Interest Rate Futures

Chapter 12
Interest Rate Futures:
Fundamentals

Definition
• Futures are marketable forward contracts.
• Forward contracts are agreements to buy or
sell a specified asset (commodity, index,
debt security, currency, etc.) at an agreed-
upon price (f) for purchase or delivery on a
specified date (delivery date: T).

Futures Exchanges
• Futures are traded on organized exchanges;,such
as the:
– Chicago Board of Trade, CBOT
– Chicago Mercantile Exchange, CME
• The exchanges provide marketability:
– Listings
– Standardization
– Locals
– Clearinghouse

Futures Exchanges
U.S. Exchanges
American Stock Exchange (AMEX)
Chicago Board of Trade (CBOT)
Chicago Board of Options Exchange (CBOE)
Chicago Mercantile Exchange (CME)
Coffee, Sugar, and Coca Exchange (NY)
Commodity Exchange (COMEX) (NY)
Kansas City Board of Trade (KCBT)
Mid-American Commodity Exchange (MidAm)
Minneapolis Grain Exchange (MGE)
New York Cotton Exchange (NYCE)
New York Futures Exchange (NYFE)
New York Mercantile Exchange (NYMEX)
Pacific Exchange (PXS)
Philadelphia Exchange (PHLX)
www.amex.com
www.cbot.com
www.cboe.com
www.cme.com
www.csce.com
www.nymex.com
www.kcbt.com
www.midam.com
www.mgex.com
www.nyce.com
www.nyfe.com
www.nymex.com
www.pacificex.com
www.phlx.com

Futures Exchanges
Non-U.S. Markets
Amsterdam Exchange (AEX)
Australian Stock Exchange (ASX)
Brussels Exchange (BXS)
Bolsa de Mercadorias y Futuros, Brazil (BM&F)
Copenhagen Stock Exchange (FUTOP)
Deutsche Termin Borse, Germany (DTB)
Eurex (EUREX)
International Petroleum Exchange, London (IPE)
Hong Kong Futures Exchange (HKFE)
Kuala Lumpur Options and Financial Futures Exchange (KLOFFE)
London International Financial Futures and Options Exchange
(LIFFE)
Marche a Terme International de France (MATIF)
Marche des Options Negociables de Paris (MONEP)
MEFF Renta Fija And Variable, Spain (MEFF)
New Zealand Futures and Options Exchange (NZFOE)
Osaka Securities Exchange (OSA)
Singapore International Monetary Exchange (SIMEX)
Stockholm Options Exchange (SOM)
Sydney Futures Exchange (SFE)
Tokyo International Financial Futures Exchange (TIFFE)
Toronto Stock Exchange (TSE)
Winnipeg Commodity Exchange (WCE)
www.aex.nl
www.asx.com
www.bxs.be
www.bmf.com.br
www.xcse.dk
www.exchange.de
www.eurexchange.com
www.ipe.uk.com
www.hkfe.com
www.kloffe.com.my
www.liffe.com
www.matif.com
www.monep.fr
www.meff.es
www.nzfoe.com
www.ose.or.jp
www.simex.com.sg
www.omgroup.com
www.sfe.com.au
www.tiffe.com
www.tse.com
www.wce.mba.ca

Futures Exchanges
Alliances
Eurex is an alliance of DTB, CBOT, and exchanges in
Switzerland and Finland
GLOBEX is an alliance of CME, ME, MATIF, SIMEX
and exchanges in Brazil and the Paris Bourse.
Euronext is an alliance of exchanges in Amsterdam,
Brussels, and Paris
www.eurexchange.com
www.globexalliance.com

Futures Exchanges
• Futures exchanges are typically structured as membership
organization with a fixed number of seats and with the seat
being a precondition for direct trading on the exchange.
• On most futures exchanges, there are two major types of
futures traders/members: commission brokers and locals.
– Commission brokers buy and sell for their customers.
They carry out most of the trading on the exchanges,
serving the important role of linking futures traders.
– Locals, on the other hand, trade from their own
accounts, acting as speculators or arbitrageurs. They
serve to make the market operate more efficiently.

Futures Exchanges
• Standardization
– The futures exchanges provide standardization
by specifying the grade or type of each asset
and the size of the underlying asset.
– Exchanges also specify how contract prices are
quoted. For example:
• The contract prices on T-bill futures are quoted in
terms of an index equal to one hundred minus a
discount yield.
• A T-bond is quoted in terms of dollars and 1/32s of a
T-bond with a face value of $100.

Futures Exchanges
• Continuous Trading
– Many security exchanges use market-makers or
specialists to ensure a continuous market.
– On many futures exchanges, continuous trading also is
provided, but not with market-makers or specialists
assigned by the exchange to deal in a specific contract.
– Instead, futures exchanges such as the CBOT, CME, and
LIFFE provide continuous trading through locals who are
willing to take temporary positions in one or more
futures.

Futures Exchanges
• Delivery Procedures
– Only a small number of contracts that are entered into
lead to actual delivery.
– Most futures contracts are closed prior to expiration.
– Nevertheless, detailed delivery procedures are
important to ensure that the contract price on a futures
contract are determined by the spot price on the
underlying asset and that the futures price converges to
the spot price at expiration.

Futures Exchanges
• Alliances and 24-Hour Trading
– In addition to providing off-hour trading via electronic
trading systems, 24-hour trading is also possible by using
futures exchanges that offer trading on the same contract.
– The CME, LIFFE, and SIMEX all offer identical contracts
on 90-day Eurodollar deposits.
– This makes it possible to trade the contract in the U.S.,
Europe, and the Far East.
– Moreover, these exchanges have alliance agreements
making it possible for traders to open a position in one
market and close it in another. A similar alliance exists
between SFE, CBOT, and LIFFE on U.S. T-bond contracts.

Futures Exchanges
• The exhibit on the next slide lists various interest
rate futures contracts traded on the CBOT, CME,
LIFFE, and other exchanges.
• Of these contracts, the four most popular are
– T-bonds
– T-notes
– Eurodollar deposits
– T-bills

Contract Exchange Contract Size
Treasury Bond
5-Year Treasury Note
Treasury Note
3-Month Treasury Bill
3-Month Eurodollar
1-Month LIBOR
Municipal Bond Index
3-Month Euroyen
10-year Japanese Government
Bond Index
Long Gilt
3-Month Sterling Interest Rate
CBOT
CBOT
CBOT
CME
CME
CME
CBOT
SIMEX
TSE
LIFFE
LIFFE
T-bond with $100,000 face value (or multiple of that)
T-note with $100,000 face value (or multiple of that)
T-note with $100,000 face value (or multiple of that)
$1,000,000
$1,000,000
$3,000,000
$1,000 times the closing value of the Bond BuyerTM
Municipal Bond Index (a price of 95 means a contract size
of $95,000)
100,000,000 yen
100,000,000 yen face value
50,000 British pound
500,000 British pound
Futures Exchanges

T-Bill Futures
• T-bill futures contracts call for the delivery (short
position) or purchase (long position) of a T-bill with
a maturity of 91days and a face value (F) of $1
million. Futures prices on T-bill contracts are quoted
in terms of an index.
• This index, I, is equal to 100 minus the annual
percentage discount rate, RD, for a 90-day T-bill:
(%)
R
100
I D



T-Bill Futures
• Given a quoted index value or discount yield,
the actual contract price on the T-bill futures
contract is:
000
,
000
,
1
$
100
)
360
/
90
%(
R
100
f D
0



T-Bill Futures
• Example: A T-bill futures contract quoted at a
settlement index value of 95.62 (RD = 4.38%) would
have a futures contract price (f0) of $989,050 and an
implied YTMf of 4.515%:
050
,
989
$
000
,
000
,
1
$
100
)
360
/
90
(
38
.
4
100
f0 


04515
.
1
050
,
989
$
000
,
000
,
1
$
YTM
1
f
F
YTM
91
/
365
f
91
/
365
0
f


















T-Bill Futures
• Expiration months on T-bill futures are March, June,
September, and December, and extend out about two
years.
• The last trading day occurs during the third week of
the expiration month, on the business day preceding
the issue of spot T-bills.
• Under the terms of the contract, delivery may occur
on one of three successive business days with the
delivered T-bill having a maturity of 89, 90, and 91
days.

Eurodollar Futures Contract
• A Eurodollar deposit is a time deposit in a bank
located or incorporated outside the United States.
• A Eurodollar interest rate is the rate that one large
international bank is willing to lend to another large
international bank.
• The average rate paid by a sample of London
Euro-banks is known as the London Interbank Offer
Rate (LIBOR).
• The LIBOR is higher than the T-bill rate, and is used
as a benchmark rate on bank loans and deposits.

• The CME's futures contract on the Eurodollar
deposit calls for the delivery or purchase of a
Eurodollar deposit with a face value of $1 million
and a maturity of 90 days.
• The expiration months on Eurodollar futures
contracts are March, June, September, and
December and extend up to ten years.

• Like T-bill futures contracts, Eurodollar
futures are quoted in terms of an index equal
to 100 minus the annual discount rate, with
the actual contract price found by using the
following equation:
000
,
000
,
1
$
100
)
360
/
90
%(
R
100
f D
0



• Example, given a settlement index value of
95.09 on a Eurodollar contract, the actual
futures price would be $987,725:
725
,
987
$
000
,
000
,
1
$
100
)
360
/
90
(
91
.
4
100
f0 



• The major difference between the Eurodollar and T-bill
contracts is that Eurodollar contracts have cash settlements
at delivery, while T-bill contracts call for the actual delivery
of the instrument.
• When a Eurodollar futures contract expires, the cash
settlement is determined by the futures price and the
settlement price.

• The settlement price or expiration futures index
price is 100 minus the average three-month LIBOR
offered by a sample of designated Euro-banks on the
expiration date:
Expiration Futures Price = 100 - LIBOR

T-Bond Futures Contracts
• The most heavily traded long-term interest rate
futures contract is the CBOT’s T-bond contract.
• The contract calls for the delivery or purchase of a
T-bond with a maturity of at least 15 year.
• The CBOT has a conversion factor to determine the
actual price received by the seller.
• The futures contract is based on the delivery of a T-
bond with a face value of $100,000.

• The delivery months on the contracts are March, June,
September, and December, going out approximately two
years.
• Delivery can occur at any time during the delivery month.
• To ensure liquidity, any T-bond with a maturity of 15 years is
eligible for delivery, with a conversion factor used to
determine the actual price of the deliverable bond.
• Since T-bonds futures contracts allow for the delivery of a
number of T-bonds at any time during the delivery month, the
CBOT's delivery procedure on such contracts is more
complicated than the procedures on other futures contracts.

• T-bond futures prices are quoted in dollars and
32nds for T-bonds with a face value of $100.
• Thus, if the quoted price on a T-bond futures were
of 106-14 (i.e., 106 14/32 or 106.437), the price
would be $106,437 for a face value of $100,000.

• The actual price paid on the T-bond or revenue
received by the seller in delivering the bond on the
contract is equal to the quoted futures price times the
conversion factor, CFA, on the delivered bond plus
any accrued interest:
Seller’s Revenue = (Quoted Futures Price)(CFA) + Accrued Interest

• Example: At the time of delivery, if the
delivered bond has a CFA of 1.3 and accrued
interest of $2 and the quoted futures price is
94-16, then the cash received by the seller of
the bond and paid by the futures purchaser
would be $124.85 per $100 face value:
Seller’s Revenue = (94.5)(1.3) + 2 = 124.85

T-Note Futures Contracts
• T-note contracts are similar to T-bond contracts,
except that they call for the delivery of any T-note
with maturities between 6 1/2 and 10 years;
• The five-year T-note contracts are also similar to T-
bond and T-note contracts except that they require
delivery of the most recently auctioned five-year T-
note.
• Both contracts, though, have delivery procedures
similar to T-bond contracts.

Forward Contracts and Forward
Rate Agreements (FRA)
• Forward contracts for interest rate products are
private, customized contracts between two financial
institutions or between a financial institution and one
of its clients.
• Interest rate forward contracts predate the
establishment of the interest rate futures market.
• A good example of an interest rate forward product
is a forward rate agreement, FRA.

• A FRA requires a cash payment or provides a cash
receipt based on the difference between a realized
spot rate such as the LIBOR and a pre-specified
rate.
• For example, the contract could be based on a
specified rate of Rk = 6% (annual) and the three-
month LIBOR (annual) in five months and a
notional principal, NP (principal used only for
calculation purposes) of $10M.

• In five months the payoff would be
– If the LIBOR at the end of five months exceeds the specified
rate of 6%, the buyer of the FRA (or long position holder)
receives the payoff from the seller.
– If the LIBOR is less than 6%, the seller (or short position
holder) receives the payoff from the buyer.
 
)
365
/
91
(
LIBOR
1
)
365
/
91
(
06
.
LIBOR
)
M
10
($
Payoff




• If the LIBOR were at 6.5%, the buyer would be
entitled to a payoff of $12,267 from the seller;
• If the LIBOR were at 5.5%, the buyer would be
required to pay the seller $12,297.

• In general, a FRA that matures in T months and is
written on a M-month LIBOR rate is referred to as a
T x (T+M) agreement.
• Thus, in this example the FRA is a 5 x 8 agreement.
• At the maturity of the contract (T), the value of the
contract, VT is
 
)
365
/
M
(
LIBOR
1
)
365
/
M
(
R
LIBOR
NP
V k
T




• FRAs originated in 1981 amongst large London
Eurodollar banks that used these forward agreements
to hedge their interest rate exposure.
• Today, FRAs are offered by banks and financial
institutions in major financial centers and are often
written for the bank’s corporate customers.
• They are customized contracts designed to meet the
needs of the corporation or financial institution.

• Most FRAs do follow the guidelines established by
the British Banker’s Association.
• Settlement dates do tend to be less than one year (e.g.,
3, 6, or 9 months), although settlement dates going
out as far as four years are available.
• The NP on a FRA can be as high as a billion and can
be drawn in dollars, British pounds and other
currencies.

• FRAs are used by corporations and financial
institutions to manage interest rate risk in the same
way as financial futures are used.
• Different from financial futures, FRAs are contracts
between two parties and therefore are subject to the
credit risk of either party defaulting.
• The customized FRAs are also less liquid than
standardized futures contracts.

Futures Positions
• A futures holder can take one of two positions on a
futures contract: a long position (or futures
purchase) or a short position (futures sale).
– In a long futures position, the holder agrees to buy the
contract's underlying asset at a specified price, with the
payment and delivery to occur on the expiration date (also
referred to as the delivery date).
– In a short futures position, the holder agrees to sell an
asset at a specific price, with delivery and payment
occurring at expiration.

Clearinghouse
• To provide contracts with marketability, futures
exchanges use clearinghouses.
• The exchange clearinghouse is an adjunct of the
exchange.
• It consists of clearinghouse members (many of
whom are brokerage firms) who guarantee the
performance of each party of the transaction and act
as intermediaries by breaking up each contract after
the trade has taken place.

Clearinghouse: Example
• Suppose in early June Speculator A buys a
September T-bill Futures contract from Speculator B
for f0 = $987,500 (IMM = 95, RD = 5)
– A is long
– B is Short

Clearinghouse
• The clearinghouse (CH) would come in after
Speculators A and B have reached an agreement on
the price of the September T-bill contract, becoming
the effective seller on A's long position and the
effective buyer on B's short position.
• Once the clearinghouse has broken up the contract,
then A's and B's contracts would be with the
clearinghouse. The clearinghouse, in turn, would
record the following entries in its computers.

Clearinghouse
Clearinghouse Record:
1.
2.
Speculator A agrees to buy September T-bill at $987,500
from the clearinghouse.
Speculator B agrees to sell September T-bill at $987,500 to
the clearinghouse.

Clearinghouse
• The intermediary role of the clearinghouse
makes it easier for futures traders to close
their positions before expiration.
• To see this, suppose that in June, short-term
interest rates drop, leading speculators such as
C to want to take a long position in the
September T-bill contract.

Clearinghouse
• Seeing a profit potential from the increased demand for long
positions in the September contract, suppose Speculator A
agrees to sell a September T-bill futures contract to
Speculator C for $988,750 (RD = 4.5% and Index = 95.5).
• Upon doing this, Speculator A now would be short in the new
September contract, with Speculator C having a long
position, and there now would be two contracts on September
T-bills.
• After the new contract between A and C has been established,
the clearinghouse would step in and break it up.
• For Speculator A, the clearinghouse's records would now
show the following.

Clearinghouse
Clearinghouse Records for Speculator A:
1.
2.
Speculator A agrees to BUY September T-bill from the
clearinghouse for $987,500.
Speculator A agrees to SELL September T-bill to the
clearinghouse for $988,750.
The clearinghouse accordingly would close Speculator
A's positions by paying her $1,250 at expiration.

Clearinghouse
• Since Speculator A's short position effectively closes
her position, it is variously referred to as a closing,
reversing out, or offsetting position or simply as an
offset.
• Thus, the clearinghouse makes it easier for futures
contracts to be closed prior to expiration.
• The expense and inconvenience of delivery causes
most futures traders to close their positions instead
of taking delivery.

Clearinghouse
• As the delivery date approaches, the number
of outstanding contracts, referred to as open
interest, declines, with only a relatively few
contracts still outstanding at delivery.

Clearinghouse
• At expiration (T), the contract prices on futures
contracts established on that date (fT) should be
equal (or approximately equal for some contracts) to
the prevailing spot price on the underlying asset
(ST).
• If fT does not equal ST at expiration, an arbitrage
opportunity would exist. Arbitrageurs could take a
position in the futures market and an opposite
position in the spot market.
T
T S
f 

Clearinghouse
• For example, if the September T-bill futures contracts
were trading at $990,000 on the delivery date in
September and the spot price on T-bills were trading at
$990,500, an arbitrageur could
– go long in the September contract,
– take delivery by buying the T-bill at $990,000 on the futures
contract,
– then sell the bill on the spot at $990,500 to earn a risk-free
profit of $500.
• The arbitrageur’s efforts to take a long position,
though, would drive the contract price up to $990,500.

Clearinghouse
• On the other hand, if fT exceeds $990,500, then an
arbitrageur would reverse their strategy, pushing fT
down to $990,500.
• Thus at delivery, arbitrageurs will ensure that the
price on an expiring contracts is equal to the spot
price.
• As a result, closing a futures contract with an
offsetting position at expiration will yield the same
profits or losses as purchasing (selling) the asset on
the spot and selling (buying) it on the futures
contract.

Clearinghouse
• Example: Suppose near the delivery date on the
September contract the spot T-bill price and the
price on the expiring September futures contracts
are $990,000 (RD = 4% or Index = 96).
• To close his existing short contract, Speculator B
would need to take a long position in the
September contract, while to offset her existing
long contract, Speculator C would need to take a
short position.

Clearinghouse
• Suppose Speculators B and C take their offsetting
positions with each other on the expiring
September T-bill contract priced at fT = ST =
$990,000.
• After the clearinghouse breaks up the new contract,
Speculator B would owe the clearinghouse $2,500
and Speculator C would receive $1,250 from the
clearinghouse.

Clearinghouse
Clearinghouse Records for Speculator B:
1.
2.
Speculator B agrees to SELL September T-bill to CH
for $987,500.
Speculator B agrees to BUY September T-bill from CH
at $990,000.
Speculator B would pay the CH $2,500.

Clearinghouse
Clearinghouse Records for Speculator C:
1.
2.
Speculator C agrees to BUY September T-bill at
$988,750.
Speculator C agrees to SELL September T-bill for
$990,000.
CH would pay Speculator C $1,250.

Clearinghouse
To recapitulate:
– The contract prices on September T-bill contracts went
from $987,500 on the A and B contract, to $988,750 on
the A and C contract, to $990,000 on the B and C contract
at expiration.
– Speculators A and C each received $1,250 from the
clearinghouse.
– Speculator B paid $2,500 to the clearinghouse.
– The clearinghouse with a perfect hedge on each contract
received nothing (other than clearinghouse fees attached
to the commission charges).
– No T-bill was actually purchased or delivered.

Margins
• Since a futures contract is an agreement, it has no initial
value.
• Futures traders, however, are required to post some
margin -- security or good faith money with their
brokers.
• Depending on the brokerage firm, the customer's margin
requirement can be satisfied either in the form of cash or
cash-equivalents.
• Futures contracts have both initial and maintenance
margin requirements.

Margins
• The initial (or performance) margin is the amount
of cash or cash equivalents that must be deposited by
the investor on the day the futures position is
established.
• The futures trader does this by setting up a margin
(or commodity) account with the broker and
depositing the required cash or cash equivalents.
• The amount of the margin is determined by the
margin requirement, defined as a proportion (m) of
the contract value (usually 3% to 5%).

Margins
• Example: If the initial margin requirement is 5%,
then Speculators A and B in our example would be
required to deposit $49,375 in cash or cash
equivalents in their commodity accounts as good
faith money on their September futures contracts:
m[Contract Value] = .05[$987,500] = $49,375

Margins
• At the end of each trading day, the futures trader’s account is
adjusted to reflect any gains or losses based on the settlement price
on new contracts.
• In our example, suppose the day after Speculators A and B
established their respective long and short positions, the settlement
index value on the September T-bill was 95.5 (ft = 988,750, RD =
4.5%). The value of A's and B's margin accounts would therefore
be:
A: Account Value = $49,375 + ($988,750 - $987,500) = $50,625
B: Account Value = $49,375 + ($987,500 - $988,750) = $48,125

Margins
• With a lower rate and higher futures price, A’s long
position has increase in value by $1,250 and B’s short
position has decreased by $1,250.
• When there is a decrease in the account value, the
futures trader’s broker has to exchange money through
the clearing firm equal to the loss on the position to the
broker and clearinghouse with the gain.
• This process is known as marking to market. Thus in
our case, B’s broker and clearing firm would pass on
$1,250 to A’s broker and clearing firm.

Margins
• To ensure that the balance in the trader’s account
does not become negative, the brokerage firm
requires a margin to be maintained by the futures
traders.
• The maintenance (or variation) margin is the
amount of additional cash or cash equivalents that
futures traders must deposit to keep the equity in
their commodity account equal to a certain
percentage (e.g., 75%) of the initial margin value.

Margins
• If the maintenance margin requirements were equal
to 100% of the initial margin, then A and B would
have to keep the equity values of their accounts
equal to $49,375.
• If Speculator B did not deposit the required margin
immediately, then he would receive a margin call
from the broker instructing him to post the required
amount of funds.
• If Speculator B did not comply with the margin call,
the broker would close the position.

Futures Hedging
• Futures markets provide corporations,
financial institutions, and others with
– a tool for hedging their particular spot positions
against adverse price movements,
– for speculating on expected spot price changes,
and
– for creating synthetic debt and investment
positions with better rates than direct positions.
Of theses uses, the most extensive one is hedging.

Futures Hedging
• Two hedging positions exist:
•Long hedge
•Short hedge

Futures Hedging
In a long hedge (or hedge purchase), a hedger takes
a long position in a futures contract to protect
against an increase in the price of the underlying
asset or commodity.
• Long hedge positions on debt securities are used by
money-market managers, fixed-income managers,
and dealers to lock in their costs on future security
purchases.

Futures Hedging
• In a short hedge, a hedger takes a short futures
position to protect against a decrease in the price of the
underlying asset.
• Short hedge positions are used:
– by bond and money market managers, investment bankers,
and dealers who are planning to sell securities in the future
– by banks and other intermediaries to lock in the rates they
pay on future deposits
– by corporate treasurers and other borrowers who want to
lock in the future rates on their loans or who want to fix the
rates on the floating rate loans.

Long Futures Hedge: Example
• Consider the case of a money market manager who
is expected a cash inflow of $9,875,000 in
September that he plans to invest in a 90-day jumbo
certificates of deposit, CD, with a face value of
$10M.
• Fearing that short-term rates could decrease (causing
CD prices to increase), suppose the manager goes
long in ten September Eurodollar futures trading at
RD = 5% or f0 = $987,500.

• Given equal spot and expiring futures prices at
expiration, the manager will find that
– Any additional costs of buying the jumbo CD above the
$9,875,000 price on the spot market will be offset by a profit
from his futures position.
– Any benefits from the costs of the CD being less than the
$9,875,000 price would be negated by losses on the
Eurodollar futures position.
• As a result, the manager’s costs of buying CDs on the
spot and closing his futures position would be
$9,875,000.

• In the exhibit on the next slide, the third row shows three
possible costs of buying the $10M face value CD at the
September delivery date of $9,850,000 $9,875,000 and
$9,900,000 given settlement LIBORs of 6%, 5%, and 4%.
• The fourth row shows the profits and losses from the long
futures position in which the offset position has a contract or
cash settlement price (fT) equal to the spot price (ST).
• The last row shows the net costs of $9,875,000 resulting from
purchasing the CDs and closing the futures position.

Positions 6% 5% 4%
(1) September Spot RD
(2) September Spot and futures Price
(3) Cost of $10M face value 90-day CD
(4) Profit on Futures
6%
$985,000
$9,850,000
($25,000)
5%
$987,500
$9,875,000
0
4%
$990,000
$9,900,000
$25,000
Net Costs: Row (3) – Row (4) $9,875,000 $9,875,000 $9,875,000
Initial Position: Long in 10 September Eurodollar futures contracts at
RD = 5 (Index = 95, f0 = $987,500) to hedge $9,875,000 CD investment
in September.
Profit on futures = 10 (Spot Price - $987,500)

Short Futures Hedge: Example
• Consider the case of a fixed-income manager who in July
anticipates needing cash in September that she plans to obtain
by selling ten 6% T-bonds, each with a face value of
$100,000 and currently trading at par.
• Suppose that the September T-bond futures contract is trading
at 100, and at the time of the anticipated September sale, the
T-bonds will be at a coupon date with a maturity of exactly
15 years and no accrued interest at that date.
• If the manager wants to lock in a September selling price on
her T-bonds of $100,000 per bond, she could go short in 10
September T-bond futures contracts.

• At the September expiration, if the cheapest-to-
deliver bond is the 15-year, 6% coupon bond with
a conversion factor of 1, then the treasurer would
receive $1M in revenue at delivery from selling her
T-bonds on the spot market and closing the futures
contract by going long in the expiring September
contract trading at price equal to the spot price on
the 15-year, 6% T-bond.

• In the exhibit on the next slide:
– The second row shows three revenue amounts from
selling the ten T-bonds at three possible spot T-bond prices
of 95, 100, 105.
– The third row shows the profits and losses from the
futures position.
– The last row shows the hedged revenue from aggregating
both positions.
• Thus, regardless of the spot price, the manager
receives $1,000,000 from selling the bonds and
closing the futures positions.

Initial Position: Short in 10 September T-bond futures contracts
at f0 = 100 to hedge a September sale of 10 T-bonds. At the delivery
date the 10 T-bonds each have a maturity of 15 years, no accrued interest,
and can be delivered on the futures contracts with a conversion factor of 1.
Positions 95 100 105
(1) September spot and futures Price
(2) Revenue from sale of 10 T-bonds
(3) Profit on futures
$95,000
$950,000
$50,000
$100,000
$1,000,000
0
$105,000
$1,050,000
($50,000)
Net Revenue: Row (2) + Row (3) $1,000,000 $1,000,000 $1,000,000
Profit on futures = 10 ($100,000 – Spot Price)

• It should be noted that in determining the
futures positions, hedgers need to take into
account the cheapest-to-deliver bond, accrued
interest, and a conversion factor that is likely
to be different than 1.

Hedging Risk
• The above examples represent perfect
hedging cases in which certain revenues or
costs can be locked in at a future date.
• In practice, perfect hedges are the exception
and not the rule.

Hedging Risk
• There are three types of hedging risk that
preclude one from obtaining a zero risk
position:
1. Quality Risk
2. Timing Risk
3. Quantity Risk

Hedging Risk
Quality Risk
• Quality risk exists when the commodity or asset being hedged
is not identical to the one underlying the futures contract.
• The manager in our long hedge example, for instance, may be
planning to purchase commercial paper instead of a T-bill.
• In such hedging cases, futures contracts written on a different
underlying asset are often used to hedge the spot asset. These
types of hedges are known as cross hedges.
• Unlike direct hedges in which the future's underlying asset is
the same as the asset being hedged, cross-hedging cannot
eliminate risk, but can minimize it.

Hedging Risk
Timing risk
• Timing risk occurs when the delivery date on the
futures contract does not coincide with the date the
hedged asset needs to be purchased or sold.
• For example, timing risk would exist in our long
hedging example if the manager needed to buy the
CDs on the first of September instead of at the
futures' expiration at the end of the September.

Hedging Risk
Timing Risk
• If the spot asset is purchased or sold at a date that differs
from the expiration date on the futures contract, then the
price on the futures (ft) and the spot price (St) will not
necessarily be equal.
• The difference between the futures and spot price is called
the basis (Bt).
• The basis tends to narrow as expiration nears, converging
to zero at expiration (BT = 0).
• Prior to expiration, the basis can vary, with greater
variability usually observed the longer the time is to
expiration.

Hedging Risk
Timing Risk
• Given basis risk, the greater the time difference between
buying or selling the hedged asset and the futures'
expiration date, the less perfect the hedge.
• To minimize timing risk or basis risk, hedgers often select
futures contracts that mature before the hedged asset is to
be bought or sold but as close as possible to that date.
• For very distant horizon dates, though, hedgers sometimes
follow a strategy known as rolling the hedge forward. This
hedging strategy involves taking a futures position, then at
expiration closing the position and taking a new one.

Hedging Risk
Quantity Risk
• Because of the standardization of futures
contracts, futures hedging also is subject to
quantity risk.

Websites
• Chicago Mercantile Exchange: www.cme.com
• Chicago Board of Trade: www.cbot.com
• Commodity Futures Trading Commission:
www.cftc.gov
• National Futures Association:
www.nfa.futures.org

Websites
• For more information on futures and links to other sites
with futures information go to
www.citylink-uk.com.
• Current prices on futures contracts on Eurodollar and T-
bill and other futures can be obtained by going to
www.cme.com and clicking on “Quotes” in “Market Data”
and then clicking on “Interest Rate Products.”
• For T-bonds, T-notes, and other futures go to
www.cbot.com and click on “Quotes and Data.”

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