Risk Management: An Introduction to Financial Engineering 23 Risk Management: An Introduction to Financial Engineering

Chapter 23 – Index of Sample Problems Slide # 02 - 03 Futures price Slide # 04 - 05 Contract value Slide # 06 - 07 Contract profit or loss Slide # 08 - 09 Lifetime values Slide # 10 - 11 Futures hedge Slide # 12 - 15 Futures options Slide # 16 - 17 Interest rate swap

2: Futures price Given the following table, what is the price per troy ounce that will be used for today’s marking-to-market for the September contract? Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276

3: Futures price The price per troy ounce that will be used for today’s marking-to- market for the September contract is 612.7 cents per troy ounce. Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276

4: Contract value Given the following table, what is this day’s closing contract price for one December futures contract? Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276

5: Contract value Today’s closing contract price for one December futures contract: Contract price = 5,000  616.6  .01 = $30,830 Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276

6: Contract profit or loss Assume that you originally bought one July futures contract at a quoted price of 586.7. What is your total profit or loss as of today’s close? Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276 fs

7: Contract profit or loss Total profit = 5,000  (611.0 – 586.7)  .01 = $1,215 Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276

8: Lifetime values You purchased 5 September futures contracts as soon as they were available. What is the total dollar difference between the highest and the lowest values for your account? Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276

9: Lifetime values Total dollar difference = 5  5,000  (831.1 – 476.8)  .01 = $88,575 Silver – 5,000 troy oz.; cnts per troy oz. Open High Low Settle Chg Lifetime Interest Jul 598.1 614.1 598.0 611.0 14.4 849.3 435.6 1,269 Sep 598.3 615.2 597.9 612.7 14.3 831.1 476.8 21,268 Dec 601.9 621.3 601.8 616.6 848.7 439.8 18,276

10: Futures hedge You are a dairy farmer. You expect to have 600,000 pounds of milk for January delivery. You hedge your position at a time when the futures prices are as quoted below. In January, the actual market price is 13.13. How much more would you have made or lost in total had you not taken the hedge position? Milk– 200,000 lbs.; cents per lb. Open High Low Settle Chg Lifetime Interest Jan 12.41 12.72 12.02 .01 12.46 11.99 489

11: Futures hedge Milk– 200,000 lbs.; cents per lb. Open High Low Settle Chg Lifetime Interest Jan 12.41 12.72 12.02 .01 12.46 11.99 489

12: Futures options You buy one May 415 call on gold. What is the total price per troy ounce that you will spend to acquire one troy ounce of gold? Ignore trading costs. Gold – 100 troy ounces; $ per troy ounce Price Call Apr May Jun Put 415 7.80 12.10 15.40 4.30 7.30 11.20 420 5.30 9.80 12.70 7.60 10.80 13.70

13: Futures options Total cost per troy ounce = $415 + $12.10 = $427.10 Gold – 100 troy ounces; $ per troy ounce Price Call Apr May Jun Put 415 7.80 12.10 15.40 4.30 7.30 11.20 420 5.30 9.80 12.70 7.60 10.80 13.70

14: Futures options You sell one April 420 put on gold. What is the total amount of the option premium you will receive? Ignore trading costs. Gold – 100 troy ounces; $ per troy ounce Price Call Apr May Jun Put 415 7.80 12.10 15.40 4.30 7.30 11.20 420 5.30 9.80 12.70 7.60 10.80 13.70

15: Futures options Option premium = $7.60  100 = $760 Gold – 100 troy ounces; $ per troy ounce Price Call Apr May Jun Put 415 7.80 12.10 15.40 4.30 7.30 11.20 420 5.30 9.80 12.70 7.60 10.80 13.70

16: Interest rate swap Company X can borrow at prime + 2 or at a fixed rate of 8.5%. Company Y can borrow at prime + 3 or at a fixed rate of 8%. Company X wants a fixed rate loan. Company Y wants a variable rate loan. Can you arrange an interest rate swap that is beneficial to Company A, to Company B and to the dealer?

17: Interest rate swap Company X: Company Y: borrows at prime + 2 borrows at 8% pays 8.25% fixed pays prime + 2.5 Dealer: pays prime + 2 receives prime + 2.5 pays 8% receives 8.25%

23 End of Chapter 23