CHAPTER 4
Using Futures Markets
In this chapter, we discuss the different ways that futures
markets serve different members of society. This chapter is
organized into the following sections:
1. Price Discovery
2. Speculation
3. Hedging
Chapter 4
1
Price Discovery
Because the futures market incorporates the collective
opinion of many buyers and sellers, the futures market can
be used to reveal information about future spot prices.
The usefulness of forecasting future spot prices, based on
current futures prices, depends upon three factors:
1. Information: the need for information about future spot
prices.
2. Accuracy: the accuracy of the futures market forecasts
of those prices.
3. Performance: the performance of futures market
forecasts relative to alternative forecasting techniques.
Chapter 4
2
Information
Interest Rates and Home Buying
You are in the market for a new home and you want to
have an idea of how interest rates will behave in the next
year. By examining the WSJ, you can discover what the
market as a whole thinks about the future course of
interest rates. If the interest rate (yield) on bonds to be
delivered in six months is three percentage points lower
than current interest rates, then there is good reason to
expect that interest rates will fall over the next six months.
Furniture Manufacturer
A furniture manufacturer needs to print its catalog for the
next year and needs to include prices. Furniture prices will
depend in part upon next year’s lumber prices. The
furniture manufacturer can review the lumber futures
market to estimate the costs of the wood.
The person using the futures market to estimate the future
course of interest rates or the future course of lumber
prices is using the futures market for its price discovery
benefit.
Chapter 4
3
Accuracy
We would like the estimator of the expected future spot
price to be accurate. If it is not accurate, its usefulness is
limited. A forecast estimate is unbiased if, on average, the
forecast is correct. However, even if a forecast estimate is
unbiased, the range might be so wide that its usefulness is
limited.
Example
I predict that the points scored by the winner in the NBA
finals game will be between 50 and 150 points. On
average, I might be right, but the range is so wide that it
not particularly useful.
Futures prices sometimes have large errors and these may
differ across commodities.
Chapter 4
4
Performance
Evidence suggests that while futures markets have large
errors, they are generally better at predicting the future
than any other available methods of forecasting.
Because of this property, military researchers have
suggested using futures contracts to predict terrorist
attacks.
Chapter 4
5
Forecasting Oil Prices
A Case Study
Table 4.1 illustrates a case of a large forecast error.
Table 4.1
Forecast Errors for Alternative Forecasts
Commodity
Horizon
Futures Error
No--Change Error
Crude Oil
1 Month
.0148
.0268
2 Month
.0268
.0499
3 Month
.0456
.0720
6 Month
.1057
.1469
1 Month
.0074
.0085
2 Month
.0182
.0196
3 Month
.0284
.0305
6 Month
.0628
.0553
1 Month
.0129
.0155
2 Month
.0261
.0281
3 Month
.0397
.0440
6 Month
.0956
.0893
Heating Oil
Leaded Gasoline
Source: Cindy W. Ma, “Forecasting Efficiency of Energy Futures Prices,” The
Journal of Futures Markets, 9:5, October 1989, pp. 393-419.
Chapter 4
6
Forecasting Performance for Different
Commodities
Quality of forecasts differ across commodities.
Table 4.2
Forecasting Power of Commodity Futures
Forecasting Power for All Maturities
Broilers
Eggs
Hogs
Oats
Forecasting Power for Most Maturities
Cattle
Pork bellies
Soybeans
Soymeal
No Forecasting Power
Lumber
Soyoil
Cocoa
Corn
Wheat
Coffee
Copper
Cotton
Gold
Platinum
Silver
Forecasting Power for Some Maturities
Orange juice
Plywood
Source: Eugene F. Fama and Kenneth R. French, ‘Commodity Futures Prices:
Some Evidence on Forecast Power, Premiums, and the Theory of Storage,”
Journal of Business, 60:1, 1987, pp. 55-73.
Chapter 4
7
Speculation
A speculator is a trader who enters the market to profit
from short term price changes. In doing so, he/she
assumes risk that other individuals are trying to dispose of.
Most individuals have no heavy exposure in the futures
market. As such when they enter the futures market it is for
speculation.
There are three kind of speculators:
1. Scalpers
2. Day Traders
3. Position Traders
Chapter 4
8
Scalpers
A scalper is an individual that enters the futures market to
profit from very short term price movements. A scalper is
generally trying to guess the short term psychology of the
market.
How Long of Intervals?
– From the next few seconds to the next few minutes.
– Requires the scalper to be in the trading pit to observe the
behavior of other buyers and sellers.
– Generally involves a great many trades earning a small
profit on each trade. One study shows that scalpers make
about 70 trades per day.
By trading very frequently, scalpers provide liquidity to the
market.
Chapter 4
9
Scalpers’ Behavior Study
Table 4.3
Mr. X's Trades Over 31 Trading Days
Total Transactions
2,106
Number of Contracts Traded
(Round turns-buy and sell 1 contract)
2,178
Number of Trades
(Zero net position to a zero net position)
729
Profitable
353 (48%)
Unprofitable
157 (22%)
Scratch
219 (30%)
Source: William L. Silber, “Marketmaker Behavior in an Auction Market: An
Analysis of Scalpers in Futures Market,” Journal of Finance, September 1984,
39:4, pp. 937B953.
Chapter 4
10
Services Provided by Scalpers
1. Provide a party willing to take the opposite side of a
trade for an off-the-floor trader.
2. Actively trade, thereby generating price quotations and
allowing the market to discover prices more effectively.
3. By competing for trades, help to close the bid-asked
spread, thereby reducing execution costs for other
traders.
4. Attract hedging activity, because hedgers know their
orders can be executed.
Chapter 4
11
Day Traders
Day traders attempt to profit from trades that occur during
a single trading day.
Day traders close all of their positions before the end of the
trading day. As such, day traders have no position in the
futures market overnight.
By closing all of their positions at the end of the day, day
traders are able to reduce their risk. Holding a position
overnight is a risky proposition as the supply of many
commodities is driven by weather.
Example: orange juice concentrated
Traded by the Citrus Associates of NY Cotton
Exchange Florida.
Weather is crucial to orange juice prices.
In November, a trader holds a short position in orange juice
futures. The trader checks the Florida Weather two days
before trading closes, and no evidence of damaging
weather exists, so the trader holds his position overnight.
Overnight, a strong cold front damages a large portion of
the orange crop. This trader suffers a large loss.
Chapter 4
12
Position Traders
A position trader is a speculator that holds a position
overnight. Sometimes they may hold them for weeks or
months.
There a two types of position traders:
– Outright Position
– Spread Position
These two types of trades will be discussed in turn.
Chapter 4
13
Outright Positions
This is simply taking a naked position in a commodity. For
example, a trader thinks that long-term interest rate will
increase, and consequently futures prices for bonds will
fall. Therefore, the trader sells a futures contract on U.S.
Treasury bonds.
If long-term interest rates rise as the trader expected, the
trader will earn a profit.
The risk is that the long-term interest rate will decline
rather than increase. In which case the position trader will
lose money.
Chapter 4
14
Spread Positions
Spread positions involve trading multiple contracts on the
same or related commodities.
The idea is to profit when the difference in prices between
the two related commodities changes.
There are two basic types of spreads:
1. Inter-commodity spread
In an inter-commodity spread, a trader takes a position in two
or more different but related commodities.
2. Intra-commodity spread
In an intra-commodity spread, a trader takes a position in two
or more maturity months for the same good.
Example:
Wheat and corn are substitutes for each other for certain
uses (e.g., ethanol production and cattle feed). Therefore,
we would expect a certain relationship to exist between the
prices of the two commodities. That is, the prices of these
two commodities should follow some pattern.
Chapter 4
15
Spread Position
Inter-Commodity Case
Table 4.5 illustrates the case of a spread speculator who
believes that the difference between futures price of wheat
and corn is too high.
Table 4.5
An Inter-Commodity Spread
The wheat and corn contracts are both for 5,000 bushels.
Date
Futures Market
February 1
Sell 1 JUL wheat contract at 329.50 cents per bushel.
Buy 1 JUL corn contract at 229.00 cents per bushel.
June 1
Buy 1 JUL wheat contract at 282.75 cents per
bushel.
Sell 1 JUL corn contract at 219.50 cents per bushel.
Corn Loss:
B$.095 per bushel x 5,000 bushels =
B$475.00
Wheat Profit:
$.4675 per bushel x 5,000 bushels =
$2,337.50
Total Profit: $1,862.50
Notice that the spread has narrowed as expected resulting
in a profit on the transactions.
Chapter 4
16
Spread Position
Inter-Commodity Case
Insert figure 4.1 and 4.2 below
Chapter 4
17
Spread Position
Intra-Commodity Case
Tables 4.6 and 4.7 will be used to illustrate a more
complex spread, “the butterfly spread.”
Table 4.6
Copper Futures Prices on November 10
Delivery Month
(of following year)
Price
(cents per pound)
JUL
67.0
SEP
67.5
DEC
70.5
Chapter 4
18
Spread Position
Intra-Commodity Case
Table 4.7
A Butterfly Spread in Copper
The copper contract trades on the Commodity Exchange, Inc., a division of the
New York Mercantile Exchange (NYMEX). Each contract is for 25,000 pounds.
Date
Futures Market
November 10
April 15
Sell 1 JUL copper contract at 67 cents per pound.
Buy 2 SEP copper contracts at 67.5 cents per pound.
Sell 1 DEC copper contract at 70.5 cents per pound.
Buy 1 JUL copper contract at 65 cents per pound.
Sell 2 SEP copper contracts at 67 cents per pound.
Buy 1 DEC copper contract at 68.5 cents per pound.
Profits and Losses:
JUL: +$.02 x 25,000 pounds = +$500
SEP: -$.005 x 2 contracts x 25,000 pounds =
-$250
DEC: +$.02 x 25,000 pounds = +$500
Total Profit: $750
Chapter 4
19
Speculative Profits
Evidence suggests that some individuals earn good returns
by speculating but many do not. When you incorporate the
value of your time as well as the opportunity cost of funds
that you invest, many positive returns disappear.
Table 4.8
Evidence on Speculative Profits
Study
Stewart (1949)
Houthakker (1957)
Rockwell (1967)
Ross (1975)
Chang and Stevenson (1985)
Hartzmark (1987)
Key Results
75% of speculators lost money.
Small speculators lost in grains, but made
profits in cotton.
Small speculators lose consistently after considering transaction costs.
Speculators made money before commissions and lost money including commissions.
Small speculators make profits.
Large speculators do not earn significant
profits; large hedgers do not have significant
losses.
Leuthold, Garcia, and Lu (1994)
Large reporting traders in frozen pork bellies
earn significant profits.
Chapter 4
20
Technical Trading Systems
Technical analysis is a method of analyzing markets that
uses only market data (price, volume, open interest, etc) to
predict future price movements.
Table 4.9
Evidence on Technical Trading Systems
Study
Key Results
Tomek and Querin (1984)
The chance for a technical trading rule to
work is small.
Neftci and Policano (1984)
Some predictive power for T-bills, gold, and
soybeans, but none for copper.
Lukac, Brorsen, and Irwin
(1988a)
Examination of 12 different technical trading
systems found that 7 generate profits, thus
providing some support for technical
analysis.
Lukac, Brorsen, and Irwin
(1988b)
Technical trading systems are similar, and
generate trading signals at similar times.
Lukac, Brorsen, and Irwin (1989)
Trading systems require users to specify
parameters, but past data do not help choose
best parameters.
Chapter 4
21
Commodity Funds
A commodity fund is a financial institution that accepts
funds from a variety of participants and uses those funds to
speculate in the futures market. To succeed, commodity
funds must be able to earn speculative profits, presumable
through technical trading systems.
Table 4.10
Studies of Commodity Funds
Study
Key Results
Irwin and Brorsen (1985)
Returns vary widely by year; interest earnings
are a large part of total earnings; 65% of funds
lost money; including funds in a stock and bond
portfolio reduced portfolio risk.
Cornew (1986)
Funds only use 20% of total funds as margin deposits; 80% of funds earn interest.
Murphy (1986)
Performance of technically oriented funds is
inferior to stocks and TBbills; adding funds to
stock and bond portfolios reduces overall risk;
no evidence that funds outperform a buyBandBhold strategy.
Irwin and Brorsen (1985)
Funds place 28% of equity in margins.
Elton, Gruber, and Rentzler
(1987)
Overall performance is not attractive alone or as
an addition to a stock and bond portfolio; past
performance is not a good guide to future
performance.
Edwards and Ma (1988)
Pre-public trading results reported in fund
prospectuses do not help predict subsequent
fund performance and are substantially greater
than post-public performance.
Chapter 4
22
Hedging
A hedger is an individual who enters the futures market in
order to reduce a preexisting risk.
A preexisting position might include:
1. A commodity that you own: you have a silver mining
company and have silver stored. You own the commodity.
2. An anticipatory hedge: a commodity that you will acquire in
the future. If you are a new silver mining company and just
have initiated mining operations. You expect to
acquire/have silver in the future.
3. An anticipatory hedge: a commodity that you will need in
the future. You are a manufacturer of film, and silver is an
essential input for film production. You will need to acquire
silver to produce the film for next year sales.
Each of these positions can be hedged.
Chapter 4
23
Hedging Horizon
The hedge horizon is the amount of time that you need to
protect the price (hedge) for.
In some instances, you will have a predefined hedging
horizon. The silver mining company has just started mining
the silver ore. The process of going from mining to refined
silver takes 15 months. The silver mining company may
wish to hedge until the silver is mined and refined.
In other instances, there will be no specific hedging
horizon.
Chapter 4
24
A Long Hedge
A long hedge involves purchasing a futures contract.
Example
A film manufacturing company that needs silver in the future
would purchase a futures contract for silver. By doing so, the
company will know with certainty how much it will have to
pay for the silver in the future. Thus the firm has reduced
its risk.
Suppose that the film manufacturer needs 50,000 troy
ounces of silver in two months. The silver prices are as
follows:
Table 4.12
Silver Futures Prices on May 10
The COMEX division of NYMEX trades a silver contract for 5,000 troy ounces.
Price
Contract
(cents per troy ounce)
Spot
JUL
SEP
1052.5
1068.0
1084.0
Chapter 4
25
A Long Hedge
The film manufacturer estimates that to pay higher than
1068.0 cents per ounce could jeopardize profitability. Thus,
the company enters the futures market to hedge against
the possibility of higher silver prices. The transactions are
as follows:
Table 4.13
A Long Hedge in Silver
Date
Cash Market
Futures Market
May 10
Anticipates the need for 50,000
troy ounces in two months and
expects to pay 1068 cents per
ounce, or a total of $534,000.
Buys ten 5,000 troy ounce
JUL futures contracts at 1068
cents per ounce.
July 10
The spot price of silver is now
1071 cents per ounce. The
manufacturer buys 50,000
ounces, paying $535,500.
Since the futures contract is
at maturity, the futures and
spot prices are equal, and the
ten contracts are sold at 1071
cents per ounce.
Opportunity loss: -$1,500
Futures profit: $1,500
Net Wealth Change = 0
Chapter 4
26
A Short Hedge
A short hedge involves selling a futures contract to reduce
risk.
You ,a silver mine owner, are concerned about future silver
prices and its impact on your company’s profitability. You
may want to sell a futures contract to reduce risk.
By doing so, you will know exactly how much your
company will receive. Thus, you have reduced risk.
Suppose that you expect to have 50,000 troy ounces of
sliver in two months. The silvers prices are as follows:
Table 4.12
Silver Futures Prices on May 10
The COMEX division of NYMEX trades a silver contract for 5,000 troy ounces.
Price
Contract
(cents per troy ounce)
Spot
JUL
SEP
1052.5
1068.0
1084.0
Chapter 4
27
A Short Hedge
You estimate that a price of 1068.0 cents per ounce
satisfies your company’s profitability goals. Thus, the
company enters the futures market to hedge against the
possibility of lower silver prices. The transactions are as
follows:
Table 4.14
A Short Hedge in Silver
Date
Cash Market
May 10
Anticipates the sale of 50,000
troy ounces in two months and
expects to receive 1068 cents
per ounce, or a total of
$534,000.
July 10
The spot price of silver is now
1071 cents per ounce. The
miner sells 50,000 ounces,
receiving $535,500.
Profit $1,500
Net Wealth Change = 0
Chapter 4
Futures Market
Sells ten 5,000 troy ounce
July futures contracts at 1068
cents per ounce.
Buys 10 contracts at 1071.
Futures loss: -$1,500
28
Do Hedgers Need Speculators?
Hedgers, as a group, need speculators to take positions
and bear risk only for the mismatch in contracts demanded
by long and short hedgers.
If long and short hedgers had exactly offsetting needs,
hedgers would not need speculators.
Chapter 4
29
Cross-Hedging
In many cases, there will not be a futures contract
available that exactly matches our needs. In this case, we
need to engage in a cross-hedge.
A cross-hedge is needed when the characteristics of the
spot and futures positions do not match perfectly.
Some of the mismatches are:
–
Maturity: the hedging horizon may not match the futures
expiration date.
–
Quantity: the quantity to be hedged may not match the
futures contract quantity.
–
Quality: the physical characteristics of the commodity to
be hedged may differ from the characteristics required for
futures contract.
Chapter 4
30
Cross-Hedging
Maturity
Futures contracts may not mature at exactly the time that
you need delivery of the good. The film manufacturer
needs silver almost continuously. However, COMEX silver
futures trade only for delivery in February, April, May, Jul,
September and December. Thus, the futures expiration
dates and the hedging horizon don’t match perfectly.
Quantity
COMEX silver contracts are for 5,000 troy ounces.
However, a film manufacturer may only need 7,500
ounces. This company has a problem selecting the number
of contracts it needs for its production line.
Quality
For film manufacturing, silver needs to be in pellet form
and it does not need to be as pure as silver bullion.
COMEX silver contracts specifies that deliverable silver
must be 1,000 ounce ingots that are 99.9 percent pure, not
exactly the silver quality that the film manufacturer needs.
Chapter 4
31
Micro-Hedging versus Macro Hedging
Micro-Hedging
Micro-hedging occurs when a futures position is matched
against a specific asset or liability item on the balance
sheet.
Example: a bank hedging rates on one-year certificates of
deposits from the liability side of its balance sheet.
Macro-Hedging
Macro-hedging occurs when a hedge is structured to offset
the net risk associated with the hedger’s overall
asset/liability mix.
Example: a bank that uses interest rates to equate the
interest rate exposure of its assets with the interest rate
exposure of its liabilities.
Chapter 4
32
Stack Hedges versus Strip Hedges
Strip Hedge
Strip hedging occurs when a trader enters the futures
market and takes a series of futures positions of
successively longer expirations.
Stack Hedge
Stack hedging occurs when a trader enters the futures
market and takes a number of positions that can be
stacked in the front month and then rolled forward.
Chapter 4
33
Risk-Minimization Hedging
Sometimes we wish to minimize our risk, but do not have a
specific time horizon.
In other situations, we may need to cross-hedge.
In either case, purchasing one future for each position in
the cash market may not perfectly get rid of risk.
That is, the futures contract that we are using to hedge
may not move exactly with our cash position.
In this case, we may want to compute the risk-minimizing
hedge ratio.
Chapter 4
34
Risk-Minimization Hedging
Soybeans Case
Figure 4.3 shows 300 days of historical soybean cash prices.
Insert Figure 4.3 below
Chapter 4
35
Risk-Minimization Hedging
Soybeans Case
Suppose that you are a soybean meal processor. You hold
soybeans for regular use in your business. From this
inventory, you purchase soybeans and sell soybeans to
your customers.
You have an ongoing inventory of 1,000,000 bushel of
soybeans. Suppose the cash price of soybeans is
currently $7.19 (or 719.5 cents/bushel). As such, the
inventory is currently valued at $7,190,000.
You wish to minimize the price risk associated with holding
the inventory. You realize that if the price of soybeans were
to drop substantially, you would experience a loss in value
on the soybeans that you have in inventory. Such a loss
would be devastating to your profits. You wish to hedge
the price risk of the inventory that you hold.
Because the inventory is an ongoing asset, the processor
does not have a specified horizon. As such, the processor
wishes to engage in a risk-minimizing hedge.
Chapter 4
36
Risk-Minimization Hedging
Soybeans Case
Since you have the asset (you own the soybeans), the
hedge would involve selling futures contracts.
As soybeans futures trade in 5,000 bushel contracts, the
temptation is to sell 200 contracts, to match your inventory
on a 1:1 basis.
This approach might not be the risk-minimizing hedge. To
calculate the risk-minimizing number of contracts to sell,
we must compute the Hedge Ratio (HR).
Hedge Ratio (RH)
The number of futures contracts to hold for a given position
in a commodity.
Futures Position
HR  
Cash Market Position
Chapter 4
37
Risk-Minimization Hedging
Soybeans Case
To minimize your risk, you should trade HR futures
contracts.
The profits or losses on a portfolio for a day are:
Pt 1  Pt  S t 1  S t  HR Ft 1  Ft 
Where
Pt+1 = The value of the portfolio at time t+1
Pt = The value of the portfolio at time t
St+1 = The value of the spot position at time t+1
St = The value of the spot position at time t
Ft+1 = The value of the future position at time t+1
Ft = The value of the futures position at time t
Chapter 4
38
Risk-Minimization Hedging
Soybeans Case
The variance of a portfolio of one unit of the spot asset and
one unit of a futures contract can be computed as follows:
 P2   S2  HR 2 F2  2 HR SF  S  F
Where:
 P2  Variance on the portfolio Pt
 S2  Variance of St
 F2  Variance of Ft
 SF  Correlatio n coefficien t between St and Ft
Chapter 4
39
Risk-Minimization Hedging
Soybeans Case
The trader minimizes the variance on the portfolio by
selecting a hedge ratio as follows:
HRRM  
 SF S F
COVSF


 F2
 F2
Where:
COVSF= The covariance between the stock price and
the exercise price
HRRM = Risk-minimizing hedge ratio
The easiest way to compute the hedge ratio is by
estimating the following regression:
( St 1  St )     ( Ft 1  Ft )   t
Where
α = the constant regression parameter
β = the slope parameter
εt = random error term with mean = 0 and standard
deviation = 1
Chapter 4
40
Risk-Minimization Hedging
Soybeans Case
This regression will output:

the risk-minimizing hedge ratio
R2 
a measure of hedging effectiveness
Where
0  R2  1
The closer to 1 the better the chance that the hedge will
work.
There are at least 3 candidate measures of St and Ft that
can be used in the above regression:
Price level
Price change
Percentage price changes
It is recommended that price change and percentage
price change be used.
Chapter 4
41
Risk-Minimization Hedging
Soybeans Case
Step 1: estimate the price change and percentage price
changes for the soybean using the previous 60 days daily
data of soybean prices.
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Cash (S)
890327
890328
890329
890330
890331
890403
890404
890405
890406
890407
890410
890411
890412
890413
890414
890417
890418
890419
890420
890421
Future (F) Chg (S) Chg (F)
755
749.5
1
-5.5
747.5
1
-2
725
1
-22.5
723
1
-2
697.5
72
-25.5
702
1
4.5
702
1
0
701
1
-1
699
1
-2
707
3
8
708
1
1
715.5
1
7.5
716
1
0.5
722.5
1
6.5
736
3
13.5
738.5
1
2.5
737.5
1
-1
741
1
3.5
754.5
1
13.5
.
.
.
.
.
.
.
.
.
.
59
60
890616
890619
717.5
733
1
3
0
15.5
Where :
Chg (S) = change in cash price
Chg (F) = change in futures price
Chapter 4
42
Risk-Minimization Hedging
Soybeans Case
Step 2: run a regression analysis in Excel (recall that to do
this in Excel you need to go to “Tools”, “Data Analysis”,
“Regression”. The Y variable will be the change in the
commodity price. The X variable will be the change in the
futures price.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.11726695
R Square
0.013751537
Adjusted R Square
-0.003551067
Standard Error
15.62544125
Observations
59
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
MS
F Significance F
1 194.0458 194.0458 0.794767 0.376411
57 13916.8 244.1544
58 14110.85
Coefficients Standard Error t Stat
P-value Lower 95%Upper 95%Lower 95.0%
Upper 95.0%
4.879820628 2.035745 2.397068 0.019828 0.803311 8.95633 0.803311 8.95633
-0.185935589 0.208566 -0.891497 0.376411 -0.603581 0.23171 -0.603581 0.23171
Chapter 4
43
Risk-Minimization Hedging
Soybeans Case
Step 3: interpret the results.
From the above regression, we have:
  0.0103
  0.5159
R 2  0.4758
Results: in order to complete the risk-minimizing hedge, we
should sell 0.5159 bushel of soybean futures contracts for
each bushel that we have in inventory. Since we have
1,000,000 bushel of soybeans in inventory, we should sell:
0.5159 X 1,000,000 = 515,900 bushel of soybeans in the
futures market.
Chapter 4
44
Risk-Minimization Hedging
Soybeans Case
Soybeans are traded in 5,000 bushel futures contracts, we
should sell:
# Contracts 
# Contracts 
Amount To Be Hedged
Contract Quantity
515,900
 103.18
5000
You should sell 103 Soybean Contracts.
Chapter 4
45
Risk-Minimization Hedging
Soybeans Case
Step 4: evaluate the performance of the hedge. Figure 4.4
shows the wealth change from day 61 forward.
Insert Figure 4.4 Here
Comparing the unhedged and the hedged strategies, both
strategies lost money. However, the hedged strategy loss
was lower.
Recall that the regression in this case accounted for only
47.58 percent of the variance in the cash price (R2 =
0.4758)
Chapter 4
46
Hedging and Quantity Risk
Quantity Risk
In the case of a soybean farmer, the size of the futures
position used in the hedge depends on the farmer’s
expectations on the size of the crop.
Crop size can be affected by elements outside the control
of the farmers (e.g., weather).
Chapter 4
47
Costs and Benefits of Hedging
There are six market imperfections that make hedging
important and that can impose real costs to companies,
including:
1. Taxes
2. Costs of financial distress
3. Transaction costs of hedging
4. Principal-agent problems
5. Costliness of diversification
6. Differences between internal and external financing
costs
Chapter 4
48
Taxes
Suppose that you own a gold mine. You expect to mine
1,000 ounce of gold.
Your cost of producing the gold is $300/oz.
The futures price for gold is $400/oz, which is your
expected sales price.
The actual price could be $300 or $500 with equal
probability.
Your tax rate is 20% and your company has a $20,000 tax
credit that can be used to offset income taxes.
Table 4.15 shows the impact of taxes if your company is
unhedged or hedged.
Chapter 4
49
Taxes
Table 4.15
How Taxes Provide an Incentive to Hedge
Unhedged Firm
Sale Price of Gold
Hedged Firm
$300
$500
Gold Revenue
$300,000
$500,000
$300,000
$500,000
Futures Result
0
0
+100,000
-100,000
-300,000
-300,000
-300,000
-300,000
Pre-Tax Profit
0
$200,000
$100,000
$100,000
Tax Obligation
0
-40,000
-20,000
-20,000
Add Tax Credit (if applicable)
0
+20,000
+20,000
+20,000
Net Income
0
$180,000
$100,000
$100,000
Less Production Cost
Expected AfterBTax Net
Income
$90,000
$300
$500
$100,000
By hedging, the gold mine company was able to use the
$20,000 tax credit.
Empirical evidence on taxes and hedging is mixed. Some
argue that taxes do affect hedging decisions. Others argue
that hedging allows firms to increase their debt capacity
and acquire tax credits.
Chapter 4
50
Cost of Financial Distress
The costs associated with bankruptcy and financial
distress may motivate firms to hedge. Bankruptcy and
financial distress costs include:
1. Accountant and lawyers fees
2. Loss of customers
3. Exit of lines of business
4. Loss of tax shields
Hedging can reduce the probability of financial distress.
Chapter 4
51
Transaction Costs of Hedging
Selling a futures contract will add costs to the company.
Thus, these costs are a disincentive to hedge. A company
might simply take the risk rather than paying the cost of
selling the futures contract.
Chapter 4
52
Principal-Agent Problems
Managers and shareholders often have conflicting interest.
Managers tend to be more risk averse than shareholders.
They have much of their wealth tied up in an individual firm
while the owners might hold a portfolio containing the
stocks of several firms.
As such, managers might tend to hedge more than what
the shareholders would like them to.
Chapter 4
53
Costliness of Diversification
Many business owners have much or all of their personal
wealth tied up in a single business. This is commonly the
case among farmers.
In this case, they become much like managers in the
sense that they are risk averse. This lack of diversification
on the part of the owner can create an incentive to hedge.
Chapter 4
54
Differences Between Internal and
External Financing Costs
External financing refers to borrowing or issuing new
securities.
Internal financing refers to retained earnings and cash
reserves.
Obtaining external financing is generally more expensive
than using internal financing.
Without hedging companies may be forced to seek
external financing to solve their cash flow shortages.
Chapter 4
55