?

5. What is the Effective annual return of the Superior Performance IPO fund?