Campbell R. Harvey. Fuqua School of Business. Duke University. charvey@mail.duke.edu. http://www.duke.edu/~charvey. Overview. Forward contracts. Futures contracts. The relationship between forwards and futures. ID: 757787

- Views :
**0**

**Direct Link:**- Link:https://www.docslides.com/myesha-ticknor/futures-global-financial-management
**Embed code:**

Download this presentation

DownloadNote - The PPT/PDF document "Futures Global Financial Management" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.

Slide1

Futures

Global Financial Management

Campbell R. Harvey

Fuqua School of Business

Duke University

charvey@mail.duke.edu

http://www.duke.edu/~charvey

Slide2Overview

Forward contracts

Futures contracts

The relationship between forwards and futures

Valuation

Using forwards and futures to hedge in Practice

Foreign exchange risk

Stock market risk

Interest rate risk

Slide3Applications for Hedge Instruments

A mining company expects to produce 1000 ounces of gold 2 years from now if it invests in a new mine:

Avoid that the loan for financing the investment cannot be repaid because the gold price moved

A bank expects repayment of a loan in 1 year, and wishes to use proceeds to redeem 2-year bond

Lock in current interest rate between 1 and 2 years from now in order to avoid shortfall if interest rates have changed

A hotel chain buys hotels in Switzerland, financed with a loan in US-dollars:

Make sure that the company can repay the loan, even if Swiss franc proceeds diminished because of exchange rate movement

Slide4Forward Contracts

A

forward contract

is a contract made today for

future delivery

of an asset at a

prespecified price

.

no money or assets change hands prior to maturity.

Forwards are traded in the over-the-counter market.

The

buyer

(long position) of a forward contract is

obligated

to:

take delivery of the asset at the maturity date.

pay the agreed-upon price at the maturity date.

The

seller

(short position) of a forward contract is

obligated

to:

deliver the asset at the maturity date.

accept the agreed-upon price at the maturity date

Slide5Foreign Exchange Risk:

Foreign Currency Futures

Foreign currency futures are traded on the CME.

Foreign currency futures are traded on:

British Pound: 62,500BP

Canadian Dollar: 100,000CD

German Mark: 125,000DM

Japanese Yen: 12,500,000Y

Swiss Franc: 125,000SF

French Franc: 250,000FF

Australian Dollar: 100,000AD

Mexican Peso: 500,000MP

Delivery Months: March, June, Sept., Dec.

Prices are quoted as USD per unit of the foreign currency.

USD/SF = 0.7106

USD/Y = 0.8543

USD/BP = 1.6592

USD/DM = 0.6166

Mar contracts, Open on Tuesday January 21 1997

Slide6Hedging with Foreign Currency Futures

Currency mismatching:

Assets and liabilities in different currencies

Expect receipts and payments in different currencies.

Use currency futures to hedge

Example

:

Company has just signed a contract to sell 25 large earth movers to a German mining company:

Total price DM35 million.

Delivery and payment of the earth movers at the end of June.

Current (Jan) USD/DM exchange rate: 0.6136

June futures price for DM: 0.6223

Total outlay today is $21 million; can borrow this amount at 8.4% p. a.

Is this a worthwhile project?

When would the project make a loss?

Slide7Does the project make a loss?

Borrow $21 million

Repay 1.035*$21m=$21.735m

Make zero profit if USD/DM=0.621

Do you expect to make a loss or a profit?

If you want to hedge:

receive

DM in June

sell

a June DM futures contract

How many contracts do you have to sell? (DM contracts are DM 125,000)

deliver

DM in June at an exchange rate of USD/DM = 0.6223

This will lock in your USD price at:

USD Price = 0.6223 USD/DM (DM35 million)

= $21.7805 million

Hedging with Foreign Currency Futures

Slide8Scenario I: Dollar rises

USD/DM exchange rate

falls

to 0.60 in June

The USD price of the earth movers on the delivery date is:

(DM 35 million)(0.60) = $21m

The

loss

on the project is:

$21m-$21.735m=-$735,000

The

profit

on the 280 DM futures contracts is:

DM35m(0.6223-0.60)USD/DM

= $780,500

Total profits are:

$780,500-$735,000=$45,500

Hedging with Foreign Currency Futures

Scenario II: Dollar falls

USD/DM exchange rate

increases

to 0.65 in June

The USD price of the earth movers on the delivery date is:

(DM 35 m)(0.65) = $22.75 m

The

profit

on the project is:

$22.75m-$21.735m=$1.015m

The

loss

on the futures contracts for DM35m is:

DM35m(0.6223-0.65)USD/DM

=$969,500

Total profits are:

$1,015,000 - $969,500=$45,500

Slide9How to make your own forward contract

Suppose a currency futures contract for the maturity and currency you need does not exist.

Make your own!

The following three transactions replicate the previous contract:

Borrow Deutsche Mark in January to repay in June

Exchange DM proceeds at spot rate into USD

Invest dollars at current interest rate until June

Why does this work?

January

June

USD

DM

Invest at 8.4%

Borrow at 4.93 %

0.6136

0.6223

DM35m

$21.7805m

$21.044m

DM34.296m

Slide10Alternatives to Forwards?

Homemade forward contracts

Combine borrowing and lending with currency spot contract to replicate forward contract

Other financial policies

The company wanted to borrow dollars anyway? How could you consolidate the transactions?

What would be the easiest way to avoid the necessity to hedge?

Slide11Forwards on Securities

The case of a security without income

What is the difference between buying a security today, and between buying a security forward?

If you purchase the security forward, you do not have to pay the purchase price today:

Can invest the money somewhere else

Securities pay income (dividends, coupons)

Only if you purchase it now, not if you buy forward

Example:

Share trades today at $25

Pays no dividends during the next three months

The risk free rate for 3 months is 6% p. a. with quarterly compounding

Slide12What is the forward price?

Consider the following two strategies:

Buy one share for $25

Sell the share forward in three months for the forward price F

What are the cash flows:

Today: Zero from forward, -$25 from buying share

3 Months: F from selling share forward - value of share

+ value of share = F

Riskless investment of $25 dollars yields F

Investing $25 at riskless rate gives:

$25*1.015=$25.375

Identical portfolios must have same return:

F=$25.375

Slide13Now suppose the share pays a dividend at the end of three months of $2

What are the cash flows now:

Today: Zero from forward, -$25 from buying share

3 Months: F from selling share forward - value of share

+ value of share +$2 dividend = F+$2

Riskless investment of $25 dollars yields F+$2

Investing $25 at riskless rate gives:

$25*1.015=$25.375

Identical portfolios must have same return:

F+$2=$25.375, hence F=$23.375

Forwards on Securities

The case of a security with income

Slide14The General Formula

Portfolio I:

Buy stock at

S

0

, Sell share forward at F

Portfolio II:

Invest

S

0

at risk free rate

Cash flows from this are:

Hence we obtain:

F= S

0(1+r

T

)-D

T

Slide15Forward Price and Arbitrage

Case 1:

F< S

0

(1+r

T

)-D

T

Then portfolio I has a lower payoff than portfolio II:

Buy portfolio II, (short) sell portfolio I

Invest in bonds

(short) sell stock

buy stock forward at F

Realize arbitrage profit -

F+ S

0

(1+r

T

)-D

T

>0

Slide16The Standard Formula

Previous formula unusual.

Assume you receive dividend up front:

Rewrite dividend as dividend yield

d

:

Then the previous formula can be rewritten:

The conventional way to express this is (use continuous compounding):

Slide17Futures Contracts

A

futures contract

is identical to a forward contract, except for the following differences:

Futures contracts are standardized contracts and are traded on organized exchanges.

Futures contracts are

marked-to-market

daily.

The daily cash flows between buyer and seller are equal to the change in the futures price.

Futures and forward prices must be identical if interest rates are constant.

Can use results on forward for futures

Slide18Futures Contracts

Futures contracts allow investors to:

Hedge

Speculate

Futures contracts are available on commodities and financial assets:

Agricultural products and livestock

Metals and petroleum

Interest rates

Currencies

Stock market indices

Slide19Valuation of Futures Contracts

An Application

A futures contract on the S&P500 Index entitles the buyer to receive the

cash value

of the S&P 500 Index at the maturity date of the contract.

The buyer of the futures contract does

not

receive the dividends paid on the S&P500 Index during the contract life.

The price paid at the maturity date of the contract is determined at the time the contract is entered into. This is called the

futures price

.

There are always four delivery months in effect at any one time.

March

June

September

December

The closing cash value of the S&P500 Index is based on the opening prices on the third Friday of each delivery month.

Slide20Hedging Stock Market Risk: S&P500 Futures Contract

Contract:

S&P500 Index Futures

Exchange:

Chicago Merchantile Exchange

Quantity:

$500 times the S&P 500 Index

Delivery Months:

March, June, Sept., Dec.

Delivery Specs:

Cash Settlement Based on the

Value of the S&P 500 Index at

Maturity.

Min. Price Move:

0.05 Index Pts. ($25 per

contract).

Slide21Valuation of Futures Contracts

An Alternative Derivation

When you buy a futures contract on the S&P500 Index, your payoff at the maturity date, T, is the difference between the cash value of the index, S

T

, and the futures price, F.

The amount you put up today to buy the futures contract is zero. This means that the

present value

of the futures contract must also be zero:

The present value of

S

T

and

F

is:

Then, using the fact that

PV(F)=PV(S

T

):

Slide22Example

On Thursday January 22, 1997 we observed:

The closing price for the S&P500 Index was 786.23.

The yield on a T-bill maturing in 26 weeks was 5.11%

Assume the annual dividend yield on the S&P500 Index is 1.1% per year,

What is the futures price for the futures contracts maturing in March, June, September, December 1997?

Slide23Example

Days to maturity

June contract: 148 days

Estimated futures prices:

For the June contact:

Similarly:

Slide24

Index Arbitrage

Suppose you observe a price of 820 for the June 1997 futures contract. How could you profit from this price discrepancy?

We want to avoid all risk in the process.

Buy low and sell high:

Borrow enough money to buy the index today and immediately sell a June futures contract at a price of 820.

At maturity, settle up on the futures contract and repay your loan.

Slide25Index Arbitrage

Suppose the futures price for the September contract was 790. How could you profit from this price discrepancy?

Buy Low and Sell High:

Sell the index short and use the proceeds to invest in a T-bill. At the same time, buy a September futures contract at a price of 790.

At settlement, cover your short position and settle your futures position.

Slide26Hedging with S&P500 Futures

Suppose a portfolio manager holds a portfolio that mimics the S&P500 Index.

Current worth: $99.845 million, up 20% through mid-November

‘

95

S&P500 Index currently at 644.00

December S&P500 futures price is 645.00.

How can the fund manager hedge against further market movements?

Lock in a price of 645.00 for the S&P500 Index by

selling

S&P500 futures contracts.

Lock in a total value for the portfolio of:

$99.845(645.00/644.00) million = $100.00 million.

Since one futures contract is worth $500(645.00) = $322,500, the total number of contracts that need to be sold is:

Slide27Hedging with S&P500 Futures

Scenario I: Stock market falls

Suppose the S&P500 Index

falls

to 635.00 at the maturity date of the futures contract.

The value of the stock portfolio is:

99.845(635.00/644.00) = 98.45 million

The

profit

on the 310 futures contracts is:

310(500)(645.00-635) = 1.55 million

The total value of the portfolio at maturity is $100 million.

Scenario II: Stock market rises

Suppose the S&P500 Index

increases

to 655.00 at the maturity date of the futures contract.

The value of the stock portfolio is:

99.845(655.00/644.00) = 101.55 million

The

loss

on the 310 futures contracts is:

310(500)(645.00-655.00) = -1.55 million

The total value of the portfolio at maturity is $100 million.

Slide28Commodity Futures

Commodities are similar in many ways to securities, but some important differences:

Storage costs can be significant:

Security (precious metals)

Physical storage (grain)

Possibility of damage

Summarized as cost of carry, usually written as constant annual percentage

q

of initial value.

Sometimes possession of commodity also provides benefits:

Demand fluctuations

Supply shortages (Oil)

Summarized as convenience yield, usually written as constant annual percentage

y of initial value.

Slide29Example: Cost of Carry

You are considering taking physical delivery of live cattle in order to execute a commodity futures arbitrage.

The cost of carry is assessed at 4% relative to the current spot price of $100.

If the contract has 2 months to maturity, the

up-front

cost of storing and feeding the cattle is:

CC = S

0

(e

qT

-1) = 100(e

0.04(2/12)

-1) =$0.669.

Slide30Replication of Forward Contracts

The payoff of a forward contract can be replicated by

borrowing money

buying the commodity

paying the cost of carry (feed for hogs, security for gold, storage for oil)

Two Implications:

If two procedures generate the same cash flows, they must cost the same

If an appropriate forward contract does not exist, we can make our own by:

transacting in the spot market and

borrowing

Slide31Valuation of Commodity Contracts

-S

0

S

T

F-S

T

0

0

-S

0

(e

qT

-1)

S

0

e

qT

0

-S

0

e

(q+r)T

F-S

0

e

(q+r)T

In the absence of arbitrage: F = S

0

e

(q+r)T

Compare this with formula for dividend paying stocks:

cost of carry is like negative dividend

same principles for valuation apply

Slide32Example: Forward Arbitrage

The spot price of wheat is 550 and the six-month forward price is 600. The riskless rate of interest is 5% p.a. and the cost of carry is 6% p.a.

Is there an arbitrage opportunity in this market?

-550

S

T

600-S

T

0

0

-550(e

0.06(0.5)

-1)

550e

0.06(0.5)

0

-550e

(0.06+0.05)0.5

600-550e

(0.06+0.05)0.5

Arbitrage Profit: 600-550e

(0.06+0.05)0.5

= $18.90

Slide33

Hedging Using Interest Rate Futures Contracts

Hedging interest rate risk can also be done by using interest rate futures contracts.

There are two main interest rate futures contracts:

Eurodollar futures

US T-bond futures

The Eurodollar futures is the most popular and active contract. Open interest is in excess of $4 trillion at any point in time.

Slide34LIBOR

The Eurodollar futures contract is based on the interest rate payable on a Eurodollar time deposit.

This rate is known as

LIBOR

(

L

ondon

I

nterbank

O

ffer

R

ate) and has become the benchmark short-term interest rate for many US borrowers and lenders.

Eurodollar time deposits are non-negotiable, fixed rate US dollar deposits in offshore banks (i.e., those not subject to US banking regulations).

US banks commonly charge LIBOR plus a certain number of basis points on their floating rate loans.

LIBOR is an annualized rate based on a 360-day year.

Example: The 3-month (90-day) LIBOR 8% interest on $1 million is calculated as follows:

Slide35Eurodollar Futures Contract

The Eurodollar futures contract is the most widely traded short-term interest rate futures.

It is based upon a 3-month $1 million Eurodollar time deposit.

It is settled in cash.

At expiration

, the futures price is 100-LIBOR.

Prior to expiration

, the quoted futures price implies a LIBOR rate of:

Implied LIBOR = 100-Quoted Futures Price

Slide36Eurodollar Futures Contract

Contract:

Eurodollar Time Deposit

Exchange:

Chicago Merchantile Exchange

Quantity:

$1 Million

Delivery Months:

March, June, Sept., and Dec.

Delivery Specs:

Cash Settlement Based on

3-Month LIBOR

Min Price Move:

$25 Per Contract (1 Basis Pt.)

Slide37

Example

Suppose in February you buy a March Eurodollar futures contract. The quoted futures price at the time you enter into the contract is 94.86.

If the LIBOR rate falls 100 basis points between February and the expiration date of the contract in March, what is your profit or loss?

The quoted price at the time the contract is purchased implies a LIBOR rate of 100-94.86 = 5.14%.

If LIBOR falls 100 basis points, it will be 4.14% at the expiration date of the contract.

This means a futures price of 100-4.14 = 95.86 at the expiration date.

Since we bought the contract at a futures price of 94.86, our total gain is 95.86-94.86 = 1.00.

Slide38Example

In dollar terms, our gain is:

The increase in the futures price is multiplied by $10,000 because the futures price is per $100 and the contract is for $1,000,000.

We divide the increase in the futures price by 4 because the contract is a 90 day (3 month) contract.

Slide39Hedging with Eurodollar

Futures Contracts (1)

Suppose a firm knows in February that it will be required to borrow $1 million in March for a period of 3 months (90 days).

The rate that the firm will pay for its borrowing is LIBOR + 50 basis points.

The firm is concerned that interest rates may rise before March and would like to hedge this risk.

Assume that the March Eurodollar futures price is 94.86.

The LIBOR rate implied by the current futures price is 100-94.86 = 5.14%.

If the LIBOR rate increases, the futures price will fall. Therefore, to hedge the interest rate risk, the firm should

sell

one March Eurodollar futures contract.

The gain (loss) on the futures contract should exactly offset any increase (decrease) in the firm

’

s interest expense.

Slide40Hedging with Eurodollar

Futures Contracts (3)

Suppose LIBOR

increases

to 6.14% at the maturity date of the futures contract.

The interest expense on the firm

’

s $1 million loan commencing in March will be:

The gain on the Eurodollar futures contract is:

Slide41Hedging with Eurodollar

Futures Contracts (4)

Now assume that the LIBOR rate

falls

to 4.14% at the maturity date of the contract.

The interest expense on the firm

’

s $1 million loan commencing in March will be:

The gain on the Eurodollar futures contract is:

Slide42Hedging with Eurodollar

Futures Contracts (5)

The

net

outlay is equal to $14,100 regardless of what happens to LIBOR.

This is equivalent to paying 5.64% (1.41% for 3 months) on $1 million.

The 5.64% borrowing rate is equal to the

current

LIBOR rate of 5.14%, plus the additional 50 basis points that the firm pays on its short-term borrowing.

The firm

’

s futures position has locked in the current LIBOR rate.

Slide43Alternatives to Interest Rate Forwards

Is there a homemade forward?

We saw that we can generally replicate futures and forward contracts by:

Buying and selling in the spot market

Borrowing

Suppose an appropriate forward/futures contract does not exist

Can we make our own forward

Which instruments should we use? How?

Slide44Using Bonds to Hedge Interest Risk

An Example of homemade interest rate forwards

Suppose you expect:

Receipt of $1 million exactly one year from today

Need it to repay a loan exactly two years from today.

You would like to invest the $1 million between years 1 and 2.

Issues:

Why is this risky?

How can you lock in the interest rate?

Which interest rate do you want to lock in?

What can you do if a suitable futures contract with the appropriate currency and maturity does not exist?

Use implied forward rates

Slide45Use Implied Forward Rates to Hedge

To lock-in the interest rate on your $1 million you need to buy a two-year zero-coupon bond and sell a one-year zero-coupon bond.

The exact transaction involves selling $1/(1+r

1

) million of the one-year zero-coupon bond and using the proceeds to purchase a two-year zero-coupon bond yielding r

2

.

This transaction will lock-in an interest rate of

1

f

1

over the second year on your $1 million.

Example:

r

1

=4.81%

r

2

=4.94%

Slide46Using Implied Forward Rates to Hedge

The one-year forward rate is

1

f

1

= 5.07%.

Slide47Using Implied Forward Rates to Hedge

Another Example

Now suppose you expect to receive $1 million two years from today and need the money to pay a debt exactly five years from today. How can you lock in the interest rate on your $1 million?

The exact transaction involves selling $1/(1+r

2

)

2

million of the two-year zero-coupon bond and using the proceeds to buy a five-year zero-coupon bond yielding r

5

.

This transaction locks in an interest rate of

2

f

3

on your $1 million.

Slide48Using Implied Forward Rates to Hedge

Example II

The

3-year forward rate starting 2 years from now

is denoted

2

f

3

and is computed as follows:

[The notation here is different from lecture note where this would be 2f5]

Using the spot rates in effect on 2/6/96, we have:

Slide49The final value of the investment should be $1(1+

2

f

3

)

3

= $1(1.0549)

3

= $1,173,927.

Using Implied Forward Rates to Hedge

Example II

Slide50Relationship Between Forward Rates:

The General Case

The t-year forward rate starting n years from today is equivalent to earning the one-year forward rates between year n and year n+t.

n n+1 n+2 ... n+t-1 n+t

n

f

1

n+1

f

1

...

n+t-1

f

1

n

f

t

Suppose you wanted to know the implicit interest rate you would earn between year n and year n+t. This involves calculating the

t-year forward rate starting n years from today

.

The general formula is:

Slide51Relationship Between Forward Rates:

Example II

Use the spot rates on 2/6/96 to calculate the one-year forward rates in years 3-5. How does this compare to

2

f

3

?

Slide52Summary

Forward and futures can be used to hedge risks:

Foreign exchange rate risk

Stock market risk

Commodity price risk

Interest rate risk

Forwards and futures are redundant instruments:

Can be replicated through transactions in spot markets and borrowing or lending

Forwards and futures are derivatives:

Value depends on value of other asset

Next Slides