Chapter 3Hedging Strategies Using Futures

1

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 and want to lock in the price

2

Arguments in Favor of Hedging

3

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

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

4

Short Hedge for Sale of an Asset A short hedge is appropriate when the hedger already owns an asset an expects to sell it at some time in the future.

Eg: It is May 15. An oil producer has negotiated a contract to sell 1 million barrels of crude oil in August 15. Quotes:

Spot price : $60 per barrel

August oil futures price:$59 per barrel

1contract = 1000 barrels

5

IllustrationThe oil producer can hedge with the following transactions:

May 15: Short 1000 August futures contracts

on crude oil

August 15: Close out futures position

Suppose spot price on August 15 proves to be $55.

- Gain in futures: $59-55 = $4 per barrel or $4million.

- Sales in spot market = $ 55m

- Net = $55+ $4 = $59million

-Effective price = $ 59 million/1 million barrels = $59/b

6

What if price of oil on August 15 proves to be $65 per barrel?Calculate gain/loss in futures position;

What is the net outcomes?

What is the effective price?

7

Long Hedge for Purchase of an Asset

A long hedge is appropriate when a company knows it will have to purchase a certain asset in the future and wants to lock in a price now.

Eg: A copper fabricator knows it will need 100,000 pounds of copper on May 15. The spot price of copper is 340 cents/pound and the May futures price is 320 cents/pound.

Each contract is for the delivery of 25,000 pound of copper.

8

IllustrationThe copper fabricator can hedge with the following transactions:

now: Take a long position in 4 May futures

contracts on copper

May 15: Close out the position.

Suppose that the price of copper on May 15 is 325 cents.

-Gain in futures: (3.25-3.20)*100,000= $5000

- Buying cost in spot: $ 325,000

- Net outcomes: ($325,000) + 5000= (320,000)

- Effective price: 320 cents per pound

9

What if price of copper on May 15 proves to be 305 cents per pound?Calculate gain/loss in futures position;

What is the net outcomes?

What is the effective price?

10

Cross hedging

Occurs when 2 assets are different.

Hedge ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure.

Hedge ratio=1 if underlying asset in futures contract is the same as the asset being hedge

When cross hedging is used, setting the hedge ratio equal to 1 is not always optimal.

11

Optimal Hedge Ratio (page 57)

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.

12

F

Sh

*

Optimal Number of ContractsQA Size of position being hedged (units)

QF Size of one futures contract (units)

VA Value of position being hedged (=spot price time QA)

VF Value of one futures contract (=futures price times QF)

13

Optimal number of contracts if no tailing adjustment

F

A

Q

Qh*

Optimal number of contracts after tailing adjustment to allow or daily settlement of futures

F

A

V

Vh*

Example (Pages 59-60)

Airline will purchase 2 million gallons of jet fuel in one month and hedges using heating oil futures

From historical data F =0.0313, S =0.0263, and = 0.928

14

7777003130

026309280 .

.

..* h

Example continued

The size of one heating oil contract is 42,000 gallons

The spot price is 1.94 and the futures price is 1.99 (both dollars per gallon) so that

Optimal number of contracts assuming no daily settlement

Optimal number of contracts after tailing

15

033700042000000277770 .,,,.

103658083000880377770 .,,,.

580830004299100088030000002941

,,.,,,,.

F

A

VV

Hedging Using Index Futures(Page 61)

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

where VA is the value of the portfolio, is its beta, and VF is the value of one futures contract

16

F

A

V

V

Example

S&P 500 futures price is 1,000

Value of Portfolio is $5 million

Beta of portfolio is 1.5

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

17

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?

18

Why Hedge Equity Returns

May want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolioSuppose 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 you earn is the risk-free return plus the excess return of your portfolio over the market.

19