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Hedging Strategies Using Futures

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Title: Hedging Strategies Using Futures


1
Hedging Strategies Using Futures
Chapter 4
2
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

3
4.1 Basic principles
  • The object of the exercise to to take a position
    that neutralizes risk as far as possible.

4
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

5
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.

6
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.
7
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.

8
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.
9
4.2 Arguments for and against hedging
  • The arguments in favor of hedging are readily
    apparent.
  • The arguments against hedging are somewhat more
    subtle.

10
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

11
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

12
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.

13
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.

14
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.

15
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.

16
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.

17
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.

18
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

19
Figure 4.1 Variation of basis over time

Futures Price
Spot Price
Futures Price
Spot Price
Time
Time
(a)
(b)
20
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

21
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

22
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

23
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.

24
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.

25
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.

26
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.

27
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.

28
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.

29
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

30
4.5 Stock index futures
  • Stock index futures can be used to hedge an
    equity portfolio.

31
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

32
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.)

33
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)
34
Changing Beta
  • What position is necessary to reduce the beta of
    the portfolio to 0.75?
  • Lets try shorting 15 contracts

35
Changing Beta
  • What position is necessary to increase the beta
    of the portfolio to 2.0?

36
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
37
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.

38
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.

39
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.

40
Exposure Netting an Example
  • Consider a U.S. MNC with three subsidiaries and
    the following foreign exchange transactions

20
30
40
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35
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25
60
20
30
41
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

20
30
40
10
35
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30
25
60
20
30
42
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
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25
60
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43
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
10
35
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40
30
25
60
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44
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
10
35
10
10
25
60
20
30
45
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
10
35
10
10
25
60
20
30
46
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
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35
10
10
25
60
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47
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
10
35
10
10
25
60
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48
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
10
25
10
25
60
10
49
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
40
10
25
10
25
60
10
50
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
20
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25
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25
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51
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
20
10
25
10
25
10
52
Exposure Netting an Example
  • Bilateral Netting would reduce the number of
    foreign exchange transactions by half

10
20
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25
10
10
53
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

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20
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25
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54
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

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15
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55
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

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20
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15
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56
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

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20
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15
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57
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

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30
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15
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58
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

10
30
15
15
10
59
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

10
30
15
15
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Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

10
15
30
10
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Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

10
15
30
10
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Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

10
15
30
10
63
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

15
30
10
64
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

15
30
10
65
Exposure Netting an Example
  • Consider simplifying the bilateral netting with
    multilateral netting

15
40
66
Exposure Netting an Example
  • Clearly, multilateral netting can simplify things
    greatly.

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40
67
Exposure Netting an Example
  • Compare this

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Exposure Netting an Example
  • With this

15
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69
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.

70
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.

71
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.

72
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
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