Lecture 6
Companies have risk
Manufacturing Risk - variable costs
Financial Risk - Interest rate changes
Goal - Eliminate risk
HOW?
Hedging & Futures Contracts
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Kellogg’s produces cereal.
A major input and variable cost is sugar.
The price of a box of cereal is inflexible (i.e. it
has an elastic demand function).
Kellogg’s is naturally “short” in sugar
“short” = a requirement to buy the commodity
in the future.
Profit Scenario for Kellogg’s
Revenue
-costs
 This is variable
Profits
•Natural profit / loss position
•To hedge their natural position, Kellogg’s
will enter into a long futures / forward
contract
Profit
Short
sugar
Long
Futures / Forward
Contract
Asset
Price
Loss
NET POSITION
Profit
Asset
Price
Loss
Farmer’s view
Profit Scenario for Farmer
Profit
Revenue  This is variable
-costs
Profits
Short
Forward /
futures
Long sugar
Asset
Price
Loss
Together
Long Hedger
Short Hedger
Natural position: Short sugar
Natural position: Long sugar
Risk: Purchase price of
sugar
Risk: Sales price of sugar
Hedge: Short contract
Hedge: Long contract
Commodity Futures
-Sugar
-Corn
-OJ
-Wheat
-Soy beans -Pork bellies
Financial Futures
-Tbills
-Yen
-Stocks
-Eurodollars
Index Futures
-S&P 500 -Value Line Index
-Vanguard Index
-GNMA
Types of Contracts
1- Spot Contract - A K for immediate sale & delivery
of an asset.
2- Forward Contract - A K between two people for
the delivery of an asset at a negotiated price on a
set date in the future.
3- Futures Contract - A K similar to a forward
contract, except there is an intermediary that
creates a standardized contract. Thus, the two
parties do not have to negotiate the terms of the
contract.
Forward
Futures
Private contract between two
parties
Traded on an exchange
Not standardized
Standardized
Usually one specified delivery date
Range of delivery dates
Settled at end of contract
Settled daily
Delivery or final settlement usual
Usually closed out prior to
maturity
Some credit risk
Virtually no credit risk
Fundamentals of Futures and
Options Markets, 6th Edition,
Copyright © John C. Hull 2007
2.
10
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Not an actual sale
Always a winner & a loser (unlike stocks)
K are “settled” every day. (Marked to Market)
Hedge - K used to eliminate risk by locking in
prices
Speculation - K used to gamble
Margin - not a sale - post partial amount
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
Long position
Short position
◦ Also called “Short sale”
◦ Defined as
 1. An obligation to buy back the contract
 2. An obligation to deliver the asset in the future

Asset Short Sale
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The amount (percentage) of a Futures
Contract Value that must be on deposit with a
broker.
Since a Futures Contract is not an actual sale,
you need only pay a fraction of the asset
value to open a position = margin.
CME margin requirements are 15%
Thus, you can control $100,000 of assets
with only $15,000.
Example:
 You decide to enter into 3 long oil contracts. Each
contract has a size of 5,000 barrels. The futures
contract price of one barrel of oil is $65. If the margin
requirement is 15%, how much money must you put on
deposit with your broker?
Example:

You decide to enter into 3 long oil contracts. Each contract has a size
of 5,000 barrels. The futures contract price of one barrel of oil is $65.
If the margin requirement is 15%, how much money must you put on
deposit with your broker?
Long position  3  5,000  65
 $975,000
Margin requiremen t  $975,000  .15
 $146,250
You are speculating in Hog Futures. You think that the
Spot Price of hogs will rise in the future. Thus, you go
Long on 10 Hog Futures. If the price drops .17 cents per
pound ($.0017) what is total change in your position?
30,000 lbs x $.0017 loss x 10 Ks = $510.00 loss
50.63
-$510
50.80
cents
per lbs
Since you must settle your account
every day, you must give your broker
$510.00
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You are an Illinois farmer. You planted 100 acres of
wheat this week, and plan on harvesting 20,000 bushels
in March. If today’s futures wheat price is $1.56 per
bushel, and you would like to lock in that price, what
would you do?
Since you are long in Wheat, you will need to go short on
March wheat. Since1 contract= 5,000 bushels, you
should short four contracts today and close your
position in March.

Example – Commodity Speculation: No Margin
You think you know everything there is to know about pork bellies
(bacon) because your butler fixes it for you every morning. Because you
have decided to go on a diet, you think the price will drop over the next
few months. On the CME, each PB K is 38,000 lbs. Today, you decide to
short three May Ks @ 44.00 cents per lbs. In Feb, the price rises to 48.5
cents and you decide to close your position. What is your gain/loss?
Nov: Short 3 May K (.4400 x 38,000 x 3 ) =
+ 50,160
Feb: Long 3 May K (.4850 x 38,000 x 3 ) =
- 55,290
Loss of 10.23 % =
- 5,130

Example –Commodity Speculation: With Margin
You think you know everything there is to know about pork bellies
(bacon) because your butler fixes it for you every morning. Because you
have decided to go on a diet, you think the price will drop over the next
few months. On the CME, each PB K is 38,000 lbs. Today, you decide to
short three May Ks @ 44.00 cents per lbs. In Feb, the price rises to 48.5
cents and you decide to close your position. What is your gain/loss?
Nov: Short 3 May K (.4400 x 38,000 x 3 ) =
+ 50,160
Feb: Long 3 May K (.4850 x 38,000 x 3 ) =
- 55,290
Loss =
Loss
------------
Margin
5130
=
--------------------
50160 x.15
5130
=
------------ =
7524
- 5,130
68% loss
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In June, farmer John Smith expects to harvest 10,000 bushels
of corn during the month of August. In June, the September
corn futures are selling for $2.94 per bushel (1K = 5,000
bushels). Farmer Smith wishes to lock in this price.
Show the transactions if the Sept spot price drops to $2.80.
Revenue from Crop: 10,000 x 2.80
28,000
June: Short 2K @ 2.94 = 29,400
Sept: Long 2K @ 2.80 = 28,000
Gain on Position------------------------------Total Revenue
.
1,400
$ 29,400
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In June, farmer John Smith expects to harvest 10,000 bushels
of corn during the month of August. In June, the September
corn futures are selling for $2.94 per bushel (1K = 5,000
bushels). Farmer Smith wishes to lock in this price.
Show the transactions if the Sept spot price rises to $3.05.
Revenue from Crop: 10,000 x 3.05
30,500
June: Short 2K @ 2.94 = 29,400
Sept: Long 2K @ 3.05 = 30,500
Gain on Position------------------------------Total Revenue
.
-1,100
$ 29,400
Basis Risk = Spread between the Futures Price and Spot Price
Futures
Price
Spot Price
Spot Price
Futures
Price
Time
Time
(a)
(b)
Fundamentals of Futures and
Options Markets, 6th Edition,
Copyright © John C. Hull 2007
2.
22
Basis Strengthens
Futures
Price
Spread between spot price and
futures price gets smaller
Basis Weakens
Spot
Price
Spread between spot price and
futures price gets larger
Time
t1
t2
Fundamentals of Futures and
Options Markets, 6th Edition,
Copyright © John C. Hull 2007
3.
23
The art in hedging is finding the exact
number of contracts to make the net
gain/loss = $ 0.
This is called the Hedge Ratio
Value Asset
# of Ks = ---------------------------------- X Hedge Ratio
Value of Contract
HR Goal - Find the # of contracts that
will perfectly offset asset position.
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Previous example: An Illinois farmer planted 100 acres of
wheat this week, and plans on harvesting 20,000 bushels in
March. If today’s futures wheat price is $1.56 per bushel and
since the farmer is long in wheat, the farmer will need to go
short on March wheat contracts. Since1 contract= 5,000
bushels, the farmer will short four contracts today and close
the position in March.
20,000
4 contracts = ------------------------ X 1.0
5,000
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•
•
•
Hedging the risk of one asset with a contract on
another asset.
Example
You manage a stock mutual fund and wish to
hedge against a drop in the stock prices.
Since there is no contract on your specific mutual
fund, you must use a different asset.
You decide to use the S&P 500 Index K
Profit
Short
S&P 500
Contract
Long
Stock Mutual Fund
+2
Asset
Price
-2
Loss
8
10
Risk: Contract price behavior is different than the price
behavior of the mutual fund
Profit
Short
S&P 500
Contract
+2
+1
Long
Stock Mutual Fund
Asset
Price
-2
Loss
8
10
•Assume the mutual fund has a total value of $725,000.
•One S&P 500 index futures contract has a price of 1,450.
•S&P Contract Value = (price) x 250
•S&P Contract Value = (1450) x 250 = 362,500
•Using a hedge ratio of 1.0, the # of contracts is as follows.
725,000
2 contracts = ------------------------ X 1.0
362,500
•Profit / loss is as follows
•Recall…Mutual Fund price dropped from 10 to 8….a 20%
decline
•Recall…Index futures price dropped from 10 to 9….a 10%
Asset Position
Futures Position
decline
Starts
Long $725,000
Short 2 contracts
362,500 x 2 = 725,000
position
Finish
Long 2 contracts to close
Price drop 20%
Price drops 10%
725,000 x .8 = 580,000
1450 x .9 x 2 x 250 = 652,500
loss $145,000
gain $ 72,500
Net position LOSS = $ 72,500
BAD HEDGE
 im
Bi  2
m
Covariance
between the stock
market index and
an asset
Variance of the stock market index
Beta of Mutual Fund = 2.0
Profit
Short
S&P 500
Contract
+2
+1
Long
Stock Mutual Fund
Asset
Price
-2
Loss
8
10
•Assume the mutual fund has a total value of $725,000.
•One S&P 500 index futures contract has a price of 1,450.
•S&P Contract Value = (price) x 250
•S&P Contract Value = (1450) x 250 = 362,500
•Using a hedge ratio of 2.0, the # of contracts is as follows.
725,000
4 contracts = ------------------------ X 2.0
362,500
•Profit / loss is as follows
•Recall…Mutual Fund price dropped from 10 to 8….a 20%
decline
•Recall…Index futures price dropped from 10 to 9….a 10%
Asset Position
Futures Position
decline
Starts
Long $725,000
Short 4 contracts
362,500 x 4 = 1,450,000
position
Finish
Long 4 contracts to close
Price drop 20%
Price drops 10%
725,000 x .8 = 580,000
1450 x .9 x 4 x 250 = 1,305,000
loss $145,000
gain $ 145,000
Net position Gain / Loss = $ 0
PERFECT HEDGE
Goal (Hedge) - To create an exactly opposite reaction
in price changes, from your cash position.
Commodities - Simple because assets types are
standard.
Financials - Difficult because assets types are infinte.
- You must attempt to approximate your position with
futures via “Hedge Ratios.”
Example
If today is October 2008, what is the value of the following bond?
An IBM Bond pays $115 every Sept for 5 years. In Sept 2013 it pays an
additional $1000 and retires the bond.
The bond is rated AAA (WSJ AAA YTM is 7.5%)
Cash Flows
Sept 2009 2010 2011 2012 2013
115
115 115 115 1115
Example continued
If today is October 2008 what is the value of the following bond?
An IBM Bond pays $115 every Sept for 5 years. In Sept 2013 it pays an additional $1000 and
retires the bond.
The bond is rated AAA (WSJ AAA YTM is 7.5%)
115
115
115
115
1,115
PV 




2
3
4
1.075 1.075 1.075 1.075 1.0755
 $1,161.84
1600
1400
Price
1200
1000
800
600
400
200
0
0
2
4
5 Year 9% Bond
6
8
10
1 Year 9% Bond
12
14
Yield
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All interest bearing instruments are priced to
fit the term structure
This is accomplished by modifying the asset
price
The modified price creates a New Yield, which
fits the Term Structure
The new yield is called the Yield To Maturity
(YTM)
Example
 A $1000 treasury bond expires in 5 years. It
pays a coupon rate of 10.5%. If the market
price of this bond is 107.88, what is the YTM?
Example
 A $1000 treasury bond expires in 5 years. It
pays a coupon rate of 10.5%. If the market
price of this bond is 107.88, what is the YTM?
C0
-1078.80
C1
C2
C3
C4
C5
105
105
105
105
1105
Calculate IRR = 8.5%
1600
1400
Price
1200
1000
800
600
400
200
0
0
2
4
5 Year 9% Bond
6
8
10
1 Year 9% Bond
12
14
Yield
Bond A
Bond B
YTM = 4.00%
Maturity = 8 years
Coupon = 6% or $60
Par Value = $1,000
YTM = 3.50%
Maturity = 5 years
Coupon = 7% or $70
Par Value = $1,000
Price = $1,134.65
Price = $1,158.03
Bond A
Bond B
YTM = 4.75%
Maturity = 8 years
Coupon = 6% or $60
Par Value = $1,000
YTM = 4.25%
Maturity = 5 years
Coupon = 7% or $70
Par Value = $1,000
New Price= $1,108.61
New Price =$1,121.57
Price dropped by 2.30 %
Price dropped by 3.15 %
Yields increased 0.75%...prices dropped differently
Example - Hedge
Nov
March
Bond Position
Long $1,000
Futures Position
Short 1K @$970
Sell @ $930
loss $70
Long 1K @$900
gain $ 70
Net position = $ 0
Example - Hedge Reality
Nov
March
Bond Position
Long $1,000
Futures Position
Short 1K @$970
Sell @ $930
loss $70
Long 1K @$920
gain $ 50
Net position = $ 20 loss
You are long in $1mil of bonds (15 yr 8.3125%
bonds) The current YTM is 10.45% and the
current price is 82-17. You want to cash out now,
but your accountant wants to defer the taxes until
next year. The March Bond K is selling for 80-09.
Since each K is $100,000, you need to short 10
March Ks. In March you cash out with the Bond
price = 70-26 and the K price = 66-29. What is the
gain/loss?
You are long in $1mil of bonds (15 yr 8.3125% bonds) The current
YTM is 10.45% and the current price is 82-17. You want to cash out
now, but your accountant wants to defer the taxes until next year. The
March Bond K is selling for 80-09. Since each K is $100,000, you need
to short 10 March Ks. In March you cash out with the Bond price = 7026 and the K price = 66-29. What is the gain/loss?
Cash
Futures
Basis
Nov
$825,312
$802,812
+ (2-8)
March
$708,125
$669,062
+ (3-29)
Gain/Loss
($117,187)
$133,750
+ (1-21)
Net Gain = $16,563
(= 1-21 x $1mil)