FUTURES

&

FORWARDS

Introduction• The futures market enables various entities to

lessen price risk, the risk of loss because of uncertainty over the future price of a commodity or financial asset

• The two major market participants are the hedger and the speculator

• A futures contract is a legally binding agreement to buy or sell something in the future

• The person who initially sells the contract promises to deliver a quantity of a standardized commodity to a designated delivery point during the delivery month; the other party to the trade promises to pay a predetermined price for the goods upon delivery

Forward and Futures• Forward contract: two parties agree to exchange an asset on a

future date at a price set today.– no collateral posted– Tailor-made– OTC

• Futures Contract : a highly liquid version of a forward contract.– margin account; settlement price– Futures commission merchant– Trading pit– Exchange clearinghouse

Forward and Futures Trading Mechanics

Trading Mechanics• Most futures contracts are eliminated before the delivery

month– The speculator with a long position would sell a contract, thereby

canceling the long position– The hedger with a short position would buy a contract, thereby

canceling the short position

• Example: Suppose a speculator purchases a July soybean contract at a

purchase price of $6.12 per bushel. The contract is for 5,000 bushels of No. 2 yellow soybeans at an approved delivery point by the last business day in July.

Upon delivery, the purchaser of the contract must pay $6.12(5,000) = $30,600.

At the delivery date, the price for soybeans is $6.16. This equates to a profit of $6.16 - $6.12 = $0.04 per bushel, or $200. If the spot price on the delivery date were only $6.10, the purchaser would lose $6.12 - $6.10 = $0.02 per bushel, or $100.

Ensuring the Promise is Kept

• In 1974, Congress passed the Commodity Exchange Act establishing the Commodity Futures Trading Commission (CFTC) – Ensures a fair futures market

• A self-regulatory organization, the National Futures Association was formed in 1982– Enforces financial and membership requirements and

provides customer protection and grievance procedures

• The Clearing Corporation ensures that contracts are fulfilled– Becomes party to every trade– Ensures the integrity of the futures contract– Assumes responsibility for those positions when a member is in

financial distress

Some contracts size and margin requirements

Selected Good Faith Deposit Requirements

Data as of January 2, 2004Contract Size Value Initial Margin

per Contract

Soybeans 5,000 bushels $39,700 $1,620

Gold 100 troy ounces $41,600 $2,025

Treasury Bonds $100,000 par $108,000 $2,565

S&P 500 Index $250 x index $278,500 $20,000

Heating Oil 42,000 gallons $38,346 $3,375

•Good faith deposits (or performance bonds) are required from every member on every contract to help ensure that members have the financial capacity to meet their obligations

Quotations

Month Open Hi Lo Sett Net Chg. Life Hi

Life Lo

Open Int.

Expiration (3rd Friday of the month)

opening price

Settle price (Average of the day)

change in settle price

number of outstanding contracts (X 2 to get all contracts outstanding

Types of Orders

• A broker in commodity futures is a futures commission merchant (not the individual who places the order)

• When placing an order, the client should specify the type of order

• A market order instructs the broker to execute a client’s order at the best possible price at the earliest opportunity

• With a limit order, the client specifies a time and a price– E.g., sell five December soybeans at 540, good until canceled

• A stop order becomes a market order when the stop price is touched during trading action– When executed, stop orders close out existing commodity

positions– E.g., a short seller may use a stop order to protect himself against

rising commodity prices

Market Participants• A hedger is someone engaged in a business activity where there is an

unacceptable level of price risk• A processor earns his living by transforming certain commodities into

another form e.g., a soybean processor buys soybeans and crushes them into soybean meal and oil

• A speculator finds attractive investment opportunities in the futures market and takes positions in futures in the hope of making a profit (rather than protecting one). The speculator is willing to bear price risk. For example, a position trader is someone who routinely maintains futures positions overnight and sometimes keep a contract for weeks; a day trader closes out all his positions before trading closes for the day

• Scalpers (or locals) are individuals who trade for their own account, making a living by buying and selling contracts. Scalpers help keep prices continuous and accurate.

• Example: Scalping With Treasury Bond FuturesYou just sold 5 T-bond futures to ZZZ for 77 31/32. Now, a sell order for 5 T-bond futures reaches the pit and you buy them for 77 30/32. Thus, you just made 1/32 on each of the 5 contracts, for a dollar profit of

1/32% x $100,000/contract x 5 contracts = $156.25

ClearingHouse: Matching Trades• Every trade must be cleared by or through a member firm

of the Board of Trade Clearing Corporation• Each trader is responsible for making sure his deck

promptly enters the clearing process• After the Clearing Corporation receives trading cards• Mismatches (out trades) result in an Unmatched Trade

Notice being sent to each clearing member• After resolving all out trades, the computer prints a daily

Trade Register– Shows a complete record of each clearing member’s trades for the

day– Contains subsidiary accounts for each customer clearing through

the firm• Commodity prices may move so much in a single day that

good faith deposits for many members are seriously eroded before the day ends.– The president of the Clearing Corporation may issue a

market variation call for members to deposit more funds into their account

Dealing with Margins• Assume you are short 2 “December S&P 400

futures contracts” for 924.5 (an S&P 400 contract is for 500 times the index). The total value of the position is 2 times 500 times 924.5 or $924,500. Let ‘s assume that your initial margin is 5% or $46,225 and your maintenance margin is 4.5%, that is $41,602.5. Let’s look at when a margin call will occur…

Margins

Day F.Price Gain (loss) Equity Debt Position Margin Call 0 924.5 0 46,225 878,275 924,500 0 1 926 2 x 500 x (-1.5)=

(1,500) 44,725 878,275 923,000 Restricted

2 924 2 x 500 x 2= 2000 46,725 878,275 925,000 Over margined 3 927 2 x 500 x (-3) =

(3,000) 43,725 878,275 922,000 Restricted

4 930 (3,000) 40,725 (<41,602.50)

878,275 919,000 CALL: + $5,500 from your pocket to cover

the requirements 4 930 0 46,225 878,275 0 0 5 929 1,000 47,225 878,275 925,500 Over margined 6 925 4,000 51,225 878,275 929,500 Over margined

Some notations…

• Futures Price : the price, set today, at which the asset will be traded in the future

• At Maturity: futures price = spot price

• Trade agreements– Buy a futures, you are long in the futures market

(“+”)– Sell a futures, you are short in the futures

market(“-”)

• Assume that a buyer and seller agree on a futures price of $45. At expiration, the underlying security is priced at $53. – Buyer makes $8.00– Seller loses $8.00

• At t=0, Buyer went long on the contract at 45 • At maturity, Buyer bought from seller at 45and sold on

the spot at 53 to realize the profit of $8.• At t=0, seller went short on the contract at 45• At maturity, seller rushed to buy at 53 on the spot, and

sold at a committed 45 to buyer, to lose $8.

Speculating with futures

Hedging

• Futures contracts allow buyers and manufacturers to lock into prices and costs, respectively– If a firm wants gold, it buys contracts, promising to pay

a set price in the future (long hedge)– A gold mining company sells contracts, promising to

deliver the gold (short hedge)

• Hedge - a trading strategy in which derivative securities are used to reduce or completely offset a counterparty's risk exposure to an underlying asset.» Long hedge - created by supplementing a short

spot holding with a long futures position.» Short hedge - holding a short futures position

against the long position on the spot.

Example

A farmer expects to harvest 40,000 bushels of wheat in August. It costs him about $3.05 a bushel to plant and harvest the crop. An August futures price of $3.45 is available. How can the farmer lock the price of his crop?

Solution

Build a selling (short) hedge: sell 8 of these August futures contracts (40,000/5,000).

Time On the “spot” market On the futures market June -$3.05/bushel or

-40,000 x 3.05 = -$122,000 $3.45/bushel or 40,000 x 3.45 = $138,000

August $3.00/bushel or 40,000 x 3.00 = $120,000

-$3.00/bushel or -40,000 x 3.00 = -$120,000 (notice: spot price =futures price at maturity)

Total -2,000 +18,000 Balance +16,000

An other example

You are managing a $100,000 (face value) portfolio in T-BONDS priced at 98-10 or $98,312.5. In June, you are concern with a forthcoming increase in interest rates (within the next 6 months, around November…may be). A December T-bond futures priced at 97-00 ($97,000) is available. On November 15th interest rates increase and T-bonds drop to 96-08; the December futures contract price drops to 95-10.

Solution

You enter into a short hedge to “lock” the value of your portfolio for the next seven month.

Date Cash Market Futures Market June 1st You hold $100,000 face value T-bonds

with a current market value of -$98,312.5 --100,000 x (98+10/32)% You are long on T-Bonds

You are interested in December T-bond futures priced at 97-0--i.e., +$97,000. You make the commitment to sell those December T-bonds at this price: you are short on December T-bonds Futures

Nov. 15th Interest rates increase and the T-bond is worth 96-8. Sell your T-bonds at 96-8--i.e., +$96,250

The December T-bill futures is worth 95-10. Close (buy) your short position at 95-10--i.e., -$95,312.5

Bottom Line

You lost 96,250-98,312.5=-$2,062.5 on the Cash Market

You Gain 97,000-95,312.5=+$1,687.5 on the Futures Market

Balance -$375

Another Example

you are managing $5 million of common stock portfolio. You are concern that the market will go down in the next three months. The current 3-month S&P400 index futures is selling at 200. The price of 1 contract is $500 per index point; Assume that the portfolio value falls to $4 million two months after and that the S$P400 index futures falls simultaneously at 170.

Solutionyou are long in the “cash” market; to protect yourself,

you will go short in the futures market (short hedge) if the value of one contract is $100,000 (200 x 500), you need 50 (5,000,000/100,000) contracts to “hedge” the whole $5,000,000.

Time On the “spot” market On the futures marketToday -$5,000,000 200 x 500 x 50= $5,000,0002 month after +$4,000,000 170 x 500 x 50= -$4,250,000

(notice: spot price =futures price at maturity)Total -1,000,000 +750,000Balance -250,000

Imperfect hedge

• In practice, a contract on a similar asset may not exist---->use the closest proxy!

• For bond portfolio, a T-bond futures

• For Stock portfolio, an index futures

• For a combination, treat each asset class independently

The objective of hedging is to select a hedge ratio () such as

(change in S) – hedge ratio X (change in F) = 0

or

hedge ratio = = (change in S) / (change in F)

Imperfect hedges and bond portfolio

Imperfect hedges and bond portfolio(continued)

F

S

D

D

F

S

F for yield in change

S for yield in change

D

D

F

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S in change

F in change

S in changeh

F

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F for ifiedmod

S for ifiedmod

F for ifiedmod

S for ifiedmod

Imperfect hedges and bond portfolio(continued)

contract1ofvalue

hedgetoamounthn

F

S

D

D=hRatioHedge

modF

modS

Example

suppose an investment banker underwrites the issue of a bond that will be sold in 3 months. He has set the indenture and expect to sell the animal at par! The total issue amounts to 10,000,000 (or 10,000 bonds). Yet, he is concerned about a rise in interest rates.

Yield Coupon m maturity Duration PriceBOND 8.25% 8.25% 2 15 8.516292224 100

T_BOND (FUT) 7.70% 8% 2 20 10.04494771 103.0625

Solution

He short-hedges the new issue in the T-BOND futures market. He knows that the bond is far from being a T-BOND, but futures on this bond are not traded. Knowing that a T-Bond futures contract covers 100,000, he finds that the right amount of contracts to be sold to hedge the new issue should be 82 contracts

Solution (continued)

68.9)

2%7.7

1(

05.10D

18.8)

2%25.8

1(

52.8D

Fmod

Smod

contracts82000,100

000,000,10819.0n

819.006.103

100

9.68

8.18=Ratio Hedge

Example

• You manage a fund; you plan to sell $100,000,000 of a type of bonds in 2 months from now to reallocate the assets of the portfolio.

Yield Coupon m maturity Duration PriceBOND 7.48% 7.25% 2 26 11.45268584 97.375

T_BOND (FUT) 7.89% 8% 2 20 9.952213432 101.125

Solution:• You build a short hedge by selling 1,111 T-

Bond futures:

57.9)

2%89.7

1(

95.9D

04.11)

2%48.7

1(

45.11D

Fmod

Smod

contracts1111000,100

000,000,100111.1n

111.1125.101

375.97

9.57

11.04=ratio Hedge

Dealing With Coupon Differences• To standardize the $100,000 face value T-bond

contract traded on the Chicago Board of Trade, a conversion factor is used to convert all deliverable bonds to bonds yielding 6%

N whole theof excessin months ofnumber theX

maturity toyears wholeofnumber N

form decimalin coupon annualC

factor conversion CF

where

6

X6

2)03.1(

1

)03.1(

11

06.02(1.03)

1 CF

2N2N6

x

CCC

Hedging With Interest Rate Futures

• The hedge ratio is:

• The number of contracts necessary is given by:

)YTM1(DP

)YTM1(DPCFh

bff

ctdbbctd

ratio hedge000,100$

par value portfolio contracts #

Futures Hedging Example

A bank portfolio holds $10 million face value in government bonds with a market value of $9.7 million, and an average YTM of 7.8%. The weighted average duration of the portfolio is 9.0 years. The cheapest to deliver bond has a duration of 11.14 years, a YTM of 7.1%, and a CBOT correction factor of 1.1529.

An available futures contract has a market price of 90 22/32 of par, or 0.906875. What is the hedge ratio? How many futures contracts are needed to hedge?

9898.0078.114.11906875.0

071.10.997.01529.1

HR

98.989898.0000,100$

0$10,000,00 contracts #

On the equity side: Index futures• The fastest growing segment of the futures market is in

financial futures• Stock index futures are similar in every respect to a

traditional agricultural contract except for the matter of delivery

• Index futures settle in cash rather than by delivery of the underlying asset

• There is no actual delivery mechanism at expiration of an S&P 500 futures contract– You actually deliver the dollar difference between the

original trade price and the final price of the index at contract termination

Synthetic Index Portfolios• Large institutional investors can replicate a well-

diversified portfolio of common stock by holding– A long position in the stock index futures contract and– Satisfying the margin requirement with T-bills

• The resulting portfolio is a synthetic index portfolio

• The futures approach has the following advantages over the purchase of individual stocks:– Transaction costs will be much lower on the futures

contracts– The portfolio will be much easier to follow and manage

• As time passes, the difference between the cash index and the futures price will narrow– At the end of the futures contract, the futures price will

equal the index (basic convergence)

Imperfect hedge and equity portfolio

• In a perfect hedge

N = portfolio value/contract value• In reality, there are only index futures and your portfolio is not

exactly the same as the index!

N=portfolio value/contract value x portfolio

Using Futures Contracts to Hedge PortfoliosYou are the manager of an equity portfolio. You are bullish in the long term, but anticipate a temporary market decline. How can you use futures contracts to hedge your stock portfolio?

If you are long stock, you should be short futures. You need to calculate the number of contracts necessary to counteract likely changes in the portfolio value.

Example

Suppose that in mid-December you own a portfolio worth $3,243,750; you expect the market to plunge within the next 6 months; thus, you sell June S&P 500 futures contracts which currently trade at a settlement price of 617.00. The value of a single contract is $308,500--i.e., 500 x 617-- your portfolio has a beta of 1.15 with the S&P400; then, you decide to short 12 contracts, as you are long in the equity market:

09.12

15.1500,308$/750,243,3$

contract 1 of Value

Portfolio of Value=N

Hedge Ratio exampleDetermining the Factors for A Hedge

Suppose the manager of a $75 million stock portfolio (with a beta of 0.9 and a dividend yield of 1.0%) wants to

hedge using the December S&P 500 futures.

On the previous day, the S&P 500 closed at 1,484.43, and the DEC 00 S&P 500 futures closed at 1,517.20.

The value of the futures contract is: $250 x 1,517.20 = $379,300

And the hedge ratio is 178 contracts

contracts 17896.1779.0250$20.517,1

000,000,75$

betacontract futures P&S theof ueDollar val

portfolio theof ueDollar valHR

The Market FallsUsing the Hedge in A Falling Market

Assume the S&P 500 index falls 5%, from 1,484.43 to 1,410.20 after four months.

Given beta, the portfolio should have fallen by 5.0% x 0.9 = 4.5%, which translates to $3,375,000. However, you receive dividends of 1% x .333 x $75,000,000 = $250,000.

If you sold 178 contracts short at 1,517.20, your account will benefit by (1,517.20 – 1,410.20) x $250 x 178 = $4,761,500.

The combined positions (stock, dividends, and futures contracts) result in a gain of $1,636,500.

The Market RisesUsing the Hedge in A Rising Market

Assume the S&P 500 index rises from 1,484.43 to 1,558.70 after four months.

Given beta, the portfolio should have advanced by 5.0% x 0.9 = 4.5%, which translates to $3,375,000. You still receive dividends of 1% x .333 x $75,000,000 = $250,000.

If you sold 178 contracts at 1,517.20, your account will lose (1,517.20 – 1,558.70) x $250 x 178 = $1,846,750.

The combined positions (stock, dividends, and futures contracts) result in a gain of $1,778,250.

The Market is UnchangedUsing the Hedge in An Unchanged Market

Assume the S&P 500 index remains at 1,484.43 after three months.

There is no gain on the stock portfolio. However, you still receive dividends of 1% x .333 x $75,000,000 = $250,000.

If you sold 178 contracts short at 1,517.20, your account will benefit by (1,517.20 – 1,484.50) x $250 x 178 = $1,455,150.

The combined positions (stock, dividends, and futures contracts) result in a gain of $1,705,150.

Speculation: Active bond portfolio management Increasing Duration With Futures

• Extending duration may be appropriate if active managers believe interest rates are going to fall

• Adding long futures positions to a bond portfolio will increase duration

futures,metargt,portfolio

futurescurrent,m

etargt,portfolio

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V

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CF

1 sizecontract D

V DV

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contracts ofnumber

thus,V

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V

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targetportfolio,current,metargt,portfolio

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futures

ExampleA portfolio has a market value of $10 million, an average yield to maturity of

8.5%, and duration of 4.85. A forecast of declining interest rates causes a bond manager to decide to double the portfolio’s duration. The cheapest to deliver Treasury bond sells for 98% of par, has a yield to maturity of 7.22%, duration of 9.7, and a conversion factor of 1.1223. Determine the number of

futures contracts needed to double the portfolio duration.

long contracts 5677.55

1223.1

1 000,100)

2

%22.71

7.9(

10,000,000

2

%5.81

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7.9

CF

1 sizecontract D

V DV

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contracts ofnumber

futuresm,

targetportfolio,current,metargt,portfolio

current,portfoliotargetm,

Speculation: Active management-- Adjust Portfolio Beta

futuresequityportfolio Futures%equity%

price futures sizecontract

valueportfolio equity%contracts ofnumber

thus, valueportfolio

price futures x sizecontract contracts ofnumber %futures

equityportfolio

• You have a $25 million equity portfolio consisting of $22.5M in stocks and $2.5M in T-bills. Current beta of equity portion is 0.95. You want to increase it to 1.10. An S&P400 futures contract is quoted at 476.6. Thus, You need to be long 26 contracts:

• N=[1.1-(22.5/25) X .95] X 25,000,000/(500 X 476.6)=25.7

• It is positive thus buy 26 contracts (you cannot buy 25.7 contracts).

Example

Adjusting Market Risk: ExampleDetermining the Number of Contracts Needed to Increase

Market Exposure

Suppose the manager of a $75 million stock portfolio with a beta of 0.9 would like to increase market exposure by increasing beta to 1.5. Yesterday, DEC 00 S&P 500 futures closed at 1517.20

How can the manager use futures to accomplish this goal, assuming the composition of the stock portfolio remains unchanged?

The manager should go long futures and hold them with the stock portfolio. Specifically, he should purchase 119 S&P 500 futures contracts:

119250$20.1517

)90.050.1(million 75$contracts #

Speculation: Tactical Changes using Futures

• Investment policy statements may give the portfolio manager some latitude in how to split the portfolio between equities and fixed income securities

• The portfolio manager can mix both T-bonds and S&P 500 futures into the portfolio to adjust asset allocation without disturbing existing portfolio components

Example: Initial Situation• Portfolio market value = $175 million• Invested 82% in stock (average beta = 1.10) and 18% in bonds (average

duration = 8.7; average YTM = 8.00%)• The portfolio manager wants to reduce the equity exposure to 60%

stock• Determine:

– How many contracts will remove 100% of each market and interest rate risk

– What percentage of this 100% hedge matches the proportion of the risk we wish to retain

• Some data…Stock Index Futures September settlement = 1020.0Treasury Bond Futures September settlement = 91.05• Cheapest to deliver bond:

– Price = 95%– Maturity = 18 years– Coupon = 9 %– Duration = 8.60– Conversion factor = 1.3275

Initial Situation

Existing Asset Allocation

Stock82%

Bonds18%

Desired Asset Allocation

Stock60%

Bonds40%

Bond Adjustment

Thus, the manager should buy 521 T-bond futures

long contracts 52198.520

3275.1

1 000,100)

2

%59.91

6.8(

40%0175,000,00

2

%81

7.8

000,000,175%40

000,000,175%18

2

%81

7.8

CF / sizecontract D

V DV

VD

contracts ofnumber futuresm,

targetportfolio,current,metargt,portfolio

current,portfoliotargetm,

Stock Adjustment

• For this portfolio, the hedge ratio is:

1661020 250

60%0175,000,00 1.1000,000,175%60

000,000,175%821.1

contracts of number

price futures sizecontract

value portfolio equity%contracts of number

equityportfolio

In sum…• The portfolio manager can change the

asset allocation from 82% stock, 18% bonds to 60% stock, 40% bonds by– Buying 521 T-bond futures and– Selling 166 stock index futures

Neutralizing Cash

• It is harder to “beat the market” with the downward bias in relative fund performance due to cash

• Cash can be neutralized by offsetting it with long positions in stock index futures

• Cash can be neutralized by offsetting it with long positions in interest rate futures

Example• An all-equity fund has a benchmark that follows the SP500.• Fund size=$500M• SP500 futures=1200• Beta=1• SP500 return=11.5% (long run return)• Cash return=2.5% (long run return)• Allocation: 95% Equity, 5% cash• Cash need to be on hand in case of investors redemptions.• The fund receives periodic contributions. They have a problem: cash does

return less than equity and over long period of time, large cash positions biases the performance of a portfolio.

E(Rp)=95% x 11.5%+5% x 2.5%=11.05%…versus 11.5%One can offset this 45 BP loss by being long on SP500 futuresincrease the

beta of the portfolio by neutralizing the cash portion—I.e., N=(Cash Portfolio size)/(futures size) x beta= (5% x 500M)/(1200 x 250) x1=83

By buying 83 SPX futures, the 95% equity and 5% cash portfolio will behave exactly like a 100% equity portfolio :

475M in stock+25M in cash +83 in stock futures= 500M in stocks