FIN 413 – RISK MANAGEMENT

Futures and Forward Markets

Topics to be covered

• Spot versus futures transactions• Futures trading• Cancelling a futures position• Convergence of futures and spot prices• Operation of margin• Making/taking delivery• Forward contracts

Suggested questions from Hull

6th edition: #2.1,2.8, 2.11, 2.12, 2.215th edition: #2.1,2.8, 2.11, 2.12, 2.21

Futures contract

• An agreement between two parties (a buyer and a seller) to exchange a specified quantity of an asset (the underlying asset) during a specified future period (the delivery period of the contract) at a specified place for a price (the futures price) agreed to in advance (when the contract is first entered into).

Spot versus futures transaction

Spot transaction:

Now

Futures transaction:

Now T

Agreement is reached.

Item is exchanged for $.

Agreement is reached.

Item is exchanged for $.

Futures trading

Futures contract

Buyer

Long

Seller

Short

Takes delivery. Makes delivery.

Futures trading

Organized futures exchanges:• CBOT: corn, soybeans, wheat, Treasury bonds,

Treasury notes• CME: pork bellies, live cattle, live hogs, S&P

500 stock index, foreign currencies, Eurodollars

• WCE: canola, flaxseed, oats, western barley• ME: Canadian government bonds, S&P/TSX

Canada 60 index

Hull, pages 543: URLs of the major exchanges

History

17th century futures market for rice,

Japan 1971: Breakdown of Bretton Woods

Accord

1848: CBOT

1904: WCE

1874: CME

1972: currency futures

1975: interest-rate

futures

1982: stock-index

futures

Example

• It is June.• Vancouver food processor will require

canola in September. Buys 20 metric tons in the futures market.– Instructs its broker to buy one futures

contract (for the delivery of 20 metric tons of canola) with delivery in September.

– Broker passes the instructions to the WCE.– Instructions are forwarded to a trader on the

floor of the exchange.

Example (continued)

• The trader assesses the best price (the lowest price) available. The trader indicates a willingness to buy one September contract at that price.

• If another trader indicates a willingness to sell at that price, a deal is done.

• Otherwise, the first trader must signal a willingness to buy at a higher price.

• Eventually, an agreement will be reached, for example, $387 per metric ton or $7,740 in total.

Example (continued)

• The trader who agrees to sell canola at $387 per metric ton might represent an Alberta farmer.

• Both the food processor and the farmer have entered into a legally binding agreement.

• Futures prices are determined by the forces of demand and supply.

• Futures prices fluctuate over the life of each contract.• At any time, a futures contract has zero value to a

prospective buyer or seller.• Apart from commissions and bid-ask spreads, a futures

contract requires no initial payment or premium. The futures price simply represents the price at which the parties agree today to transact in the future.

• Futures exchanges offer electronic trading services.

Mechanics of futures trading

• A trader can buy/sell futures through:– A full-service futures broker.– A discount, online futures broker.

• Full-service broker:– Charges a commission.– Executes trades.– Provides advice and other services.– May provide online trading at reduced rates.

• Discount broker:– Charges a smaller commission.– Executes trades and provides fewer other services.

Futures markets

• Futures contracts trade on organized exchanges.

• Their terms are standardized with respect to:– The underlying asset: the required quality and

quantity are specified.– Delivery location: where delivery can be made.– Delivery period: when delivery can be made.

• www.wce.ca

Futures markets

• Futures exchanges offer the short:– The quality option.– The delivery option.– The timing option.

• The price charged to the long is adjusted accordingly.

• If the short notifies the exchange of his/her intention to deliver, the short is matched with the buyer holding the oldest outstanding long position in the contract. The long is notified to take delivery.

The minimum tick

• The exchange does not want to keep track of price changes smaller than $0.10 per metric tonne (or $2 per contract).

Transaction 1

$387

Vancouver food processor

Alberta farmer

Transaction 2

$387.03

$387

Some buyer

Some seller

$387

$387.10

$386.90

Life of Mar08 canola futures contract

1st trading

day

t1

Trader takes position in contract

Delivery period

Delivery month:March 2008

Life of contract:About 2.5 years

Last trading day:March 14, 2008

F

S

F1

S1

Question & examples

Question: Do farmers use futures contracts?

Examples: #2.8, 2.21

Spot versus futures transaction

Spot transaction:

Now

Futures transaction:

Now T

Agreement is reached.

Item is exchanged for $.

Agreement is reached.

Item is exchanged for $.Item is exchanged for $.Item is exchanged for $.

Spot versus futures transaction – during the delivery period

Spot transaction:

Now

Futures transaction:

Now T

Agreement is reached.

Agreement is reached.

Item is exchanged for $.

T

Item is exchanged for $.

Convergence of F to S

• Ignore transaction costs.• If F > S during the delivery period:

– Buy the asset for S in the spot market.– Short a futures contract.– Make delivery, selling the asset for F.

• Arbitrage profit per unit of underlying asset = (F -S)• S rises and F falls.

1st trading day DP

Normal Market

F

S

1st trading day

1st trading day DP

Inverted Market

F

S

Convergence of F to S

• Ignore transaction costs.• If F < S during the delivery period:

– Go long a futures contract, agreeing to buy the asset at F.– Wait for the short to make delivery.– Sell the asset in the spot market at the spot price at that time, S*.

• Profit per unit of underlying asset = (S*-F)• F rises and S falls.

1st trading day DP

Normal Market

F

S

1st trading day

1st trading day DP

Inverted Market

F

S

Futures price

• At any given time, a number of (canola) futures contracts are trading, identified by their delivery months.

• Mar08 and Nov08 contracts are trading currently.• Assuming a normal market:

NowMar08 Nov08

S

FMar08

FNov08

Cancelling a futures position

• Futures contract: a legally binding agreement.

• A position can be easily terminated:– Making/taking delivery.– Closing out or offsetting.– Undertaking an exchange-for-physicals

(EFP) transaction.

Offsetting

Action: Short (sell) five May 2008 cocoa futures

Obligation: Deliver 50 metric tons of cocoa to the buyer in May 2008

Offsetting action: Go long (buy) five May 2008 cocoa futures

Obligation: Zero

Action: Go long (buy) two December 2009 US T-note futures

Obligation: Buy $200,000 worth of US T-notes in December 2009

Offsetting action: Short (sell) two December 2009 US T-note futures

Obligation: Zero

EFP transaction

Trader A Trader B

Buys 1 wheat futures contract on CBOT

Sells 1 wheat futures contract on CBOT

Wants to acquire actual wheat Owns wheat and wishes to sell

Before EFP:

EFP transaction:

Exchange cancels B’s short futures position

Exchange cancels A’s long futures position

Reports EFP to the exchangeReports EFP to the exchange

Delivers wheat and receives payment from A

Receives wheat and pays B

Agrees with A to sell wheat and cancel futures

Agrees with B to purchase wheat and cancel futures

Trader BTrader A

Cancelling a futures position

• Very few traders (less than 2%) ever take or make delivery on a futures contract:– Inconvenient, expensive.– Not required to realize the benefits of

hedging.– Speculators and arbitrageurs only want to

trade the contract.

Light sweet crude oil futures

• www.nymex.com

Futures trading

Clearinghouse

CH memberCH member

BrokerBroker Broker Broker

Trader

Trader

Trader

Trader

Trader

Trader

Trader

Trader

Operation of margins

• Margin accounts:– Clearinghouse member (with the clearinghouse)– Broker (with a CH member)– Trader (with a broker)

• Margin: good faith or security deposit.• Initial margin: the initial amount put in a margin

account by a trader to establish a futures position.

• Maintenance margin: the minimum amount that a trader must keep in a margin account to maintain a futures position.

Operation of margins

• Margin accounts are marked to market daily: they are adjusted daily for net gains/losses realized on a futures position.

• Trader: at the end of each day, his/her margin account is increased by the amount of the daily gain or reduced by the amount of the daily loss.

• Broker: his/her margin account is adjusted for daily net gains/losses over the accounts of all of his/her clients.

• Clearinghouse member: his/her margin account is adjusted daily for net gains/losses over the accounts of all of his/her clients.

• Purpose of margining system: To reduce credit risk, that is, to reduce the probability of market participants sustaining losses because of defaults.

Operation of margins

• Daily marking to market is equivalent to:– Closing a futures contract at the end of each

day.– Opening a new contract at the beginning of

the next business day with zero value to the trader.

Example

A trader buys two November frozen orange juice futures contracts through her broker.

Each contract is for the delivery of 15,000 pounds of orange juice.

F1, the current futures price, is 160 cents per pound.

Initial margin: $6,000 per contractMaintenance margin: $4,500 per contractThe contract is entered into on September 8 at 160

cents/pound (F1) and closed out on September 14 at 161 cents/pound (F2).

Example (continued)

Futures price

Daily gain (loss)

Cumulative gain (loss)

Margin account balance

Margin call

($) ($) ($) ($) ($)

Sept. 8 1.60 12,000

Sept. 9

Sept. 10

Sept. 11

Sept. 12

Sept. 13

Sept. 14

1.85 7,500

Gain/loss on futures

The long:

F1

The long gains $-for-$ as F rises.

The long loses $-for-$ as F falls.

The short:

F1

The short loses $-for-$ as F rises.

The short gains $-for-$ as F falls.A futures contract is a zero-sum game.

Gain/loss on futures

Example:Price at beginning of day = F1 = $1.50Price at end of day = F2 = $1.60Long’s gain (per unit of UA) on the day = (F2 – F1) = $0.10Short’s gain (per unit of UA) on the day = (F1 – F2) = -$0.10Long’s gain + short’s gain = 0

Example: Price at beginning of day = F1 = $1.50Price at end of day = F2 = $1.30Long’s gain (per unit of UA) on the day = (F2 – F1) = -$0.20Short’s gain (per unit of UA) on the day = (F1 – F2) = $0.20Long’s gain + short’s gain = 0

Example (continued)

Futures price

Daily gain (loss)

Cumulative gain (loss)

Margin account balance

Margin call

($) ($) ($) ($) ($)

Sept. 8 1.60 12,000

Sept. 9

Sept. 10

Sept. 11

Sept. 12

Sept. 13

Sept. 14

Cumulative gain on September 14 = (F2-F1)×30,000 = ($1.61-$1.60)×30,000 = $300.

1.85 7,500 7,500 19,500

1.70 (4,500) 3,000 15,000

1.35 (10,500) (7,500) 4,500 7,500

1.56 6,300 (1,200) 18,300

1.56 0 (1,200) 18,300

1.61 1,500 300 19,800

Newspaper quotes

The National Post web site, May 25, 2007:www.canada.com/national/nationalpost/financialpost/fpmarketdata

High Low Month

Open High Low Settle

Chg Prev OpInt

404.60

298.10

Nov07 395.30

404.60

395.30

401.40

+6.20 65,613

416.60

349.00

Mar08 411.20

416.60

411.20

413.90

+3.90 1,404

410.00

350.00

Nov08 407.30

410.00

407.30

411.50

+1.60 2,522

CANOLA (WPG)20 metric tons, C$ per metric ton; 10 cents = $2 per contract

Prev. vol. 9,635 Prev. open int. 120,758

Question: Is the market normal, inverted, or mixed?

Making/taking delivery

F1: futures price at the time a position is taken. The trader agrees to buy/sell at this price.

Hull, page 33: “For all contracts the price (received by the short and paid by the long) is usually based on the settlement price immediately preceding the date of the notice of intention to deliver.”

Contradiction?

Making/taking delivery

T: the business day immediately preceding the date of the notice of intention to deliver

FT: the settlement price at time T

Effective price received by the short:FT + gain on futures= FT + (F1 – F2) + (F2 – F3) + (F3 – F4) … + (FT-1 – FT)= F1

Effective price paid by the long:FT + loss on futures= FT + (F1 – F2) + (F2 – F3) + (F3 – F4) … + (FT-1 – FT)= F1

Note: F1 is paid/received via a sequence of daily instalments over the period the position is held, because of marking to market.

Example

• The benefits of hedging can be realized by closing out a futures position just prior to the delivery period.

Example

Notation:F1: futures price at time position is taken

F2: futures price at time position is closed

S1: Spot price at time futures position is taken

S2: Spot price at time futures position is closed

Example (continued)It is June 15.A hog farmer expects to have 90,000 pounds of hogs to sell

at the end of August. To hedge, he shorts three September hog futures contracts, each for the delivery of 30,000 pounds of live hogs.

F1 = $0.75225 per poundThe farmer plans to close out his short futures position on

August 26 and to sell his hogs in the spot market at that time.

Note: This strategy will yield the farmer a price for his hogs that is close to $0.75225 per pound.

Consider two cases:• S2 = $0.73000 < $0.75225• S2 = $0.80000 > $0.75225

Case 1: S2 < F1

Spot price

Gain on futures

2 1 2

1 2 2

1

( )

( )

S F F

F S F

F

September

F1

F2S1

S2

August 26

June 15

Effective price received by the

farmer

Case 2: S2 > F1

2 2 1

1 2 2

1

( )

( )

S F F

F S F

F

September

August 26

June 15

F1

F2

S1

S2

Spot price

Loss on futures

Effective price received by the farmer

Newspaper quotes

The National Post web site, May 25, 2007:www.canada.com/national/nationalpost/financialpost/fpmarketdata

High Low Month Open High Low Settle Chg Prev OpInt

404.60 298.10 Nov07 395.30 404.60 395.30 401.40 +6.20 65,613

416.60 349.00 Mar08 411.20 416.60 411.20 413.90 +3.90 1,404

410.00 350.00 Nov08 407.30 410.00 407.30 411.50 +1.60 2,522

CANOLA (WPG)20 metric tons, C$ per metric ton; 10 cents = $2 per contract

Prev. vol. 9,635 Prev. open int. 120,758

Hull: #2.22, page 43

“When a futures contract trades on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one.”

(a) Suppose OI = 65,613A trade takes place:A goes long entering into a new contract.B goes short entering into a new contract.OI = ?ΔOI = ?

Hull: #2.22, page 43

(b) Suppose OI = 65,613A trade takes place:A goes long closing out a previous short position.B goes short closing out a previous long position.OI = ?ΔOI = ?

Hull: #2.22, page 43

(c) Suppose OI = 65,613A trade takes place:A goes long entering into new contract.B goes short entering into a new contract.OI = ?ΔOI = ?Another trade occurs.C goes long entering into a new contract.A goes short closing out the previous long position.OI = ?ΔOI?

Open interest

• Open interest = 3

$290

B1

S1

$295

B2

S2

$300

B3

S3

Open interest

• A trade takes place:B4 goes long entering into a new positionB3 goes short closing out her previous long position

$290

B1

S1

$295

B2

S2

$300

B3

S3

$298

B4

B3

Open interest

• Open interest = 3• B4 is agreeing to buy at $298. S3 is agreeing to

sell at $300. But if they take/make delivery, they will exchange the underlying asset at FT.

• The effective counterparty is the clearinghouse.

$290

B1

S1

$295

B2

S2

$300

B3

S3

$298

B4

B3

Forward contract

• An agreement between two parties (a buyer and a seller) to exchange a specified quantity of an asset (the underlying asset) at a specified future time (the delivery date of the contract) for a price (the delivery price) agreed to in advance (when the contract is first entered into).

Forwards versus futures

Futures contract Forward contract

Trades on organized futures exchange

Trades OTC

Has delivery period Has a precise delivery date

Usually closed out early Usually delivered on

Settled (marked to market) daily

Settled at maturity

Margin required Usually no margin required

Regulated Not closely regulated

Little credit risk Credit risk

Delivery price and forward price

• Delivery price: – The price specified in a forward contract. – Negotiated at inception; makes the contract

have zero value to both parties.– Doesn’t change over the life of the contract.

• Forward price:– The price that, at any point in time during

the life of a contract, makes the contract have zero value to both parties.

– Changes over the life of the contract.

Forward contract

Notation:K : the delivery priceF : the forward priceS : the spot price of the underlying assetf : the value of the contract to the long-f : the value of the contract to the short

Note: A forward contract is a zero-sum game:f + (-f ) = 0

Life of a forward contract

Without any loss of generality, assume an inverted market.

0:Inception of

contract

T: delivery date

S0

F0

FT = ST

K

f

-f

Life of forward contract

Payoff & profit at maturity

Payoff = Profit – price paid

Forward contract: price paid = 0

Thus: Payoff = Profit

The following terms are used interchangeably: payoffprofitvaluegain

Payoff to the long at maturity

Payoff at time T= FT – K

= ST – K (FT = ST)

= fT

STK

-K

0

Payoff to the short at maturity

Payoff at time T= K – FT

= K – ST (FT = ST)

= -fT

STK

K

0

Zero-sum game

Payoff to the long + payoff to the short = 0

fT + (-fT) = 0

STK

-K

0

K

Next class

• Determination of forward and futures prices