Hedging Strategies Using
Futures
Chapter 3
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.1
Margins in TURKDEX
-FOREX Futures
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Size of the contract: $1000; 1000 Euro
Maturities: February, April, June, August,
October, December
US Dollar:
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Euro:
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Initial Margin: 180 TL/contract
Maintenance Margin: 135 TL/contract
Initial Margin: 240 TL/contract
Maintenance Margin: 180 TL/contract
Long & short futures together: one initial
margin is paid
Margins in TURKDEX
-INDEX Futures
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Size of the contract: 100 shares/units
ISE-30 & ISE-100:
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Initial Margin: 500 TL/contract
Maintenance Margin: 375 TL/contract
Long & short futures together: one initial
margin is paid
Hedger
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Use futures markets to reduce a particular
risk
To make profit (not an objective)
Perfect hedge: complete elimination of risk
Hedge-and-forget strategies:
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Hedge once
No change in position
Close out the position at the end of the life time of the
hedge
Short Hedges
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Appropriate when the hedger already
owns an asset, expects to sell it in the
future & want to lock in the price
Can be used when an asset is not owned
right now but will be owned at some time
in the future
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Exporters
Farmers, producers
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.5
Long Hedges
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Appropriate when the hedger knows he
will have to purchase an asset in the future
and want to lock in the price now.
Can be used to manage a short position
No delivery (generally)
High cost and inconvenience


Importers
Manufacturing companies
Arguments in Favor of Hedging
Companies should:
 focus on the main business they are in
 take steps to minimize risks arising
from interest rates, exchange rates, and
other market variables
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.7
Arguments against Hedging
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Shareholders vs companies
Competitors vs companies
Problem: there is a loss on the hedge and
a gain on the underlying asset
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.8
Convergence of Futures to Spot
(Hedge initiated at time t1 and closed out at time t2)
Futures
Price
Spot
Price
Time
t1
t2
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.9
Basis Risk
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The asset whose price to be hedged ≠ the
asset underlying the futures contract
Basis: the difference between spot price of
the asset to be hedged & futures price of
the contract used (S - F)
Strengthening of the basis:
increase in spot price > increase in futures price

Weakening of the basis:
İncrease in futures price > increase in spot price
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.10
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Basis risk: the uncertainty about the basis
when the hedge is closed out
Choice of the contract affects basis risk:
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The choice of the asset underlying the futures contract
The choice of the delivery month
Strategy: choose the contracts with futures
prices highly correlated with the price of the
asset being hedged

Time difference between the hedge
expiration and delivery month: positively
correlated with basis risk

Strategy: choose a delivery month as
close as to the delivery month
Short Hedge
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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
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.13
Long Hedge
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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
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.14
Cross Hedging
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The asset whose price to be hedged ≠ the
asset underlying the futures contract
Using heating oil futures contracts to
hedge jet fuel exposure
Hedge Ratio
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The ratio of the size of the position taken in
futures contracts to the size of the exposure
HR=1:
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if the asset underlying the futures contract is the same as
the asset being hedged
Not always optimal
A value that minimizes the variance of the value
of the hedged position: optimal hedge ratio
Optimal Hedge Ratio
Proportion of the exposure that should optimally be
hedged is
s
h*  r S
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.
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.17
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Hedge effectiveness (HE): the proportion
of the variance that is eliminated by
hedging
HE: R2 from the regression of DS against
DF
Optimal Number of Contracts
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N* = (h* NA)/QF
NA : Size of position being hedged (units)
QF : Size of one futures contract (units)
N* : Optimal number of futures contracts
for hedging
Stock Index Futures
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Stock index: tracks the changes in the
value of a portfolio of stocks
Omission of dividends
Capital gain from investing in the portfolio
Cash settlement for futures contracts on
stock indices
Marked to market of all contracts
Hedging Using Index Futures
((if the portfolio exactly mirror the index
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Stock index futures can be used to hedge
an equity portfolio
If the portfolio mirrors the index, hedge
ratio of 1 is appropriate.
N* = P/A
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N* : number of contracts to be shorted
P : current value of the portfolio
A : current value of the stocks underlying one
futures contract
Example
Current value of S&P 500 is 1,000
Size of portfolio is $1 million
One contract is on $250 times the index
What position in futures contracts on the
S&P 500 is necessary to hedge the
portfolio?
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.22
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P = 1,000,000
A = 250*1,000
N* = 1,000,000/250,000

N* =4
Hedging Using Index Futures
(if the portfolio does not exactly mirror the index)
To hedge the risk in a portfolio the
number of contracts that should be
shorted is
P
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
Fundamentals of Futures and Options Markets, 5th Edition, Copyright © John C. Hull 2004
3.24
Example
Value of S&P 500 is 1,000
Size of portfolio is $5 million
Beta of portfolio is 1.5
One contract is on $250 times the index
Risk-free interest rate: 4 % per annum
Dividend yield on index: 1 % per annum
Current futures price: $ 1,010
Futures price (3 moths later): $ 902
What position in futures contracts on the S&P
500 is necessary to hedge the portfolio (short)?
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.25
Example (continued)
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We assume that a futures contract on the S&P
500 with four months to maturity is used to
hedge the value of the portfolio over the next
three months.
One futures contract is for delivery of $250 times
the index.
(A = 250 x 1,000 = 250,000)
Fundamentals of Futures and Options Markets, 5th Edition, Copyright © John C. Hull 2004
3.26
Example (continued)

The number of futures contracts that
should be shorted to hedge portfolio is
5,000,000
1.5 
 30
250,000
Fundamentals of Futures and Options Markets, 5th Edition, Copyright © John C. Hull 2004
3.27
Example (continued)
Suppose the index turns out to be 900 in 3 months and futures price is
902. The gain from the short futures position is then
30 x (1010 – 902) x 250 = $810,000
The loss on the index is 10%. The index pays a dividend of 1% per
annum, or 0.25% per 3 months. When dividends are taken into
account, an investor in the index would therefore earn -9.75% in the 3month period. The risk free interest rate is approximately 1% per 3
months. Because the portfolio has a β of 1.5, capital asset pricing
model gives
Expected return on portfolio:
Risk free interest rate + 1.5 x (Return on index – Risk-free interest rate)
Fundamentals of Futures and Options Markets, 5th Edition, Copyright © John C. Hull 2004
3.28
Example (continued)
It follows that the expected return (%) on the portfolio during the 3 months
is
1.0+[1.5 x (-9.75-1.0)]=-15.125
The expected value of the portfolio (inclusive of dividends) at the end of
the 3 month is therefore
$5,000,000 x (1-0.15125) = $4,243,750
It follows that the expected value of the hedger’s position, including the
gain on the hedge, is
$4,243,750 + $810,000 = $5,053,750
Fundamentals of Futures and Options Markets, 5th Edition, Copyright © John C. Hull 2004
3.29
Reasons for Hedging an Equity
Portfolio
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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.)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.30
Changing Beta
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Futures contracts can be used to change the
beta of the portfolio.
What position is necessary to reduce the beta
of the portfolio from 1.5 to 0.75?
What position is necessary to increase the beta
of the portfolio from 1.5 to 2.0?
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.31
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↓ in beta, ↓ in number of contracts (short
position)
β > β* (short position)
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(β – β*) (P/A)
(1.5-0.75) (5,000,000/250,000) = 15
β < β* (long position)
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(β* – β) (P/A)
(2-1.5) (5,000,000/250,000) = 10
Exposure to the Price of an
Individual Stock
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Trade of futures contracts on selected
individual stocks
If no, hedging of an individual stock by a
stock index futures contract
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Hedging provides protection only against the risk
arising from market movements (small
proportion of total risk)
Appropriate when
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an investor feels that the stock outperform the market
but not sure about the performance of the market
Similarity with hedging a stock portfolio
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N* = β(P/A)
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Β: beta of the stock
P: total value of the shares owned
A: current value of the stocks underlying one futures contact
Example
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Hoding 20,000 IBM shares in June, each worth
$100
Expectation: volatility in the market & outperform
of IBM
Decision: use August futures contract on S&P
500 to hedge position
Β of IBM: 1.1
Current level of S&P 500: 900
Current futures price for the August contract:908
Each contract: $250 times the index
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P = 20,000 * 100 = 2,000,000
A = 900*250 = 225,000
N* = 1.1 (2,000,000/225,000) = 9,78 (10)
If IBM rises to 125 and S&P 500 rises to
1080?
Investor gains: 20,000 (125-100)=500,000
on IBM
Investor loses: 10*250*(1080908)=430,000 on futures contacts
Rolling The Hedge Forward
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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
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.37
EXAMPLE
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Company realizes that it will have 100,000
barrels of oil to sell in June 2005.
Decides to hedge its risk with hedge ratio
of 1.0.
Short futures
1,000 barrels/contract
100 contracts.
Date
Oct 2004
Futures price
Apr 2004
Sept 2004
18.20
17.40
Mar 2005
Futures price
17.00
July 2005
Futures price
Spot price
Feb 2005
16.50
16.30
19.00
June 2005
15.90
16.00
The dollar gain per barrel of oil from short futures
contracts is
(18.20-17.40) + (17.00-16.50) + (16.30-15.90) = 1.70
The oil price declined from $19 to $16. Receiving only
$1.70 per barrel compensation for a price decline of $3.00
may appear unsatisfactory. However, we cannot expect
total compensation for a price decline when futures prices
are below spot prices. The best we can hope for is to lock
in the futures price that would apply to a June 2005
contract if it were actively traded.
Fundamentals of Futures and Options Markets, 5th Edition, Copyright © John C. Hull 2004
3.40
TOTAL GAIN/LOSS
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(18.20-17.40)
(17.00-16.50)
(16.30-15.90)
TOTAL GAIN = $ 1.70/barrel
Lower than 19.00-16.00 = $ 3.00
(change in spot price)