long & short hedges
TRANSCRIPT
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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.
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Say a oil producer enters into a contract to sell 10mn barrel of oil
in 3 months on August 15. The price will be the market price as
on August 15.
Spot price today (May 15) = $19 per barrel.
Future price for Aug 15 delivery = $18.75 per barrel.
1 future contract = 1000 barrels.
The Co can hedge its exposure by shorting 1000 futures contracts.
If he closes out his position on Aug 15, the effect ofthe strategy would be to lock in a price close to $18.75per barrel.
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f spot price on August 15 is $17.50 per barrel. The co gets sales proceeds $17.50mn as per sales contract.
Since August is the delivery month, futures price on Aug 15
would be very close to the spot price of $17.50 on that day.
By closing out, Co gains $1.25 per barrel.
Therefore total amt comes to 17.5+1.25 =$18.75.
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f spot price on August 15 is $19.50 per barrel. The co gets sales proceeds $19.50mn as per sales contract.
Since August is the delivery month, futures price on Aug 15
would be very close to the spot price of $19.50 on that day.
By closing out, Co losses $0.75 per barrel.
Therefore total amt comes to 19.5 - 0.75 =$18.75.
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On Jan 15, Mr. F knows he will need 100000 pounds of
copper on May 15. Current spot price =$1.40 per pound &
futures price for May delivery =$1.20 per pound.
1 futures contract = 25000 pounds of copper.
The Co can hedge its exposure by taking a long position infour May futures contracts.
If he closes out his position on May 15, the effect
of the strategy would be to lock in a price close to$1.20 per pound.
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f spot price on May 15 = $1.05 per pound Since May is the delivery month, futures price on May 15
would be very close to the spot price of $1.05 on that day.
By closing out, F loses 100000 * ($1.20 - $1.05) = $15000.
It pays $105000 for the copper.
Net cost is approx $ 120000.
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Arguments in Favor of HedgingCompanies 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
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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 underlyingcan be difficult.
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Convergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2)
Time
Spot
Price
Futures
Price
t1 t2
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BASIS
Hedging is often not straightforward
Reasons
The asset whose price is to be hedged may not beexactly the same as the asset underlying thefutures contract.
The hedger may be uncertain as to the exact datewhen the asset will be bought or sold.
The hedge may require the futures contract to beclosed out before its delivery month.
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Basis Risk Basis = Spot price of asset to be hedged
futures price of contract used
If asset to be hedged and the asset underlying the futurescontract are the same, the basis should be zero at theexpiration of he futures contract.
Basis is negative in contango market most fin mkts
display contango conditions generally distant
futures are priced more than the near term futures.
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Basis Risk If spot price increases by more than the
futures price BASIS increases
strengthening of the basis
If futures price increases by more than the
spot price BASIS declines
weakening of the basis
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Short Hedge Suppose that
F1: Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
You hedge the future sale of an asset byentering into a short futures contract
Price Realized=S2+ (F1 F2) = F1 + Basis
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Long Hedge Suppose that
F1 : Initial Futures Price
F2 : Final Futures PriceS2 : 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
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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 highlycorrelated with the asset price. This is
known as cross hedging.
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Optimal Hedge Ratio
Proportion of the exposure that should optimally be
hedged is
where
WS is the standard deviation of(S, the change in the spot
price during the hedging period,
WF is the standard deviation of(F, the change in the
futures price during the hedging period
V is the coefficient of correlation between (Sand (F.
F
S
WWV
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In practice
Optimal hedge ratio is extracted from the
regression equation:
S FE F I!
h* is given by beta coefficient and error term captures
the effects of all those factors not included in the model.
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Hedging Using Index Futures
To hedge the risk in a portfolio the
number of contracts that should be
shorted is
where P is the value of the portfolio, F
is its beta, and A is the value of theassets underlying one futures contract
FP
A
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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 itback.)
Desire to hedge systematic risk
(Appropriate when you feel that you havepicked stocks that will outpeform the
market.)
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ExampleValue 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 theS&P 500 is necessary to hedge the
portfolio?
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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?
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Why Hedge Equity Returns May want to be out of the market for a while.
Hedging avoids the costs of selling and
repurchasing the portfolio Suppose stocks in your portfolio have an average
beta of 1.0, but you feel they have been chosen
well and will outperform the market in both good
and bad times. Hedging ensures that the return youearn is the risk-free return plus the excess return of
your portfolio over the market.
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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
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