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Chapter 3
Derivatives and Hedging Risk
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
 Understand
the basics of forward and
futures contracts
 Understand how derivatives can be
used to hedge risks faced by the
corporation
25-1
Derivatives, Hedging, and Risk


Derivatives defined as securities whose values
are determined by the market price of some
other assets.
When the firm reduces its risk exposure with
the use of derivatives – hedging
25-2
Forward Contracts
A
forward contract specifies that a certain
commodity will be exchanged at a
specified time in the future at a price
specified today.
Its not an option: both parties are expected to hold
up their end of the deal.
 If you have ever ordered a textbook that was not in
stock, you have entered into a forward contract.

25-3
Futures Contracts

A futures contract is like a forward contract:


It specifies that a certain commodity will be
exchanged at a specified time in the future at a
price specified today.
A futures contract is different from a forward:

Futures are standardized contracts trading on
organized exchanges with daily resettlement
(“marking to market”) through a clearinghouse.
25-4
Futures Contracts



Standardizing Features
 Contract Size
 Delivery Month
Daily resettlement
 Minimizes the chance of default
Initial Margin
 About 4-10% of contract value
 Cash or T-bills held in a street name at your
brokerage
25-5
Daily Resettlement: An Example
Suppose you want to speculate on a rise in the $/¥
exchange rate (specifically, you think that the dollar will
appreciate).
Japan (yen)
1-month forward
3-months forward
6-months forward
U.S. $ equivalent
Wed
Tue
0.007142857 0.007194245
0.006993007 0.007042254
0.006666667 0.006711409
0.00625 0.006289308
Currency per
U.S. $
Wed
Tue
140
139
143
142
150
149
160
159
Currently $1 = ¥140.
The 3-month forward price is $1=¥150.
25-6
Daily Resettlement: An Example
Currently $1 = ¥140, and it appears that the
dollar is strengthening.
 If you enter into a 3-month futures contract to
sell ¥ at the rate of $1 = ¥150 you will profit if
the yen depreciates. The contract size is
¥12,500,000
 Your initial margin is 4% of the contract value:

$3,333.33 = 0.04 × ¥12,500,000 ×
$1
¥150
25-7
Daily Resettlement: An Example
If tomorrow the futures rate closes at $1 = ¥149,
then your position’s value drops (¥ appreciated).
Your original agreement was to sell ¥12,500,000
and receive $83,333.33:
$83,333.33 = ¥12,500,000 ×
$1
¥150
But, ¥12,500,000 is now worth $83,892.62:
$83,892.62 = ¥12,500,000 ×
$1
¥149
You have lost $559.29 overnight.
25-8
Daily Resettlement: An Example
 The
$559.29 comes out of your $3,333.33
margin account, leaving $2,774.04.
 This is short of the $3,355.70 required for a
new position.
$3,355.70 = 0.04 × ¥12,500,000 ×
$1
¥149
Your broker will let you slide until you run through
your maintenance margin. Then you must post
additional funds, or your position will be closed out.
This is usually done with a reversing trade.
25-9
Futures Markets
 The
Chicago Mercantile Exchange
(CME) is by far the largest.
 Others include:
The Philadelphia Board of Trade (PBOT)
 The MidAmerica Commodities Exchange
 The Tokyo International Financial Futures
Exchange
 The London International Financial Futures
Exchange

25-10
Basic Futures Relationships
Open Interest refers to the number of contracts
outstanding for a particular delivery month.
 Open interest is a good proxy for the demand
for a contract.
 Some refer to open interest as the depth of the
market. The breadth of the market would be
how many different contracts (expiry month)
are outstanding.

25-11
Hedging

Two counterparties with offsetting risks can
eliminate risk.

For example, if a wheat farmer and a flour mill
enter into a forward contract, they can eliminate
the risk each other faces regarding the future price
of wheat.
Hedgers can also transfer price risk to
speculators, who absorb price risk from
hedgers.
 Speculating: Long vs. Short

25-12
Hedging and Speculating: Example
You speculate that copper will go up in price, so you go
long 10 copper contracts for delivery in 3 months. A
contract is 25,000 pounds in cents per pound and is at
$0.70 per pound, or $17,500 per contract.
If futures prices rise by 5 cents, you will gain:
Gain = 25,000 × .05 × 10 = $12,500
If prices decrease by 5 cents, your loss is:
Loss = 25,000 ×( –.05) × 10 = –$12,500
25-13
Hedging: How many contracts?
You are a farmer, and you will harvest 50,000 bushels
of corn in 3 months. You want to hedge against a
price decrease. Corn is quoted in cents per bushel at
5,000 bushels per contract. It is currently at $2.30
cents for a contract 3 months out, and the spot price
is $2.05.
To hedge, you will sell 10 corn futures contracts:
50,000 bushels
10 contracts =
5,000 bushels per contract
Now you can quit worrying about the price of corn
and get back to worrying about the weather.
25-14
TEST

Golden Grain Farms (GGF) expects to harvest
50,000 bushels of wheat in September. GGF
is concern about the possibility of price
fluctuations from now until September. The
futures price for September wheat is $2 per
bushel and the relevant contract calls for
5,000 bushels. Three month later, the price of
on September futures turns out to be $3.
Evaluate GGF’s number of contract and profit
or loss in the future position.
25-15
3.5 Interest Rate Futures Contracts
i.
ii.
iii.
iv.
Pricing of Treasury Bonds
Pricing of Forward Contracts
Futures Contracts
Hedging in Interest Rate Futures
25-16
i. Pricing of Treasury Bonds
Consider a Treasury bond that pays a semiannual
coupon of $C for the next T years:
 The yield to maturity is R
0
C
C
C
1
2
3
…
CF
2T
Value of the T-bond under a flat term structure
= PV of face value + PV of coupon payments
F
C
1 
PV 
 1 
T
T 
(1  R )
R  (1  R ) 
25-17
Pricing of Treasury Bonds
If the term structure of interest rates is not flat,
then we need to discount the payments at
different rates depending upon maturity.
0
C
C
C
1
2
3
…
CF
2T
= PV of face value + PV of coupon payments
C
C
C
CF
PV 


 
2
3
T
(1  R1 ) (1  R2 ) (1  R3 )
(1  R2T )
25-18
TEST

A Treasury note with a maturity of 4 years
pays interest semiannually on 9 percent
annual coupon rate. The RM1,000 face value
is returned at maturity. If the effective annual
yield for all maturities is 12 percent annually,
compute the current price of the Treasury
note.
25-19
ii. Pricing of Forward Contracts
An N-period forward contract on that T-Bond:
 Pforward C C C
CF
…
0
N N+1 N+2 N+3
N+2T
Can be valued as the present value of the forward price.
PV 
Pforward
(1  R N )
N
C
C
C
CF


 
2
3
(1  R N 1 ) (1  R N  2 ) (1  R N  3 )
(1  R N  2T )T
PV 
(1  R N ) N
25-20
Pricing of Forward Contracts: Example
Find the value of a 5-year forward contract on a 20-year T-bond.
The coupon rate is 6 percent per annum, and payments are made
semiannually on a par value of $1,000.
40 = 20 × 2
The Yield to Maturity is 5
percent.
I/Y
5
PV
–1,125.51
First, set your calculator to 2
payments per year.
N
PMT
FV
30 =
1,000
1,000 × .06
2
Then enter what you know
and solve for the value of a
20-year Treasury bond at the
maturity of the forward
contract.
25-21
iii. Pricing of Futures Contracts
 The
pricing equation given above will be
a good approximation.
 The only real difference is the daily
resettlement.
25-22
iv. Hedging in Interest Rate Futures
A mortgage lender who has agreed to loan
money in the future at prices set today can
hedge by selling those mortgages forward.
 It may be difficult to find a counterparty in the
forward who wants the precise mix of risk,
maturity, and size.
 It is likely to be easier and cheaper to use
interest rate futures contracts.

25-23
3.6 Duration Hedging
 As
an alternative to hedging with futures
or forwards, one can hedge by matching
the interest rate risk of assets with the
interest rate risk of liabilities.
 Duration is the key to measuring interest
rate risk.
25-24
Duration Hedging
 Duration
measures the combined effect
of maturity, coupon rate, and YTM on a
bond’s price sensitivity to interest rates.
 Measure
of the bond’s effective maturity
 Measure of the average life of the security
 Weighted average maturity of the bond’s
cash flows
25-25
Duration Formula
PV (C1 )  1  PV (C2 )  2    PV (CT )  T
D
PV
N
Ct  t

t
t 1 (1  R )
D N
Ct

t
t 1 (1  R )
25-26
Calculating Duration: Example
Calculate the duration of a three-year bond
that pays a semiannual coupon of $40 and
has a $1,000 par value when the YTM is 8%.
25-27
Duration
Properties:
 Longer
maturity, longer duration
 Duration increases at a decreasing rate
 Higher coupon, shorter duration
 Higher yield, shorter duration
 Zero
coupon bond: duration = maturity
25-28
TEST

SAM Berhad is issuing new bonds in order to
get additional capital for financing its
business operation. The par value is
RM2,300. The bonds offer 9 percent coupon
rate that will be compounded every six
months with maturity period of 5 years. The
required rate of return is 12 percent. Based on
the information given, calculate duration of
bond.
25-29
TUTORIAL
Q: 1, 2, 6, 9, 11, 12
Page: 792 - 793