Title: Hedging Strategies Using Futures
1Hedging Strategies Using Futures
Chapter 4
2Chapter 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
34.1 Basic principles
- The object of the exercise to to take a position
that neutralizes risk as far as possible.
4Long 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
5Hedging
- 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.
6Hedging 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.
7Forward 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.
8Forward 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.
94.2 Arguments for and against hedging
- The arguments in favor of hedging are readily
apparent. - The arguments against hedging are somewhat more
subtle.
10Arguments 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
11Arguments 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
12How 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.
13Should 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.
14Should 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.
15Should 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.
16What 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.
174.3 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.
18Basis 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
19Figure 4.1 Variation of basis over time
Futures Price
Spot Price
Futures Price
Spot Price
Time
Time
(a)
(b)
20Long 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
21Short 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
22Choice 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
23Cross-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.
24Cross-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.
25Hedging 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.
264.4 Minimum variance hedge ratio
- If the objective of the hedger is to minimize
risk, setting the hedge ratio equal to one is not
necessarily optimal.
27Notation
- 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.
28Optimal 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.
29Optimal 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
304.5 Stock index futures
- Stock index futures can be used to hedge an
equity portfolio.
31Hedging 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
32Reasons 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.)
33Example
- 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)
34Changing Beta
- What position is necessary to reduce the beta of
the portfolio to 0.75?
- Lets try shorting 15 contracts
35Changing Beta
- What position is necessary to increase the beta
of the portfolio to 2.0?
36Index 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
374.6 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.
38Exposure 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.
39Exposure 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.
40Exposure Netting an Example
- Consider a U.S. MNC with three subsidiaries and
the following foreign exchange transactions
20
30
40
10
35
10
40
30
25
60
20
30
41Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
20
30
40
10
35
10
40
30
25
60
20
30
42Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
40
10
35
10
40
30
25
60
20
30
43Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
40
10
35
10
40
30
25
60
20
30
44Exposure 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
45Exposure 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
46Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
40
10
35
10
10
25
60
10
47Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
40
10
35
10
10
25
60
10
48Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
40
10
25
10
25
60
10
49Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
40
10
25
10
25
60
10
50Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
20
10
25
10
25
10
51Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
20
10
25
10
25
10
52Exposure Netting an Example
- Bilateral Netting would reduce the number of
foreign exchange transactions by half
10
20
15
25
10
10
53Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
20
15
25
10
10
54Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
20
15
15
10
10
10
55Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
20
15
15
10
10
56Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
20
15
15
10
10
57Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
30
15
15
10
58Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
30
15
15
10
59Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
30
15
15
10
60Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
15
30
10
61Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
15
30
10
62Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
10
15
30
10
63Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
15
30
10
64Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
15
30
10
65Exposure Netting an Example
- Consider simplifying the bilateral netting with
multilateral netting
15
40
66Exposure Netting an Example
- Clearly, multilateral netting can simplify things
greatly.
15
40
67Exposure Netting an Example
20
30
40
10
35
10
40
30
25
60
20
30
68Exposure Netting an Example
15
40
694.7 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. -
704.7 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. -
714.7 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. -
724.7 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