1 - Purdue University



You are given the following two bonds:

|Term |Annual Coupon |Maturity Value |Price |

|1 |60 |1000 |1000.00 |

|2 |80 |1000 |1055.06 |

Calculate the 2 year spot interest rate.

a. 5.00%

b. 5.04%

c. 6.00%

d. 7.58%

e. 8.00%

1. You are given the following yield curve:

|Term (t) |Spot Rate |Forward Rate, f(t-1,t) |

|1 |0.050 |0.050 |

|2 |0.054 |0.058 |

|3 |0.057 |0.063 |

|4 |0.059 |0.065 |

A bond matures in four years and has a maturity value of 1000. The bond pays annual coupons of 200.

Calculate the price of the bond.

a. 1462.48

b. 1468.44

c. 1489.70

d. 1493.97

e. 1531.89

2. You are given the following yield curve:

|Term (t) |Spot Rate |Forward Rate, f(t-1,t) |

|1 |0.050 |0.050 |

|2 |0.054 |0.058 |

|3 |0.057 |0.063 |

|4 |0.059 |0.065 |

Grosso Corporation has floating rate debt whose interest rates follow the above yield curve. Grosso will pay interest based on the one year rate for each year for the next four years. The amount of debt is 1 million during the first two years and 2 million during the second two years.

Grosso Corporation enters into an Interest Rate Swap to swap the floating interest rate for a fixed interest rate.

Calculate the swap price (the fixed interest rate).

a. 0.0558

b. 0.0586

c. 0.0603

d. 0.0607

e. 0.0613

3. Moss Life Insurance Company must make payments of 100,000 in one year. Additionally, a payment of 200,000 must be made at the end of year two and a payment of 300,000 must be made at the end of three years.

Moss Life wants to exactly match these payments using the following three bonds:

Bond A is a one year bond maturing for 1000 with an annual coupon of 50.

Bond B is a two year bond maturing for 1000 with an annual coupon of 75.

Bond C is a three year bond maturing for 1000 with an annual coupon of 100.

Calculate the amount of Bond B that Moss Life with need to buy.

a. 160.677

b. 181.818

c. 186.047

d. 200.000

e. 272.727

4. The common stock of Keller Corporation pays annual dividends. A dividend of 10.50 is expected to be paid in one year. Each year thereafter, the dividend is expected to increase by 5% over the previous dividend.

Calculate the price of the stock to yield 10.25%.

a. 100.00

b. 102.44

c. 105.00

d. 200.00

e. 210.00

5. Nick sells a stock short for 25. His margin requirement is 80%. He earns X% on his margin account. There are no dividends paid on the stock. After one year, Nick purchases the stock for 20.

Nick’s return on his short sale was 30%.

If a dividend of Y was paid, Nick’s yield would have been 20%.

Calculate Y.

a. 1

b. 2

c. 3

d. 4

e. 5

6. Ian is receiving an annuity due of 100 for the next 10 years. If the interest rate is 6%, calculate the modified duration of this annuity.

a. 3.0

b. 3.8

c. 4.0

d. 4.3

e. 4.7

7. A 3 year bond pays annual coupons of 50. The bond matures for 2000.

Calculate the modified convexity at an interest rate 8%.

a. 7.4

b. 8.7

c. 9.9

d. 10.8

e. 11.6

8. Klawitter stock is currently selling for 50. The risk free interest rate is an annual effective interest rate of 6%. Tim buys a straddle. The price of a one year call for Klawitter stock with a strike price of 50 is 5.85.

Calculate the profit on the straddle if the spot price of the stock is 55 in one year. (Hint: The price of a put can be found using the Put Call Parity formula.)

a. -9.40

b. -4.40

c. -2.40

d. 0.60

e. 2.00

9. You are given the following yield curve:

|Term (t) |Spot Rate |

|1 |0.060 |

|2 |0.065 |

|3 |0.069 |

|4 |0.072 |

Calculate the 1 year deferred 3 year forward rate f(1,4).

a. 6.9%

b. 7.6%

c. 7.8%

d. 8.1%

e. 8.2%

10. Nick purchases 8 S&P 500 Futures contracts with a S&P value of 1300. Nick’s margin requirement is 10%. His maintenance margin is 90%. The margin account earns 12% compounded continuously. The margin account is marked to market weekly. At the end of the first week after the purchase, Nick receives a margin call of 10,000.

Calculate the S&P index at the end of one week.

a. 1274.7

b. 1281.7

c. 1282.0

d. 1287.0

e. 1295.0

11. Yang Corporation’s stock currently sells for 80 per share. Dividends of 4 are paid quarterly with the next dividend due in 2 months. The risk free interest rate is 6% compounded continuously.

Calculate the one year Forward Price of the stock.

a. 64.51

b. 64.59

c. 66.24

d. 68.50

e. 68.58

12. An Index currently sells for 800. The risk free interest rate is 6% compounded continuously. The dividend rate is 4%.

Calculate the cost of a Pre-Paid Forward for the Index with delivery of the Index in 9 months.

a. 764.80

b. 776.36

c. 788.09

d. 812.09

e. 824.36

13. Oil Drillers Inc. (ODI) is a company that drills for oil in the Gulf of Mexico. It cost ODI 15 in fixed costs and 10 in variable costs to produce a barrel of oil. The company hedges its profits by purchasing a one year put at a strike price of 35 for a premium of 2.25. The annual effective risk free interest rate if 4%.

Calculate the total profit of ODI if the spot price is 38.

a. 7.66

b. 9.66

c. 10.66

d. 12.00

e. 13.66

14. Katie purchases a stock for 40. The Stock does not pay any dividends. The risk free annual effective interest rate is 4%. Katie also takes a short position in a one year forward on the same stock.

Calculate the total profit to Katie at the end of one year if the spot price of the stock is 45.

a. 0.00

b. 1.60

c. 3.40

d. 5.00

e. 8.40

15. Which of the following are true:

i. A share of stock is a derivative

ii. Derivatives are used to manage risk or reduce taxes.

iii. A put gives you the right, but not the obligation, to buy a stock at the strike price at the expiration date.

a. Items i. and ii.

b. Items i. and iii.

c. Items ii. and iii.

d. None of the items are true.

e. The correct answer is not given by a., b., c., or d.

16. You own two bonds:

i. Bond A is a 10 year bond with annual coupons of 50 and a maturity value of 1200. This bond has a duration of 8.15 at an annual effective rate of 7%.

ii. Bond B is a 20 year bond with annual coupons of 200 and a maturity value of 2000. This bond has a duration of 10.42 at an annual effective rare of 7%.

Calculate the duration of these two bond portfolio at an annual effective interest rate of 7%.

a. 9.6

b. 9.7

c. 9.8

d. 9.9

e. 10.0

17. Which of the following are true:

i. A floor is purchase of a put option on a stock when we own the stock.

ii. A cap is the sale of a call option on a stock when we own the stock.

iii. A fully leveraged purchase of a stock means that you borrow the entire purchase price of the stock.

a. Items i. and ii.

b. Items i. and iii.

c. Items ii. and iii.

d. None of the items are true.

e. The correct answer is not given by a., b., c., or d.

18. The bid ask spread on Carroll Company is 45.00-45.50. The commission is 0.5%.

Calculate the total transaction costs involved in sale of 100 shares of Carroll Company.

a. 49.75

b. 50.00

c. 50.25

d. 95.00

e. 95.25

19. Shannon enters into a Covered Put on Moeller Corporation. In other words, she sells the stock short for 50. She also sells a one year put on Moeller Corporation. The put has a strike price of 50 and a premium of 3.40. The annual effective risk free interest rate is 4%.

Calculate the profit at the end of one year if the stock has a spot price of 40 at the end of one year.

a. 3.40

b. 3.54

c. 5.54

d. 10.00

e. 12.00

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