Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.1
Hedging Strategies
Using Futures
Chapter 4
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.2
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
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.3
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
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.4
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
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.5
Convergence of Futures to Spot
Time Time
(a) (b)
Futures
Price
Futures
PriceSpot Price
Spot Price
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.6
Basis Risk
? Basis is the difference
between spot & futures
? Basis risk arises because of
the uncertainty about the
basis when the hedge is
closed out
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.7
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 Asset=S2–(F2 – F1) = F1 + Basis
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.8
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 Realized=S2+ (F1 –F2) = F1 + Basis
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.9
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
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.10
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.
h S
F
* ? r s
s
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.11
Hedging Using Index Futures
(Page 82)
? To hedge the risk in a 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
b PA
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.12
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 outpeform
the market.)
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.13
Example
Value of S&P 500 is 1,000
Value of Portfolio is $5 million
Beta of portfolio is 1.5
What position in futures contracts on the
S&P 500 is necessary to hedge the
portfolio?
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.14
Changing Beta
? 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?
Options,Futures,and Other Drerivatives,5th edition ? 2002 by John C,Hull
4.15
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