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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010 Hedging Strategies Using Futures Chapter 3 (All Pages) 1

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Page 1: Ch03 hullfundamentals7thed

Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

Hedging Strategies Using Futures

Chapter 3

(All Pages)

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Page 2: Ch03 hullfundamentals7thed

Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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 (Airline Example)

Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult (Page 52 example)

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

Convergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2)

Time

Spot Price

FuturesPrice

t1 t2

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

Optimal Hedge Ratio

Proportion of the exposure that should optimally be hedged is

where

S is the standard deviation of S, the change in the spot price during the hedging period,

F is the standard deviation of F, the change in the futures price during the hedging period

is the coefficient of correlation between S and F.

F

Sh

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Tailing the Hedge

Two way of determining the number of contracts to use for hedging are Compare the exposure to be hedged with the value of

the assets underlying one futures contract Compare the exposure to be hedged with the value of

one futures contract (=futures price time size of futures contract

The second approach incorporates an adjustment for the daily settlement of futures

Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010 11

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

Hedging Using Index Futures(Page 63)

To hedge the risk in a portfolio the number of contracts that should be shorted is

where VA is the current value of the portfolio, is its beta, and VF is the current value of one futures (=futures price times contract size)

F

A

V

V

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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.) (Why Cheaper?)

Desire to hedge systematic risk (Appropriate when you feel that you have

picked stocks that will outperform the market.) (Market Neutral Trading)

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

Example – Page 64

Futures price of S&P 500 is 1,010Size of portfolio is $5.05 millionBeta of portfolio is 1.5One contract is on $250 times the index

S&P 500 Index is 1,000 Dividend Yield on index = 1%

What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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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Stock Picking

If you think you can pick stocks that will outperform the market, futures contract can be used to hedge the market risk

If you are right, you will make money whether the market goes up or down

Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010 16

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Fundamentals of Futures and Options Markets, 7th Ed, Ch3, Copyright © John C. Hull 2010

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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Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007

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Practice Problems:

All Quiz Questions Problem 3.10 Problem 3.17 Problem 3.24