CORPORATE
FINANCIAL
THEORY
Lecture 11
Hedging & Futures
Today
 We will return to Capital Budgeting & Financing.
 We will discuss how to reduce risk.
Companies have risk
 Manufacturing Risk - variable costs
 Financial Risk - Interest rate changes
Goal - Eliminate risk
HOW?
Hedging & Futures Contracts
Example – Cereal Production

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
Example – Cereal Production (continued)
•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
Example – Cereal Production (continued)
NET POSITION
Profit
Asset
Price
Loss
Example – Cereal Production (continued)
Farmer’s view
Profit Scenario for Farmer
Revenue  This is variable
-costs
Profits
Profit
Short
Forward /
futures
Long sugar
Asset
Price
Loss
Example – Cereal Production (continued)
Together
Long Hedger
Short Hedger
Natural position: Short sugar
Natural position: Long sugar
Risk: Purchase price of sugar
Risk: Sales price of sugar
Hedge: Long contract
Hedge: Short contract
Types of Forwards / Futures
Commodity Futures
-Sugar -Corn
-Wheat-Soy beans
Financial Futures
-Tbills
-Yen
-Stocks -Eurodollars
-OJ
-Pork bellies
-GNMA
Index Futures
-S&P 500
-Value Line Index
-Vanguard Index
Futures/Forward Contracts
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.
Futures Contract Concepts






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
Example: Speculation
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
Example: Hedge


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 Hedge


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
Example: Commodity Hedge


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
Margin




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: Margin

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: Margin

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
68% loss
- 5,130
Trading Places
Short and Long Trades
Financial Futures
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.”
Ex - Financial Futures
Example - Hedge
Bond Position
Futures Position
Nov
Long $1,000
Short 1K @$970
March
Sell @ $930
Long 1K @$900
loss $70
Net position = $ 0
gain $ 70
Bond Prices & Yields
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 Price Sensitivity
Bond A
YTM = 4.00%
Maturity = 8 years
Coupon = 6% or $60
Par Value = $1,000
Bond B
YTM = 3.50%
Maturity = 5 years
Coupon = 7% or $70
Par Value = $1,000
Price = $1,158.03
Price = $1,134.65
Bond Price Sensitivity
Bond B
Bond A
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 =$1,121.57
New Price= $1,081.61
Price dropped by 3.25 %
Price dropped by 4.67 %
Yields increased 0.75%...prices dropped differently
Ex - Financial Futures
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
Ex - Financial Futures
You are long in $1mil of bonds (15 yr 8.3125% bonds)
The current YTM is 10.45% and the current price is 8217. 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?
Ex - Financial Futures
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?
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)
Financial Futures
The art in Financial futures is finding the exact number
of contracts to make the net gain/loss = $ 0.
This is called the Hedge Ratio
$ Face Value Cash
# of Ks = ---------------------------------- X Hedge Ratio
$ Face Value of Futures K
HR Goal - Find the # of Ks that will
perfectly offset cash position.
Hedge Ratio Determination
1 - The Duration Model
2 - Naive Hedging Model
3 - Conversion Factor Model
4 - Basis Point Model
5 - Regression Model
6 - Yield Forecast Model
Swaps
An agreement between two firms in which each firm
agrees to exchange (or Swap) the “interest rate
characteristics” of two different financial instruments of
identical principal.
Types
Interest Rate Swaps
Currency Swaps