Question

Initial public offerings (IPO’s) 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 IPO’s, there are overpriced IPO’s. 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 IPO’s. 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 Pu. 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 Po

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).

A)Find Poand Pu

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

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

D)Using the probabilities and daily returns of underpriced IPO’s, overpriced IPO’s, and T-bills, what is the expected daily return of the Superior Performance IPO fund?

2E)What is the Effective annual return of the Superior Performance IPO fund?

Answer 1

(A)

Probability of obtaining shares in the average overpriced IPO = P_o

Probability of obtaining shares in the average underpriced IPO = P_u

Probability of not obtaining any shares = P_T = 50% = 0.5

Also here P_o = 4P_u

So, P_o + P_u + P_T = 1

4P_u + P_u + 0.5 = 1

P_u = 0.1

P_o = 4 * 0.1 = 0.4

So P_o = 0.4 = 40%

      P_u = 0.1 = 10%

(B)

Probability is of investing in a T-bill = Probability of not obtaining any shares = P_T

= 50%

(C)

Daily Return = (1 + Annual Return)(1/365) – 1

                        = (1 + 0.06) (1/365) -1

                         = 0.0001596 = 0.01596%

So daily return to the T-bill = 0.01596%

(D)

Expected daily return of the Superior Performance IPO fund = P_o * Average underpriced IPO Return + P_u * Average overpriced IPO Return + P_T * T-bill Return

                                                                                                 = 0.3 * 0.1 + 0.1 * (-0.4) + 0.5 * 0.0001596

                                                                                                  = –0.0099202 = –0.992%

So Expected daily return of the Superior Performance IPO fund is –0.992%