Davis Bros. and The Storage Shed have both announced IPOs at $32 per share. One of these is undervalued by $9, and the other is overvalued by $4, but you have no way of knowing which is which. You plan on buying 1,000 shares of each issue. If an issue is underpriced, it will be rationed, and only half your order will be filled. What is the amount of the difference between your expected profit and the amount of profit you could earn if you could get 1,000 shares of both IPO offerings?

Question

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For the undervalued stock, if you attempt to buy 1,000 shares, you will only get 500 shares at $32 each, which are actually worth $41 each (undervalued by $9), leading to a profit of $9 * 500 = $4,500. For the overvalued stock, you will buy 1,000 shares at $32 each, which are actually worth $28 each (overvalued by $4), leading to a loss of $4 * 1,000 = $4,000. The net expected profit is $4,500 - $4,000 = $500.If you could get 1,000 shares of both, for the undervalued stock, the profit would be $9 * 1,000 = $9,000, and for the overvalued stock, the loss would be $4 * 1,000 = $4,000, leading to a net profit of $9,000 - $4,000 = $5,000.The difference between the expected profit ($500) and the maximum possible profit ($5,000) is $5,000 - $500 = $4,500.