Topic $0$: Financial Instruments and Markets

You are a market maker in the stock of Pfizer $($PFE$)$ and quote a bid of $$102\mathrm{.}25$ and an ask of $$102\mathrm{.}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 $$110\mathrm{.}25$ and $$110\mathrm{.}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?