Transcript Hedging Strategies Using Futures

Hedging Strategies Using
Futures
Chapter 3
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.1
Long & Short Hedges
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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
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.2
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
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.3
Arguments against Hedging
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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 (See example pg. 50)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.4
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
3.5
Basis Risk
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Basis is the difference between spot
& futures
Basis risk arises because of the
uncertainty about the basis when the
hedge is closed out
Basis often exists because of:
Storage costs if any
 Interest factor
 Forward view of spot price
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Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.6
Choice of Contract
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Choose a delivery month that is as close
as possible to, but later than, the end of
the life of the hedge (Why?)
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 (Quality
difference + interest & storage cost if any)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.7
Short Hedge (Pg. 54 Ex. 3.3)
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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*
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*Note – Basis is at time of futures close out
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.8
Long Hedge (Pg. 55 Ex. 3.4)
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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*

*Note – Basis is at time of futures close out
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.9
Optimal Hedge Ratio
(See Spreadsheet Example & pg. 56-60)
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
3.10
Hedging Using Index Futures
(See example Page 62)
To hedge the risk in a portfolio the
number of contracts that should be
shorted is
P
b
F
where P is the value of the portfolio,
b is its beta, and F is the current
value of one futures (=futures price
times contract size)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.11
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.) (Why Cheaper?)
Desire to hedge systematic risk
(Appropriate when you feel that you have
picked stocks that will outperform the
market.) (Market Neutral Trading)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.12
Example (Pg. 62)
Futures price of S&P 500 is 1,010
Size of portfolio is $5,050,000
Beta of portfolio is 1.5
One contract is on $250 times the index
Risk Free Rate = 4%
Dividend Yield on Index = 1%
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
3.13
Example Continued (Pg. 63)
Assume Index drops to 900 and futures
drop to 902 in 3 Months:
Q: What is the gain on the futures?
30 x (1010 - 902) x 250 = $810,000
Q: What is the expected % return on the
underlying stock portfolio? from CAPM:
= RFR + (Beta x ((cap loss + div)-RFR)
= 1.0 + (1.5 x ((-10+.25) – 1.0))
= 1.0 + (1.5 x -10.75) = -15.125 %
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.14
Example Continued (Pg. 63)
Q: What would be the expected value of
the hedgers overall position in the end?
Expected portfolio value =
$5,050,000 x (1 - .15125) = $4,286,187
Gain on Futures = $810,000
Therefore, Total Value =
$4,286,187 + $810,000 = $5,096,187
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.15
Changing Beta
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Why would a trader use futures to adjust
beta of a stock portfolio? Why not just sell
or buy more stock?
What position is necessary to reduce the
beta of the portfolio to 0.75?
What position is necessary to increase the
beta of the portfolio to 2.0?
Formulas - bottom pg. 64 & top of pg. 65
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.16
Rolling The Hedge Forward
Note: Example on Pg. 66
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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 (Known as Spread Risk)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.17
Text Problems
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3.10 (Review in class)
3.17 (Review in class)
3.18 (Review in class)
3.21 (Homework Due Thursday 1/22/09)
3.22 (Recommended Study - Spreadsheet)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.18