Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.1

Hedging Strategies Using Futures

Chapter 3

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.2

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

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.3

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

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.4

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 (See example pg. 50)

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.5

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

Time

Spot Price

FuturesPrice

t1 t2

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.6

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

Basis often exists because of:Storage costs if any Interest factorForward view of spot price

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.7

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 (Why?)

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 (Quality difference + interest & storage cost if any)

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.8

Short Hedge (Pg. 54 Ex. 3.3)

Suppose thatF1 : Initial Futures PriceF2 : Final Futures PriceS2 : 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**Note – Basis is at time of futures close out

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.9

Long Hedge (Pg. 55 Ex. 3.4) Suppose that

F1 : Initial Futures PriceF2 : 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**Note – Basis is at time of futures close out

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.10

Optimal Hedge Ratio (See Spreadsheet Example & pg. 56-60)

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.

h S

F

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.11

Hedging Using Index Futures(See example Page 62)

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

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

FP

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.12

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.) (Why Cheaper?)

Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outperform the market.) (Market Neutral Trading)

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.13

Example (Pg. 62)Futures price of S&P 500 is 1,010Size of portfolio is $5,050,000Beta of portfolio is 1.5One contract is on $250 times the indexRisk Free Rate = 4%Dividend Yield on Index = 1%

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

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.14

Example Continued (Pg. 63)Assume Index drops to 900 and futures drop to 902 in 3 Months:Q: What is the gain on the futures?30 x (1010 - 902) x 250 = $810,000Q: What is the expected % return on the underlying stock portfolio? from CAPM:= RFR + (Beta x ((cap loss + div)-RFR)= 1.0 + (1.5 x ((-10+.25) – 1.0))= 1.0 + (1.5 x -10.75) = -15.125 %

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.15

Example Continued (Pg. 63)Q: What would be the expected value of the hedgers overall position in the end?

Expected portfolio value = $5,050,000 x (1 - .15125) = $4,286,187Gain on Futures = $810,000Therefore, Total Value = $4,286,187 + $810,000 = $5,096,187

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.16

Changing Beta

Why would a trader use futures to adjust beta of a stock portfolio? Why not just sell or buy more stock?

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?

Formulas - bottom pg. 64 & top of pg. 65

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.17

Rolling The Hedge ForwardNote: Example on Pg. 66

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 (Known as Spread Risk)

Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.18

Text Problems

3.10 (Review in class) 3.17 (Review in class) 3.18 (Review in class) 3.21 (Homework Due Thursday 1/22/09) 3.22 (Recommended Study - Spreadsheet)