Question

The Koepka Co. and the Johnson Co. have both announced IPOs at $42 per share. One of these is undervalued by $10.00, and the other is overvalued by $4.75, but you have no way of knowing which is which. You plan on buying 1,100 shares of each issue. If an issue is underpriced, it will be rationed, and only half your order will be filled.
a.	Assuming you could get 1,100 shares in Koepka and 1,100 shares in Johnson, what would your profit be? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)
b.	What profit do you actually expect?  (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What principle have you illustrated?

Answer 1

Let us first shorten the names of the two firms as K and J

Ans a) Assuming that we are able to get 1100 shares in each of J and K, our total investment would be

= 42 * 1100 + 42 *1100 = $92400

Let us assume that J is overvalued and K is undervalued (without loss of generality) ,then

the Value of our investment would be = 1100 *( 42-4.75)+1100*(42+10) = $40975+$57200 = $98175

The Profit would be = $98175-$92400 = $ 5,775

b) Actually, as we do not know which one is overpriced and which one is underpriced, we apply for 1100 shares of each of J and K

Assuming that J is overvalued and K is undervalued (without loss of generality), we will get 1100 shares of J and only 550 shares of K. Our actual investment would be = 1100*42+550*42 = $ 69,300

The Value of these Shares upon correction would be = 1100 * (42-4.75) + 550* (42+10)  =$40975+$28600 = $ 69575

The profit that one can expect is thus = $ 69575-$69300 = $ 275

c) I believe that the principle at work here is the difficulty in making riskless profits i.e. finding arbitrage opportuinities. In this case, if we get 1100 shares of both J and K we are able to make $ 5775 profit but it reduces to only $ 275 in actual scenario. This happens because the underpriced share will be in high demand and since we do not have the information, we have to invest in both stocks and our profits are minimised.