Chapter 4 - Hedging with Futures Contracts

Question 1

What is basis risk?

Answer 1

The risk of unexpected changes in the
basis.

Question 2

What is a cross-hedge?

Answer 2

A hedge where the futures contract
used has an underlying asset which
is similar to but not the same as the
physical commodity being hedged.

Question 3

What is hedging?

Answer 3

An attempt to reduce risk by making
transactions that reduce exposure to
market fluctuations. Hedging with
derivatives involves taking an opposite
position in the derivative instrument of
the asset to be hedged (or one that is
very close to it) that is equal in size.

Question 4

What is an imperfect hedge?

Answer 4

The result of a hedge that does not
perform as the hedger expected due
to unexpected changes in the basis. A
hedge may turn out to be imperfect if
there is a difference between the asset
underlying the futures contract and
the asset being hedged, or if the assets
match, but the hedge is lifted early and
the basis has changed unexpectedly.

Question 5

What is a long hedge?

Answer 5

A hedge that involves buying the
futures contract in anticipation of
buying the physical asset at some
point in the future. Long hedgers
are concerned that the price of the
underlying asset will rise in the future,
making it more expensive to buy.

Question 6

What is the optimal hedge ratio?

Answer 6

Represents the ratio used to calculate
how many futures contracts should
be used in a particular hedge by
comparing price volatility of the
futures and cash price.

Question 7

What is a perfect hedge?

Answer 7

A hedge in which the futures price
behaved exactly as expected relative to
the cash price.

Question 8

What is a short hedge?

Answer 8

A hedge that involves selling the
futures contract in anticipation of
selling the physical asset at some
point in the future. Short hedgers
are concerned that the price of the
underlying asset will decline in the
future, meaning they will not receive
as high a price when they are ready to
sell the underlying asset.

Question 9

Explain how futures contracts are used to reduce risk.

Answer 9

Futures can be used to reduce the risk of holding a particular asset for future sale or to reduce the risk involved
in anticipating the purchase of a particular asset. Both of these are accomplished through hedging, which is
achieved by combining the position in an underlying asset with the opposite position in a futures contract.

Question 10

Define short and long hedges.

Answer 10

• A short hedge is executed by someone who owns an asset that will be sold at some point in the future and, as
  a result, is at risk if the asset’s price falls. To offset or reduce this risk, the short hedger sells a futures contract.
• A long hedge is executed by someone who anticipates owning an asset at some point in the future and, as a
  result, is at risk if the asset’s price rises. To offset or reduce this risk, the long hedger buys a futures contract.

Question 11

Calculate the net profit or loss from a hedged transaction.

Answer 11

The overall profit or loss from a hedged transaction is derived from two sources: the cash transaction and the
hedge transaction.

Question 12

Define perfect and imperfect hedges.

Answer 12

• A perfect hedge will occur with certainty if the following two conditions are met:
  1. The end of a hedger’s holding period matches the expiration date of the futures contract.
  2. The asset being hedged matches the asset underlying the futures contract.
  Even if one or both of these conditions are not met, a hedge may still turn out to be perfect if the basis
  behaves as expected by the hedger.
• An imperfect hedge occurs when the basis behaves unexpectedly. Hedges may turn out to be imperfect if
  there is a difference between the asset underlying the futures contract and the asset being hedged, or if the
  assets match but the hedge is lifted early, and the basis has changed unexpectedly.
• A cross hedge is implemented with a futures contract whose underlying asset does not exactly match the
  asset that is being hedged.

Question 13

Explain and differentiate between market risk and basis risk.

Answer 13

• Market risk is the risk of adverse changes in the price of an asset that is currently owned or that will be owned
  in the future.
• Basis risk is the risk of unexpected changes in the basis.
  A hedge can only be justified if it can reasonably be expected that basis risk will be lower than market risk.

Question 14

Explain why some futures contracts are more prone to basis risk than others.

Answer 14

The easier it is to arbitrage a particular market, the more likely futures prices will trade in a predictable manner
relative to spot prices (on the basis of the cost of carry).
Where arbitrage is difficult or impossible to implement, futures prices may trade in an unpredictable manner
relative to spot prices, leaving a hedged position exposed to considerable basis risk.
Futures markets that have the following characteristics are easily arbitraged and, as a result, do not have
significant basis risk. When these conditions are not apparent, basis risk can be considerable.
- Large supply of the underlying asset
- Storability
- Non-seasonal production and consumption
- Ease of short selling

Question 15

Define the optimal hedge ratio.

Answer 15

The optimal hedge ratio is a number used to calculate the correct number of futures contracts to use in a hedge.
The ratio is calculated by studying the historical correlation between the price of the asset being hedged and
the futures price.

Question 16

Calculate an optimal hedge ratio given the required inputs.

Answer 16

An optimal hedge ratio, H, is calculated as follows:

H = CORRpf(SDp/SDf)

SDp = the standard deviation of changes in the spot price of the asset to be hedged

SDf = the standard deviation of changes in the futures price

CORRpf = the correlation coefficient between changes in p and f

Question 17

A home builder anticipates the need for lumber in three months.

i. What kind of price risk is the builder facing?

ii. Using lumber futures, would the home builder employ a short hedge or a long hedge to reduce or eliminate
this price risk?

Answer 17

i. The home builder is facing the risk that the price of lumber will rise.

ii. Since the home builder is at risk that prices could rise, a long hedge is needed. If prices do rise, the futures
position should show a profit to help offset the increased price in the cash market.

Question 18

Under what two conditions will a hedger know with certainty that a hedge will turn out to be perfect?

Answer 18

A hedger will know with certainty that a hedge will be perfect if there is an asset match and a maturity match.

Question 19

An orange juice distributor anticipates needing 75,000 pounds of orange juice in six months.

i. Which of the following hedge strategies would the distributor employ using orange juice futures contracts
(15,000 pounds per contract)?

a. Sell 5 orange juice futures.
b. Buy 5 orange juice futures.
c. Sell 50 orange juice futures.
d. Buy 50 orange juice futures.

ii. The distributor entered into the appropriate number of orange juice futures at $1.90 per pound. Six months
later, just prior to the contracts’ expiration, the distributor offsets the contracts at $1.80 per pound. What
is the total dollar profit or loss on the futures contracts?

a. $7,500 loss.
b. $1,500 loss.
c. $1,500 profit.
d. $7,500 profit.

iii. Upon liquidation of the futures contracts, the distributor bought 75,000 pounds of orange juice in the cash
market at $1.80 per pound. What is the distributor’s net effective purchase price per pound after taking
into account the futures profit or loss?

a. $1.70
b. $1.80
c. $1.90
d. $2.00

Answer 19

i. b. Buy 5 orange juice futures.

The distributor would buy the contracts because it is at risk that the price of orange juice will rise
over the next six months. Five contracts are needed because the distributor needs price protection
on 75,000 pounds, and each contract covers 15,000 pounds (75,000 ÷ 15,000).

ii. a. $7,500 loss.

($1.80 − $1.90) × 15,000 × 5

iii. c. $1.90

$1.80 cash price + $0.10 ($1.80 − $1.90) loss on the futures contracts. The loss must be added to the
cash price because this, in effect, increases the cost of the cash purchase. If a profit was earned, it would
be subtracted from the cash price, thereby lowering the effective purchase price.

Question 20

On April 15, a Manitoba farmer begins to implement a hedging plan for his canola crop, which will be harvested
in October. The farmer expects the canola crop to yield approximately 1,000 metric tonnes.

i. Will the farmer implement a long hedge or a short hedge?

ii. Given that the size of one canola futures contract is 20 tonnes, how many canola futures contracts should
the farmer use in his hedging program?

iii. The farmer implements the hedge at a futures price of $390. In October, the harvested canola is sold at a
price of $400 per metric tonne, and the futures contracts are offset at $410 per metric tonne. What is the
farmer’s net total dollar amount received for the 1,000 metric tonnes?

a. $380,000
b. $390,000
c. $400,000
d. $410,000

Answer 20

i. The farmer will eventually sell his canola crop in the cash market. A short hedge should be implemented to
protect the farmer from a decline in the price of canola.

ii. Since each contract represents 20 tonnes of canola, 50 contracts (1,000 tonnes ÷ 20 tonnes per contract)
should be used.

iii. a. $380,000

Cash Market: $400 × 1,000 tonnes = $400,000
Futures Market: ($390 − $410) × 20 × 50 = $20,000 loss
A loss on the futures position is subtracted from the cash market proceeds to arrive at the net total
dollar amount received for the 1,000 metric tonnes.

Question 21

In a normal commodity futures market, will a long hedger gain or lose the basis as the futures contract nears
expiration?

Answer 21

In a normal commodity futures market, the futures price is higher than the cash price (reflecting the cost of
carry). Long hedgers are long the futures because they are at risk that the cash price will rise (and therefore are
effectively – if not actually – short the cash commodity). As the futures contract nears expiration, the futures
price will fall (relative to the cash price) and the long hedger will lose the basis.

Question 22

A large, Canadian-based silver mining company knows that it will be selling 50,000 ounces of silver in six
months. The spot price of silver is currently $13.00 per ounce, while the 6-month silver futures contract is
trading at $13.60 per ounce. The cost of carrying silver is $0.10 per ounce per month.

i. If the company uses silver futures to hedge its price risk, would it be a long or short hedge?

ii. Because of significant increases in worker productivity, the company is able to bring the silver to market
after four months. The company sells the silver in the cash market at $12.25 per ounce. If this hedge is to
be considered perfect, at which of the following silver futures prices would the company need to offset the
futures contracts?

a. $12.05
b. $12.25
c. $12.45
d. $12.65

Answer 22

i. Since the mining company will be selling the cash commodity in the future, it should implement a short
hedge to protect itself from falling cash prices.

ii. c. $12.45

A perfect hedge implies no unexpected changes in the basis. The futures contracts have two months
remaining (the hedge was placed with six months remaining and lifted after four months), so
the hedge would be considered perfect if the futures contract had two months’ worth of carrying
costs ($0.10 per month × 2 months) built into its price. This equates to a futures price of $12.45
($12.25 cash price + $0.20 total carrying costs).

Question 23

A confectioner that specializes in making fine chocolate anticipates a need for 1,000 metric tonnes of cocoa in
three months. The confectioner is concerned that cocoa prices may move in an adverse way leading up to the
time the cocoa is needed. The confectioner has gathered the following information:

Current spot cocoa price $1,800 per tonne

Current 3-month cocoa futures price $1,845 per tonne

Total cost of carry ($15/tonne/month) $45

Contract size 10 tonnes

i. If the confectioner decides to hedge, will it be a long hedge or a short hedge? How many contracts are
needed?

ii. If the hedge is implemented, what is the profit or loss on the futures contracts if they are offset at a price
of $1,815 per tonne with one month left to expiration?

a. $30,000 loss.
b. $3,000 loss.
c. $3,000 profit.
d. $30,000 profit.

iii. If at the same time the futures contracts are offset the physical cocoa is purchased at $1,800 per metric
tonne, what is the confectioner’s net purchase price per metric tonne?

a. $1,785
b. $1,815
c. $1,830
d. $1,845

iv. How did the basis change over the life of the hedge?

a. It stayed the same.
b. It narrowed by $15 per tonne.
c. It narrowed by $30 per tonne.
d. It widened by $30 per tonne.

Answer 23

i. The confectioner will need to implement a long hedge by buying 100 contracts (1,000 tonnes ÷ 10 tonnes
per contract).

ii. a. $30,000 loss.

($1,815 − $1,845) × 10 × 100

iii. c. $1,830

$1,800 cash price + $30 ($1,815 − $1,845) loss on the futures contracts.

iv. c. It narrowed by $30 per tonne.

The basis was initially $45 ($1,845 − $1,800) and it narrowed to $15 ($1,815 − $1,800) by the time the
contracts were offset.

Question 24

XYZ Airlines wants to hedge a purchase of 1 million gallons of jet fuel that it will make in 3 months. Because there are no futures contracts on jet fuel, XYZ uses heating oil futures (42,000 gallons per contract) to hedge its market risk. In order to keep basis risk to a minimum, XYZ uses a hedge ratio based on a historical study of jet fuel and heating oil prices. Its most recent study concludes that the standard deviation of changes in the price of jet fuel and heating oil over a recent 3-month period was 0.065 and 0.043, respectively. The correlation between changes in prices was 0.89. Based on this study, what is the optimal hedge ratio?

Answer 24

From the previous question, the hedge ratio is 1.345. Each heating oil contract covers 42,000 gallons and XYZ needs to hedge 1 million gallons of jet fuel.
(1,000,000 / 42,000) x 1.345 = 32.024
Because XYZ is a buyer of jet fuel, they will need protection from an increase in the price of jet fuel. Therefore, XYZ should buy 32 heating oil futures contracts.

Question 25

Explain the hedging strategies you learned in this chapter in your own words.

Answer 25

Short Hedge (Example):

• Buy 1000 units of a commodity at $420
• Short the 3-month future at $435
• Come expiration you sell the asset for $400 ($20 loss)
• Come expiration you offset the future for $400 ($35 profit)
• Assuming the the futures contract was priced at fair value at the beginning of the contract, reflecting only the cost of carry, the cost of carry that YOU would have had to incur since you physically held the asset would’ve been $15

Therefore, your NET profit = -20 + 35 - 15 = $0

This example illustrates how PERFECT HEDGES LOCK IN PRICES while IMPERFECT HEDGES do not!

Long Hedge (Example):

• Anticipating needing to buy a commodity down the road and you want the current spot price
• Buy the future at $21.20
• Buy the asset when you need it at $21.40 (at expiry)
• Offset the futures contract at expiry for $21.40
• You paid $21.40 for the physical asset, however, you made $0.20 on your futures contract position

Therefore, your NET profit = 21.40 - 0.20 = $21.20

Imperfect Hedge (Example):

• Buy one-year futures contract at $2.70 when the cash price is at $2.60
• You end up needing the asset earlier than expected (at six months lets say) and it just so happens that at the same time strong world demand and strikes at production facilities cause the market to go into backwardation (an inverted market)
• The cash price is now $3.00 and the future is only worth $2.80
• You end up buying at $3.00, $0.40 higher than the price at the beginning of the hedge, however, you’ve made $0.10 on your futures position; which partially offsets the higher cost but not completely