1. You are among the OTC market makers in the stock of Bio-Engineering, Inc. and quote a bid of 102 1/4 and an ask of 102 1/2. Suppose that you have a zero inventory.
2. (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 an inventory, but please state what assumption your valuation is based on.)
3. (b) Before trading begins on Day 2 the company announces trial testing of a cure for acne in mice. The quoted bid and ask jump to 110 1/4 and 110 1/2. 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?
4. (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?
5. Topic 2: Performance Measures
6. Suppose a 5-year zero-coupon Treasury bond with face value $1000 has a 5% yield (annually compounded).
7. (a) What price does this bond sell for?
8. (b) Suppose another zero-coupon Treasury bond also has a 5% yield, a face value of
9. $1000 but sells for $325.57. What is the maturity of this bond? 1
10. Which of the following investments do you prefer?
11. (a) Purchase a zero-coupon bond, which pays $1000 in ten years, for a price of $550. (b) Invest $550 for ten years in Chase at a guaranteed annual interest rate of 5.5%.
12. Suppose you get for free one of following two securities: (a) an annuity that pays $10,000 at the end of each of the next 6 years; or (b) a perpetuity that pays $10,000 forever, but payments do not begin until 10 years from now (the first cash payment from this security is 11 years from today).
13. Which security would you choose if the annual interest rate is 5%?
14. Does your answer change if the interest rate is 10%? Explain why or why not.
15. Suppose a hedge fund manager earns 1% per trading day. There are 250 trading days per year. Answer the following questions:
16. (a) What will be your annual return on $100 invested in her fund if she allows you to reinvest in her fund the 1% you earn each day?
17. (b) What will be your annual 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?
18. (c) Can you summarize when it is proper to "annualize" using APR (annual percentage rate) versus EAR (effective annual rate)?
19. 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.
20. (a) Suppose that you have purchased a 3-year zero-coupon bond with face value of $1000 and a price of $850. If you hold the bond to maturity, what is your annual rate of return?
21. (b) Now suppose you have purchased a 3-year bond with face value of $1000, a 7% annual coupon, and a price of $975. Assuming that you hold the bond to maturity, is the IRR greater or less than the return on the bond in part (a)?
22. Excel Question. Download the monthly S&P 500 prices from January 1950 until today http://finance.yahoo.com/ (click investing, click S&P 500, click historical prices, click monthly, click get prices, click download to spreadsheet).
23. (a) What is your best estimate for next month's return?
24. (b) What would have been your annualized HPR if you invested as of the start of the index?
25. (c) In what month occurred the lowest monthly return? What happened?