FIN 413 – RISK MANAGEMENT
Futures and
Forward Markets
Topics to be covered
•
•
•
•
•
•
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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, 2.21
5th 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:
Item is exchanged for $.
Now
Agreement is reached.
Futures transaction:
Item is exchanged for $.
Now
T
Agreement is reached.
Futures trading
Buyer
Long
Takes delivery.
Futures
contract
Seller
Short
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
1848:
CBOT
17th century futures
market for rice,
Japan
1904:
WCE
1972:
currency
futures
1982:
stock-index
futures
1874:
CME
1971:
Breakdown of
Bretton Woods
Accord
1975:
interest-rate
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
Alberta farmer
Transaction 1
$387
Vancouver food
processor
Some seller
$387

$387.10 
$386.90 

Transaction 2
$387.03
$387
Some buyer
• The exchange does not want to keep track of price
changes smaller than $0.10 per metric tonne (or $2
per contract).
Life of Mar08 canola futures contract
F
F1
S
Last trading day:
March 14, 2008
S1
1st
trading
day
t1
Delivery period
Trader takes
position in
contract
Delivery month:
March 2008
Life of contract:
About 2.5 years
Question & examples
Question: Do farmers use futures contracts?
Examples: #2.8, 2.21
Spot versus futures transaction
Spot transaction:
Item is exchanged for $.
Now
Agreement is reached.
Futures transaction:
Item is exchanged for $.
Now
T
Agreement is reached.
Spot versus futures transaction –
during the delivery period
Spot transaction:
Item is exchanged for $.
Now
T
Agreement is reached.
Futures transaction:
Item is exchanged for $.
Now
T
Agreement is reached.
Convergence of F to S
Inverted Market
Normal Market
F
S
S
F
1st trading
day
DP
1st trading
day
•
•
Ignore transaction costs.
If F > S during the delivery period:
•
•
Arbitrage profit per unit of underlying asset = (F -S)
S rises and F falls.
– Buy the asset for S in the spot market.
– Short a futures contract.
– Make delivery, selling the asset for F.
DP
Convergence of F to S
Inverted Market
Normal Market
F
S
S
F
1st trading
day
DP
1st trading
day
•
•
Ignore transaction costs.
If F < S during the delivery period:
•
•
Profit per unit of underlying asset = (S*-F)
F rises and S falls.
DP
– 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*.
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:
FNov08
FMar08
S
Now
Mar08
Nov08
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
Before EFP:
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
EFP transaction:
Trader A
Trader B
Agrees with B to purchase wheat and Agrees with A to sell wheat and
cancel futures
cancel futures
Receives wheat and pays B
Delivers wheat and receives payment
from A
Reports EFP to the exchange
Reports EFP to the exchange
Exchange cancels A’s long futures
position
Exchange cancels B’s short futures
position
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 member
CH member
Broker
Broker
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 contract
Maintenance margin: $4,500 per contract
The contract is entered into on September 8 at 160
cents/pound (F1) and closed out on September 14 at
161 cents/pound (F2).
Example (continued)
Futures
price
Daily gain
(loss)
Cumulative
gain (loss)
Margin
account
balance
Margin call
($)
($)
($)
($)
($)
Sept. 8
1.60
Sept. 9
1.85
Sept. 10
Sept. 11
Sept. 12
Sept. 13
Sept. 14
12,000
7,500
Gain/loss on futures
The long:
The long gains $-for-$ as F rises.
F1
The long loses $-for-$ as F falls.
The short:
The short loses $-for-$ as F rises.
F1
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 = $1.50
Price at end of day = F2 = $1.60
Long’s gain (per unit of UA) on the day = (F2 – F1) = $0.10
Short’s gain (per unit of UA) on the day = (F1 – F2) = -$0.10
Long’s gain + short’s gain = 0
Example:
Price at beginning of day = F1 = $1.50
Price at end of day = F2 = $1.30
Long’s gain (per unit of UA) on the day = (F2 – F1) = -$0.20
Short’s gain (per unit of UA) on the day = (F1 – F2) = $0.20
Long’s gain + short’s gain = 0
Example (continued)
Futures
price
Daily gain
(loss)
Cumulative
gain (loss)
Margin
account
balance
Margin call
($)
($)
($)
($)
($)
Sept. 8
1.60
Sept. 9
1.85
12,000
7,500
7,500
19,500
Sept. 10
1.70
(4,500)
3,000
15,000
Sept. 11
1.35
(10,500)
(7,500)
4,500
Sept. 12
1.56
6,300
(1,200)
18,300
Sept. 13
1.56
0
(1,200)
18,300
Sept. 14
1.61
1,500
300
19,800
Cumulative gain on September 14 = (F2-F1)×30,000
= ($1.61-$1.60)×30,000 = $300.
7,500
Newspaper quotes
The National Post web site, May 25, 2007:
www.canada.com/national/nationalpost/financialpost/fpmarketdata
CANOLA (WPG)
20 metric tons, C$ per metric ton; 10 cents = $2 per contract
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
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 pound
The 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 > $0.75225
Case 1: S2 < F1
F1
Gain on futures
F2
S1
S2
Spot price
June 15
August 26
Effective price received by the farmer
September
 S2  ( F1  F2 )
 F1  ( S2  F2 )
 F1
Case 2: S2 > F1
F2
Loss on futures
S2
F1
Spot price
S1
June 15
August 26
September
Effective price received by the farmer  S2  ( F2  F1 )
 F1  ( S2  F2 )
 F1
Newspaper quotes
The National Post web site, May 25, 2007:
www.canada.com/national/nationalpost/financialpost/fpmarketdata
CANOLA (WPG)
20 metric tons, C$ per metric ton; 10 cents = $2 per contract
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
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 = 65,613
A 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 = 65,613
A 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 = 65,613
A 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
B1
B2
B3
$290
$295
$300
S1
S2
S3
• Open interest = 3
Open interest
B1
B2
B3
B4
$290
$295
$300
$298
S1
S2
S3
B3
• A trade takes place:
B4 goes long entering into a new position
B3 goes short closing out her previous long position
Open interest
B1
B2
B3
B4
$290
$295
$300
$298
S1
S2
S3
B3
• 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.
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 Trades OTC
exchange
Has delivery period
Has a precise delivery date
Usually closed out early
Usually delivered on
Settled (marked to market) Settled at maturity
daily
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 price
F : the forward price
S : the spot price of the underlying asset
f : 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.
FT = ST
S0
K
F0
f
T: delivery date
0:
Inception of
contract
-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:
payoff
profit
value
gain
Payoff to the long at maturity
Payoff at time T
= FT – K
= ST – K
(FT = ST)
= fT
0
K
-K
ST
Payoff to the short at maturity
Payoff at time T
= K – FT
= K – ST
(FT = ST)
= -fT
K
0
K
ST
Zero-sum game
Payoff to the long +
payoff to the short = 0
fT + (-fT) = 0
K
0
K
-K
ST
Next class
• Determination of forward and futures prices