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You are a market maker in the stock of Pfizer (PFE) and quote a bid of $102.25 and an ask of $102.50. Suppose that you have zero inventory.
(a) On Day 1, you receive market buy orders for 10,000 shares and market sell orders for 4,000 shares. How much do you earn on the 4,000 shares that you bought and sold? What is the value of your inventory at the end of the day? (Hints: It is possible to have negative inventory. Further, there is more than one correct way to value your inventory, but please state what assumption your valuation is based on.)
(b) Before trading begins on Day 2, the company announces promising clinical trial results for its latest COVID-19 vaccine. Your quoted bid and ask jump to $110.25 and $110.50, respectively.
During Day 2, you receive market sell orders for 8,000 shares and buy orders for 2,000 shares. What is your total profit or loss over the two-day period? What is the value of your inventory at the end of Day 2?
(c) Discuss the following. What is a market maker’s objective? Is there anything you could have done during Day 1, consistent with a market maker’s objective, that would have improved your performance over the two-day period?

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