Hedging Strategies Using Futures

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Hedging Strategies Using Futures
Chapter 4
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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

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4.1 Basic principles

• The object of the exercise to to take a position
  that neutralizes risk as far as possible.

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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

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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.

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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

Now you can quit worrying about the price of corn
and get back to worrying about the weather.
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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.

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Forward Market Hedge an Example

• You are a U.S. importer of British woolens and
  have just ordered next years 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 yeara long forward
contract on the pound.
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4.2 Arguments for and against hedging

• The arguments in favor of hedging are readily
  apparent.
• The arguments against hedging are somewhat more
  subtle.

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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

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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

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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 wellthis could
  decrease profit margins.

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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.

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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.

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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.

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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 firms use of
  foreign exchange risk management.

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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.

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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

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Figure 4.1 Variation of basis over time

Futures Price
Spot Price
Futures Price
Spot Price
Time
Time
(a)
(b)
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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 AssetS2 (F2 F1) F1 Basis

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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 RealizedS2 (F1 F2) F1 Basis

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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

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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.

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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.

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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.

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4.4 Minimum variance hedge ratio

• The hedge ratio is

• If the objective of the hedger is to minimize
  risk, setting the hedge ratio equal to one is not
  necessarily optimal.

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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.

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Optimal Hedge Ratio

• Proportion of the exposure that should optimally
  be hedged is
• 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.

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Optimal Number of Contracts

• The number of futures contracts required
  is
• where
• NA size of the position being hedged (units),
• QF size of one futures contract (units),
• N Optimal number of futures contracts

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4.5 Stock index futures

• Stock index futures can be used to hedge an
  equity portfolio.

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Hedging Using Index Futures(Page 82)

• To hedge the risk in a (long) portfolio the
  number of contracts that should be shorted is
• where P is the value of the portfolio,
• b is its beta, and
• A is the value of the assets underlying one
  futures contract

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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.)

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Example

• Value of SP 500 is 1,000
• Value of Portfolio is 5 million
• Beta of portfolio is 1.5
• What position in futures contracts on the SP
  500 is necessary to hedge the portfolio?

Go short 30 contracts (each futures contract is
on 250 times the index)
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Changing Beta

• What position is necessary to reduce the beta of
  the portfolio to 0.75?

• Lets try shorting 15 contracts

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Changing Beta

• What position is necessary to increase the beta
  of the portfolio to 2.0?

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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 SP 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 SP500 is 3. Is there an arbitrage?

F0 S0e(rq )T
F0 1,300 e(.05-.03 )
1,326
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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.

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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 its not a perfect hedge, it may be too
  expensive or impractical to hedge each currency
  separately.

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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.

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Exposure Netting an Example

• Consider a U.S. MNC with three subsidiaries and
  the following foreign exchange transactions

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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25
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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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35
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25
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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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40
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35
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25
60
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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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40
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25
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25
60
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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Bilateral Netting would reduce the number of
  foreign exchange transactions by half

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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15
30
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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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15
30
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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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30
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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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30
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Exposure Netting an Example

• Consider simplifying the bilateral netting with
  multilateral netting

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Exposure Netting an Example

• Clearly, multilateral netting can simplify things
  greatly.

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Exposure Netting an Example

• Compare this

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Exposure Netting an Example

• With this

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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.

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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 hedgers uncertainty
  as to what the basis will be at maturity or the
  hedge.
• Basis risk is greater for consumption assets than
  for investment assets.

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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.

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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

• Stock index futures can also be used to change
  the beta of a portfolio without changing the
  stocks comprising the portfolio