1. You are among the OTC market makers in the stock of Moderna and quote a bid of $102.25 and an ask of $102.50. Suppose that you have a 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, e.g., by short-selling. Further, there is more than one correct way to value an inventory, but please state what assumption your valuation is based on.) (b) Before trading begins on Day 2 the company announces promising vaccine trial results. The 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) 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? 2. Suppose a hedge fund manager earns 1% per trading day (which is unrealistically high!) There are 250 trading days per year. Answer the following questions: (a) What will be your total return (HPR) on $100 invested in her fund at the beginning of the year if she allows you to reinvest in her fund the 1% you earn each day? What is your average return per trading day, computed using the geometric average? (b) What will be your total return assuming she puts all of your daily earnings into a zero-interest-bearing checking account and pays you everything earned at the end of the year? What is your average return per trading day, computed using the simple (arithmetic) average? 1 (e) Can you summarize when it is proper to use arithmetic vs. geometric average? 3. Here are some alternative investments you are considering for one year. (i) Bank A promises to pay 8% on your deposit compounded annually. (ii) Bank B promises to pay 8% on your deposit compounded daily. Compare the effective annual rate (EAR) on these investments. 4. Excel Question. Download the monthly Russell 2000 prices from January 1988 un- til today http://finance.yahoo.com/ (click Russell 2000, click Historical Data, click Monthly, click Apply, click Download Data). What would have been your annualized HPR if you invested as of the start of the index? 2. Suppose a hedge fund manager earns 1% per trading day (which is unrealistically high!) There are 250 trading days per year. Answer the following questions: (a) What will be your total return (HPR) on $100 invested in her fund at the beginning of the year if she allows you to reinvest in her fund the 1% you earn cach day? What is your average return per trading day, computed using the geometric average? (b) What will be your total return assuming she puts all of your daily earnings into a zero-interest-bearing checking account and pays you everything earned at the end of the year? What is your average return per trading day, computed using the simple (arithmetic) average? 1 (c) Can you summarize when it is proper to use arithmetic vs. geometric average? 3. Here are some alternative investments you are considering for one year: (i) Bank A promises to pay 8% on your deposit compounded anmally. (ii) Bank B promises to pay 8% on your deposit compounded daily. Compare the effective annual rate (EAR) on these investments 4. Excel Question. Download the monthly Russell 2000 prices from January 1988 un- til today http://finance.yahoo.com/ (click Russell 2000, click Historical Data, click Monthly, click Apply, click Download Data). What would have been your annualized HPR if you invested as of the start of the index
