Hedging Strategies Using Futures
Chapter 4
Chapter Outline
4.1 Basic principles
4.2 Arguments for and against hedging
4.3 Basis risk
4.4 Minimum variance hedge ratio
4.5 Stock index futures
4.6 Rolling the hedge forward
4.7 Summary
4.1 Basic principles
• The object of the exercise to to take a
position that neutralizes risk as far as
possible.
Long & Short Hedges
• A long futures hedge is appropriate when
you know you will purchase an asset in
the future and want to lock in the price
• A short futures hedge is appropriate when
you know you will sell an asset in the
future & want to lock in the price
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 and speculators absorb
price risk from hedgers.
Hedging: How many contacts?
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.
Forward Market Hedge
• If you are going to owe foreign currency in
the future, agree to buy the foreign currency
now by entering into long position in a
forward contract.
• If you are going to receive foreign currency
in the future, agree to sell the foreign
currency now by entering into short position
in a forward contract.
Forward Market Hedge: an Example
You are a U.S. importer of British woolens and
have just ordered next year’s inventory.
Payment of £100M is due in one year.
Question: How can you fix the cash outflow in
dollars?
Answer: One way is to put yourself in a position
that delivers £100M in one year—a long
forward contract on the pound.
4.2 Arguments for and against hedging
• The arguments in favor of hedging are
readily apparent.
• The arguments against hedging are
somewhat more subtle.
Arguments in Favor of Hedging
• Companies should focus on the main
business they are in and take steps to
minimize risks arising from interest rates,
exchange rates, and other market variables
Arguments against Hedging
• Shareholders are usually well diversified and
can make their own hedging decisions
• It may increase risk to hedge when competitors
do not.
• Explaining a situation where there is a loss on
the hedge and a gain on the underlying can be
difficult
How hedging could increase risk.
• Consider single competitor in a commodity
industry dominated by competitors who do
not hedge.
• If the competitor hedges the raw materials
and then prices of raw materials fall, the
price of the finished product will fall as
well—this could decrease profit margins.
Should the Firm Hedge?
• Not everyone agrees that a firm should
hedge:
– Hedging by the firm may not add to
shareholder wealth if the shareholders can
manage exposure themselves.
– Hedging may not reduce the non-diversifiable
risk of the firm. Therefore shareholders who
hold a diversified portfolio are not helped when
management hedges.
Should the Firm Hedge?
• In the presence of market imperfections, the firm
should hedge.
– Information Asymmetry
• The managers may have better information than the
shareholders.
– Differential Transactions Costs
• The firm may be able to hedge at better prices than the
shareholders.
– Default Costs
• Hedging may reduce the firms cost of capital if it reduces the
probability of default.
Should the Firm Hedge?
• Taxes can be a large market imperfection.
– Corporations that face progressive tax rates
may find that they pay less in taxes if they can
manage earnings by hedging than if they have
“boom and bust” cycles in their earnings
stream.
What Risk Management Products do
Firms Use?
• Most U.S. firms meet their exchange risk
management needs with forward, swap, and
options contracts.
• The greater the degree of international
involvement, the greater the firm’s use of
foreign exchange risk management.
4.3 Basis risk
• It may be difficult to find a forward contract
on the asset that you are trying to hedge.
• There may be uncertainty regarding the
maturity date.
• These problems give rise to basis risk.
Basis Risk
• Basis is the difference between spot &
futures:
Basis = Spot price of asset to be hedged – Futures price of contract used
• Basis risk arises because of the uncertainty
about the basis when the hedge is closed out
Figure 4.1 Variation of basis over time
Futures
Price
Spot Price
Futures
Price
Spot Price
Time
(a)
Time
(b)
Long Hedge
• Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
• You hedge the future purchase of an asset
by entering into a long futures contract
• Cost of Asset=S2 –(F2 – F1) = F1 + Basis
Short Hedge
• Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
• You hedge the future sale of an asset by
entering into a short futures contract
• Price Realized=S2+ (F1 –F2) = F1 + Basis
Choice of Contract
• Choose a delivery month that is as close as
possible to, but later than, the end of the life
of the hedge
• When there is no futures contract on the
asset being hedged, choose the contract
whose futures price is most highly
correlated with the asset price. There are
then 2 components to basis
Cross-Hedging
Minor Currency Exposure
• The major currencies are the: U.S. dollar,
Canadian dollar, British pound, Swiss franc,
Mexican peso, Japanese yen, and now the
euro.
• Everything else is a minor currency, like the
Polish zloty.
• It is difficult, expensive, or impossible to
use financial contracts to hedge exposure to
minor currencies.
Cross-Hedging
Minor Currency Exposure
• Cross-Hedging involves hedging a position in one
asset by taking a position in another asset.
• The effectiveness of cross-hedging depends upon
how well the assets are correlated.
– An example would be a U.S. importer with liabilities in
Czech koruna hedging with long or short forward
contracts on the euro. If the koruna is expensive when
the euro is expensive, or even if the koruna is cheap
when the euro is expensive it can be a good hedge. But
they need to co-vary in a predictable way.
Hedging Contingent Exposure
• If only certain contingencies give rise to
exposure, then options can be effective
insurance.
• For example, if your firm is bidding on a
hydroelectric dam project in Canada, you
will need to hedge the Canadian-U.S. dollar
exchange rate only if your bid wins the
contract. Your firm can hedge this
contingent risk with options.
4.4 Minimum variance hedge ratio
• The hedge ratio is
Size of the
exposure
Size of the
position taken
in the futures
contracts
• If the objective of the hedger is to minimize
risk, setting the hedge ratio equal to one is
not necessarily optimal.
Notation
dS Change in the spot price, S, during the life of the hedge
dF Change in the futures price, F, during the life of the
hedge
sS is the standard deviation of dS
sF is the standard deviation of dF
r is the coefficient of correlation between dS and dF.
Optimal Hedge Ratio
Proportion of the exposure that should optimally be
hedged is
sS
h r
sF
*
where
sS is the standard deviation of dS, the change in the spot
price during the hedging period,
sF is the standard deviation of dF, the change in the
futures price during the hedging period
r is the coefficient of correlation between dS and dF.
Optimal Number of Contracts
The number of futures contracts required is
NA
N h 
QF

where
NA
QF
N*

size of the position being hedged (units),
size of one futures contract (units),
Optimal number of futures contracts
4.5 Stock index futures
• Stock index futures can be used to hedge an
equity portfolio.
Hedging Using Index Futures
(Page 82)
• To hedge the risk in a (long) portfolio the
number of contracts that should be shorted
is
P
N b
A

where P is the value of the portfolio,
b is its beta, and
A is the value of the assets underlying one
futures contract
31
Reasons for Hedging an Equity Portfolio
• Desire to be out of the market for a short
period of time. (Hedging may be cheaper
than selling the portfolio and buying it
back.)
• Desire to hedge systematic risk
(Appropriate when you feel that you have
picked stocks that will outperform the
market.)
Example
Value of S&P 500 is 1,000
Value of Portfolio is $5 million
Beta of portfolio is 1.5
P
N b
A

What position in futures contracts on the S&P 500
is necessary to hedge the portfolio?
$5,000,000
N  1.5 
 30
$1,000  250

Go short 30 contracts
(each futures contract is on $250 times the index)
Changing Beta
• What position is necessary to reduce the
beta of the portfolio to 0.75?
P

• Let’s try shorting 15 contracts N  b
A
$5,000,000
15  b
250,000
15
b 
 0.75
20
Changing Beta
• What position is necessary to increase the
beta of the portfolio to 2.0?
P
N b
A

$5,000,000
N  2.0 
$250,000


N  40
Index Arbitrage
• The spot-futures parity relation developed
in chapter 3 is the basis for a common
trading strategy known as index arbitrage.
– Suppose the S&P 500 futures price for delivery
in one year is 1,340.
– The current level is 1300.
– The risk-free rate is 5% and the dividend yield
on the S&P500 is 3%. Is there an arbitrage?
F0 = S0e(r–q )T
F0 = 1,300 e(.05-.03 ) = 1,326
4.6 Rolling The Hedge Forward
• We can use a series of futures contracts to
increase the life of a hedge
• Each time we switch from 1 futures
contract to another we incur a type of basis
risk, rollover basis.
Exposure Netting
• A multinational firm should not consider deals in
isolation, but should focus on hedging the firm as a
portfolio of currency positions.
– As an example, consider a U.S.-based multinational
with Korean won receivables and Japanese yen
payables. Since the won and the yen tend to move in
similar directions against the U.S. dollar, the firm can
just wait until these accounts come due and just buy yen
with won.
– Even if it’s not a perfect hedge, it may be too expensive
or impractical to hedge each currency separately.
Exposure Netting
• Many multinational firms use a reinvoice
center. Which is a financial subsidiary that
nets out the intrafirm transactions.
• Once the residual exposure is determined,
then the firm implements hedging.
Exposure Netting: an Example
Consider a U.S. MNC with three subsidiaries and the
following foreign exchange transactions:
$20
$30
$40
$10
$10 $35
$25
$20
$30
$60
$30 $40
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$20
$30
$40
$10
$10 $35
$25
$20
$30
$60
$30 $40
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$10 $35
$25
$20
$30
$60
$30 $40
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$10 $35
$25
$20
$30
$60
$30 $40
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$10 $35
$25
$20
$30
$60
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$10 $35
$25
$20
$30
$60
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$10 $35
$25
$60
$10
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$10 $35
$25
$60
$10
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$25
$25
$60
$10
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$40
$10
$25
$25
$60
$10
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$20
$10
$25
$25
$10
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$20
$10
$25
$25
$10
$10
Exposure Netting: an Example
Bilateral Netting would reduce the number of foreign
exchange transactions by half:
$10
$20
$15
$25
$10
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$20
$15
$25
$10
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$20
$15
$15 $10
$10
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$20
$15
$15
$10
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$20
$15
$15
$10
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$30
$15
$15
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$30
$15
$15
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$30
$15
$15
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$15
$30
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$15
$30
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$10
$15
$30
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$15
$30
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$15
$30
$10
Exposure Netting: an Example
Consider simplifying the bilateral netting with
multilateral netting:
$15
$40
Exposure Netting: an Example
Clearly, multilateral netting can simplify things
greatly.
$15
$40
Exposure Netting: an Example
Compare this:
$20
$30
$40
$10
$10 $35
$25
$20
$30
$60
$30 $40
Exposure Netting: an Example
With this:
$15
$40
4.7 Summary
• There are a variety of ways a firm can
hedge exposure to the price of an asset
using futures.
• Hedging reduces risk, but for a variety of
theoretical and practical reasons, many
companies do not hedge.
4.7 Summary
• An important concept in hedging is basis risk.
– The basis is the difference between the spot price of an
asset and the futures price.
– Basis risk is created by a hedger’s uncertainty as to
what the basis will be at maturity or the hedge.
– Basis risk is greater for consumption assets than for
investment assets.
4.7 Summary
• The Hedge ratio is the ratio of the size of the
position taken in futures contracts to the size of
the exposure.
– A hedge ratio of 1.0 is not always optimal.
– A hedge ratio different from 1 may offer a reduction in
the variance.
– The optimal hedge ratio is the slope of the best fit line
when changes in the spot price are regressed against
changes in the futures price.
4.7 Summary
• Stock index futures can be used to hedge
the systematic risk in an equity portfolio.
– The number of futures required is the of the
b portfolio ×
Dollar value of portfolio
Dollar value of 1 forward
– Stock index futures can also be used to change
the beta of a portfolio without changing the
stocks comprising the portfolio