Long & Short Hedges

8/7/2019 Long & Short Hedges

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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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I

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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I

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


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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I

f spot price on May 15 = $1.05 per pound Since May is the delivery month, futures price on May 15


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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Long & Short Hedges

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