Math 373 Test 4 Fall 2012

Math 373 Test 4 Fall 2012 December 10, 2012 1. ( 3 points) List the three conditions that must be present for arbitrage to exist. 1) No investment 2) No risk 3) Guaranteed positive cash flow

2. (5 points) The bid and ask prices for a share of Kim Korp is 42.50 and 43.05. Ande purchases 1000 shares of Kim Korp stock. Ande pays a commission of 0.10 per share. Lori sells 1000 shares of Kim Korp stock. Lori pays a commission of X%. The total transaction costs for Lori and Ande are 841.25. Determine X. Ande: (1000)(43.05) (1000)(0.10) 43,150 Lori: (1000)(42.50)(1 x) 42,500(1 x) Transaction Costs: 43,150 42,500(1 x) 841.25 42,308.75 (1 x) 42,500 0.9955 1 x x 0.0045

3. (4 points) The S&P 500 Index has a current spot price of 1410. The dividend rate payable continuously on the S&P 500 Index is 2.1%. The risk free interest rate compounded continuously 3.4%. Calculate the price for an 8 month prepaid forward on the S&P 500 Index. S0 1410 0.021 r 0.034 8 ( 0.021) P t 12 8 0 F S e 1410e 1,390.3975 0, 12

4. (4 points) Circle each of the following which will always generate a positive profit if the price of the underlying asset goes to zero: Short Call Bull Spread Short Put Purchased Collar 5. (1 point) A Bermuda style option can be exercised at any point before the expiration date. True or False A Bermuda style option can only be exercised during specified periods. 6. (1 point) The profit on a long stock is equal to the payoff on a long forward contract. True or False

7. (8 points) You are given the following spot yield rate curve: Time Spot Yield Rate 1 2.6% 2 3.4% 3 3.9% Kevin purchases a 3 year interest rate swap which allows him to swap a floating rate interest rate for a fixed interest rate on a loan. The swap provides that Kevin can swap interest rates on 1 million the first year, 2 million the second year, and 3 million the third year. Calculate the fixed interest rate as a result of the swap. Time Spot Yield Rate Forward 1 2.6% 0.026 2 3.4% 2 (1.034) 1 0.042 1.026 3 3.9% 3 (1.039) 1 0.049 2 (1.034) R Q P f i i i QP i i 2 3 1 1 1 (1) (0.026) (2) (0.042) (3) (0.049) 1.026 1.034 1.039 2 3 1 1 1 (1) (2) (3) 1.026 1.034 1.039 0.2353 5.52 4.26%

8. (4 points) Describe two ways to create a synthetic long forward. 1) Buy a call and sell a put with the same strike price and expiration date 2) Buy a stock with borrowed money

9. (6 points) Anji buys 4 futures contracts on the S&P 500 Index. The futures price is 1500 and the risk free interest rate is 7.8% compounded continuously. The margin requirement for the futures contract is 16% and the maintenance margin is 75%. The futures contracts are marked to market weekly. After one week, the futures price has decreased to 1425. Determine the additional amount that Anji will need to contribute to the margin account at the end of the first week. Notional Value: (4)(250)(1,500) = 1,500,000 Margin: Notional Value (0.16) = (1,500,000)(0.16) = 240,000 Maintenance Margin: (240,000)(0.75) = 180,000 After 1 Week Margin with interest: (0.078) 1 e 52 240,000 240,360.27 Margin after futures price decreases: 240,360.27 (1,500 1,425)(4)(250) = 165,360.27 Margin Call: Maintenance margin current margin 180,000 165,360.27 = 14,639.73

10. (7 points) Weilan enters into a floor on the stock of Wang Manufacturing. Wang has a current spot price of 68 and does not pay dividends. The premium for a 6 month European-style 68-strike call on the stock of Wang Manufacturing is 6.50. The annual effective risk free interest rate is 10.25%. Calculate the payoff and profit if the spot price of Wang stock is 77 in 6 months. Put Premium: C P S 0 1 2 K 1 i 68 6.50 P 68 (1.1025) 1 2 6.50 P 3.24 P 3.2619 *Note: 1.1025 1 2 1.05 Buy 68 K Put Buy Stock Total Payoff FV Cost Profit Payoff FV Cost Profit Payoff Profit Max(0,68-S t) (3.2619)(1.05) 0-3.425 Spot at Exp 68(1.05) 77-71.4 0+77-3.425+5.6 0 3.425-3.425 77 71.4 5.6 77 2.175

11. (2 points) Circle the graph of a Bull Spread.

12. (4 point) List the five ways that Futures Contracts vary from Forward Contracts. 1) Futures are liquid. 2) Futures are marked to market daily. Forwards are settled at expiration date. 3) Futures are standardized. Forwards are customized. 4) Futures have a daily price limit. 5) Futures minimize credit risk.

13. (7 points) The current price of Oh Corporation is 200. Oh Corporation does not pay a dividend. The annual effective risk free interest rate is 5.7%. The premium for a 6 month 190 strike European-style call on Oh Corporation is 22.50. The premium for a 6 month 210 strike European-style call on Oh Corporation is 12.25. Kevin purchases a 6 month collar on Oh Corporation. Determine the range of spot prices at expiration for which Kevin would have a positive profit. Purchase a collar: Buy a put and a sell call with a higher strike price. Put premium with 190 Strike price: 22.50 P 200 P 7.31 190 1.057 1 2 Call premium with 210 Strike price: 12.25 Payoff and Profit Tables: Buy 190 Strike Put Spot at Exp Payoff FV Cost Profit Max(0, 190-S t) 1 2 (7.31)(1.057) Payoff FV Cost S t < 190 190-S t 7.51 190 S t 7.51 190 0 7.51-7.51 210 0 7.51-7.51 S t >210 0 7.51-7.51 Sell 210 Strike Call Spot at Exp Payoff FV Cost Profit -Max(0, S t-210) 1 (12.25)(1.057) 2 Payoff FV Cost S t < 190 0-12.59 12.59 190 0-12.59 12.59 210 0-12.59 12.59 S t >210 -S t +210-12.59 -S t +210 +12.59

Total Spot at Exp Payoff Profit S t < 190 190-S t 190-S t-7.51+12.59=195.08-s t 190 0-7.51+12.59=5.08 210 0-7.51+12.59=5.08 S t >210 -S t+210-7.51-s t+210+12.59=-s t+215.08 The spot prices at expiration for which Kevin would have a profit are in the range (0, 215.08).

14. (1 point) The payoff on a zero coupon bond is always zero. True or False The profit on a zero coupon bond is always zero not the payoff. 15. (1 point) If the spot price of the stock at expiration is greater than the spot price of the stock at time zero, the purchase and subsequent sale of a stock will always generate a positive profit. True or False The profit is S t S 0(1+i) so S t could be greater than S 0 but not be greater than S 0(1+i).

16. (8 points) Leavitt Oil LTD (LOL) enters into a 3 year swap on crude oil. The swap allows LOL to purchased 50,000 barrels of oil at the end of each year for the next three years. The swap price for the oil is 101 per barrel. You are given the following forward oil prices and spot interest rates: Time Oil Forward Price Spot Interest Rates 1 F 4.00% 2 100 5.10% 3 115 6.25% Determine F. F 100 115 101 101 101 1.04 (1.051) (1.0625) 1.04 (1.051) (1.0625) 2 3 2 3 F 186.41 272.76 1.04 F 86.3488 1.04 F 89.80

17. (3 points) The current spot price on the stock of Boyce Bicycles is 72. Boyce does not pay dividends. The annual effective risk free interest rate is 7.5%. Determine the maximum profit that can be realized from a short one year forward contract on the stock of Boyce Bicycles. Max profit for a short forward is when the spot price is 0. F 0,1= 72(1.075) = 77.4 Short Forward Spot at Exp Payoff FV Cost Profit 0 77.4 0 =77.4 0 77.4

18. (5 points) The current spot price of the stock of Kang Bank is 123. Kang does not pay dividends. The annual effective risk free interest rate is 6.3%. The one year forward price on the stock of Kang Bank is 129. Assume there are no transaction costs. State explicitly what actions you would take at time zero to take advantage of the arbitrage that exists in this situation. Theoretical Forward: 123(1.063)=130.749 Arbitrage Opportunity: Buy Low and sell high. We will buy the real forward and sell the synthetic forward. Buy one year forward with price $129. Sell stock for $123 and lend the $123 received from the sale.

19. (4 points) The stock of KeChupp Industries has a bid-ask price spread of 51.00 to 52.00. The annual risk free interest rate for borrowing is 6% compounded continuously. The annual risk free interest rate for lending is 5% compounded continuously. The transaction costs associated with buying or selling a bond or stock aret. Under this scenario, arbitrage exists for a 6 month forward if the forward price exceeds 54.75. Determine T. 0.06 2 F (52 2 T ) e 54.75 52 2T 54.75 0.03 e 2T 53.13 52 T 0.5659

20. (2 points) Draw the graph of a straddle.

21. (6 points) Aman Airlines owns a swap on jet fuel. The swap is for 100,000 gallons of jet fuel at the end of one year and 100,000 gallons of jet fuel at the end of 2 years. The swap price is 125 per gallon. The forward prices of jet fuel and the one year forward interest rates are listed below: Time Jet Fuel Forward Price One Year Forward Interest Rate 1 123 4.0% 2 135 7.0% Calculate the market value of Aman s swap. First find the spot rates: r 1=f 0,1=0.04 (1+r 2) 2 = (1+r 1)(1+f 1,2) (1+r 2) 2 = (1.04)(1.07) r 2=1.054893 Market Value per Gallon: 123 125 135 125 7.06326 2 1.04 (1.054893) Market Value: (7.06326)(100,000)=706,326.38

22. The stock of Cheng Consulting has a current spot price of 22. The risk free interest rate is 8%. a. (2 points) A one year European style put option with a strike price of 21 is in the money. True or False The strike price needs to be greater than the spot price for this to be true. b. (2 points) A 6 month American style call option with a strike price of 21 is in the money. True or False

23. (4 points) Elliot sells short the stock of DJL Inc. The current spot price of DJL stock is 18.50. DJL does not pay a dividend. The annual effective interest rate is 6.8% Elliot closes out his position in DJL at the end of 18 months. Complete the following payoff and profit table. (SHOW YOUR WORK!!) Spot Price at End of 18 Months Payoff Future Value of Cost Profit -Spot Price @ Exp 18 (18.50)(1.068) 12 Payoff FV Cost 13.50-13.50-20.42 6.92 16.00-16.00-20.42 4.42 18.50-18.50-20.42 1.92 21.00-21.00-20.42-0.58 23.50-23.50-20.42-3.98

24. (6 points) The stock of MacDonald Corporation has a current spot price of S 0. MacDonald stock pays a quarterly dividend of 1.50 with the next dividend payable in 2 months. The risk free interest rate compounded continuously is 6%. The price for a 9 month prepaid forward on MacDonald Corporation is 316.61. Calculate S 0. F S PV ( Dividends) P 9 0 0, 12 0 2 5 8 ( 0.06) ( 0.06) ( 0.06) 12 12 12 316.61 S 1.5e 1.5e 1.5e 316.61 S 4.39 0 S 0 321

25. (3 points) List the three perspectives on derivatives. 1) End users 2) Intermediaries 3) Economic observers