Chapter23
•Risk Management: An
Introduction to Financial
Engineering
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 23 – Index of Sample
Problems
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Slide # 02 - 03
Slide # 04 - 05
Slide # 06 - 07
Slide # 08 - 09
Slide # 10 - 11
Slide # 12 - 15
Slide # 16 - 17
Futures price
Contract value
Contract profit or loss
Lifetime values
Futures hedge
Futures options
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 Lifetime
Open
High
Low 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 14.4
848.7
439.8
18,276
3: Futures price
The price per troy ounce that will be used for today’s marking-tomarket 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 Lifetime
Open
High
Low 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 14.4
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 Lifetime
Open
High
Low 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 14.4
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 Lifetime
Open
High
Low 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 14.4
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 Lifetime
Open
High
Low 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 14.4
848.7
439.8
18,276
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 Lifetime
Open
High
Low 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 14.4
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 Lifetime
Open
High
Low 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 14.4
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 Lifetime
Open
High
Low 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 14.4
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 Lifetime
Open
High
Low Interest
Jan 12.41 12.72 12.02 12.72
.01
12.46
11.99
489
11: Futures hedge
600,000
Profit forfeited 
 200,000  (13.13  12.72)  .01  $2,460
200,000
Milk– 200,000 lbs.; cents per lb.
Open
High
Low Settle Chg Lifetime Lifetime
High
Low
Jan 12.41 12.72 12.02
12.72
.01
12.46
11.99
Open
Interest
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
Call
May
Call
Jun
Put
Apr
Put
May
Put
Jun
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
Call
May
Call
Jun
Put
Apr
Put
May
Put
Jun
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
Call
May
Call
Jun
Put
Apr
Put
May
Put
Jun
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
Call
May
Call
Jun
Put
Apr
Put
May
Put
Jun
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:
borrows at prime + 2
pays 8.25% fixed
Dealer:
pays prime + 2
receives prime + 2.5
pays 8%
receives 8.25%
Company Y:
borrows at 8%
pays prime + 2.5
Chapter23
•End of Chapter 23
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.