2 hedging with futures

7/31/2019 2 Hedging With FUTURES

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Hedging with FUTURES


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LONG Hedge

Spot Market: asset will be bought (losewhenprice increases);

Futures Market: LONG position (gainwhen price

increases).

SHORT Hedge

Spot Market: asset will be sold (losewhen pricedecreases);

Futures Market: SHORTposition (gainwhenprice decreases).


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3 things we need to know1. Risk Factor

Variable that determines the possible loss

2. Position on Risk Factor (spot market)

When do we lose? When price increases?

When price decreases?

3. Position on hedging contract (F market) LONG (if you lose on spot market when

price increases)

SHORT (if you lose on spot market whenprice decreases)


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Example short hedge

May 15:

SELL 1 mil. Barrels crude oil at August 15

SM15=$19

FM15=$18.75

SHORT 1000 barrels August FUTURESand lock in a price of $18.75


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August 15 (possibility 1)

Spot market: SA15 = $17.50 which means + $17.5 mil.

Futures market: F

A15

= $17.50 ~ close to the spot pricebecause August is the delivery month

Profit:$18.75 - $17.50 = $1,25 / barrel

i.e. + $1.25 mil. from the Futures position

Result:$18.75 mil.


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August 15 (possibility 2)

Spot market: SA15 = $19.50 which means + $19.5 mil.

Futures market: FA15 = $19.50 ~ close to the spot price because

August is the delivery month

Loss:$18.75 - $19.50 = $0.75 / barrel

i.e. - $0.75 mil. from the Futures position

Result:$18.75 mil.


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Roll over the hedge

To undertake a one-year hedgetransaction, an investor must sell one-

year futures. This is often difficultbecause a futures contract with thismaturity tends to be illiquid.

One alternative is to hedge forwardusing more liquid, shorter maturitycontracts.


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Arguments in Favor of

HedgingPrediction is expensive;

Usually companies make no prediction of market

variables they need their cash flow to be certain.

They hedge to avoid unpleasant pricemovements;

Thus they focus on their main activities.


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Arguments against Hedging

Shareholders are usually well diversified and canmake their own hedging decisions; (Ex. build portfolio of copper producer and copper user

companies.)

However hedging might be more expensive for shareholders.

It may increase risk to hedge when competitors donot hedging becomes risky

Explaining a situation where there is a loss on the

hedge and a gain on the underlying can be difficulthedging strategies should be set by a companysboard of directors and clearly communicated tocompanys management and shareholders.


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BASIS = Spot price Futures price$2.50

$2.20

$2.00

$1.90

t1 t2

b1

b2

Spotprice

Futuresprice


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Basis risk - 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 contractCost of Asset= S2 (F2 F1)= F1+ b2

The lower the basis

the better

If basis weakens hedgersposition improves


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Basis risk - 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 contractPrice Realized= S2+(F1F2)= F1+b2

If basis strengthenshedgers position improves


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Basis risk (contd)Investment assets vs. consumption assets;

The case of different asset in the hedgingcontract

S2+F1 F2

F1 + (S*2 F2) + (S2 S*2)

Basis if the asset beinghedged were theunderlying asset

Basis from the differencebetween the 2 assets


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Choice of Contract

Choose a delivery month that is as close aspossible to, but later than, the end of the lifeof the hedge;

When there is no futures contract on theasset being hedged, choose the contract

whose futures price is most highly correlatedwith the asset price. When the correlation isdifferent from 1 we have the 2 components ofbasis.


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Optimal Hedge Ratio

The payoffof S

i.e. thehedgedasset

Payoff

Price ofunderlying

+-

S0

S0+S

S0-S

The payoff ofFutures on

another asset

F

S


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Optimal Hedge Ratio (contd)

Long hedge Short hedgeSpotMarket

- (S2S1) - S + (S2S1) + S

FuturesMarket + h(F2F1) + F - h(F2F1) - F

Hedgers

payoffhF -S S - hF

We need to make the hedgers payoff as certain as

possible i.e. we need to minimize its variance.


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Optimal Hedge Ratio (contd)Proportion of the exposure that should optimally

be hedged is:

where

sSis the standard deviation of DS, the change in

the spot price during the hedging period;

sF is the standard deviation of DF, the change inthe futures price during the hedging period;

r is the coefficient of correlation between DSand DF.

hS

F

rs

s


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Optimal Hedge Ratio (contd)

h* = regression coefficient of Son F;

Hedge effectiveness;

Parameters are estimated from historicaldata;

Ideally the length of each time interval is thesame as the length of the time interval forwhich the hedge is in effect (we should haveprevious realizations of the change we try toestimate).


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Optimal number of contracts

NA size of position being hedged (units);

QF size of one futures contract (units);N* optimal number of futures contracts forhedging

F

A

Q

NhN

*

*


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Hedging Using Index FuturesIf we have a portfolio that mirrors the index (weare long on the stocks that are in the index withthe same weights) then the number of contracts

that should be shorted is

The hedge ratio is 1!A

PN

*

value of theportfolio

value of the assetsunderlying onefutures contract


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Hedging Using Index Futures

To hedge the risk in a portfolio that does notmirror the index, the number of contracts thatshould be shorted is

where P is the value of the portfolio, b is its

beta, andA is the value of the assetsunderlying one futures contract

A

PN b*


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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 theS&P 500 is necessary to hedge theportfolio?


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Reasons for Hedging an Equity Portfolio1. Desire to be out of the market for a short period of

time. (Hedging may be cheaper than selling theportfolio and buying it back).

2. Desire to hedge systematic risk (Appropriate whenyou feel that you have picked stocks that willoutperform the market.)

3. Can do the same with a single stock when theinvestor feels the stock will outperform the market oran investment bank wants to protect its new issueagainst market moves.


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Changing Beta - reducing

Until now we used the futures contract to reducethe Beta to 0.

What position is necessary to reduce the beta ofthe portfolio? (> *)

A

P

A

PN

** bb

Short this toreduce beta to

0

Long this toincrease beta to

*

ShortN*to obtain thenew *for your

portfolio


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Changing Beta - increasingWhat position is necessary to increase the betaof the portfolio? (*> )

A

P

A

PN bb **

Short this toreduce beta to0

Long this to

increase beta to*

LongN*to obtain thenew *for your

portfolio


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Rolling The Hedge Forward

We can use a series of futures contractsto increase the life of a hedge;

Each time we switch from 1 futurescontract to another we incur a type of

basis risk (rollover basis). Can postpone the rollover in the hope the basis

will improve.


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Rolling The Hedge Forward - Ex.

April2002

June2003

July2003

March2003

Feb.2003

Oct.2002

Sept.2002

SA=$19

Short:

FO=$18.20

FO=$17.40

Close:

+$0.80

Short:

FM=$17.00

FM=$16.50

Close:

+$0.50

Short:

FJul.=$16.30

SJune=$16FJul.=$16.50

Close:

+$0.50

+$1.70 for aloss of

$3


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Price ofOUTPUTincreases

Price ofOUTPUTdecreases

Hedgedcompany

Unhedgedcompany

Profitmargin

Price ofoutput

Price of INPUT increasesPrice of INPUT decreases

2 hedging with futures

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