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
Futures
Forwards
Design flexibility Standardized
Can be customized
Credit risk
Clearinghouse risk Counterparty risk
Liquidity risk
Depends on trading Negotiated exit
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
•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
Selected Good Faith Deposit Requirements
Data as of January 2, 2004
Contract
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
Quotations
Month
Open
Expiration opening
(3rd Friday price
of the
month)
Hi
Lo
Sett
Net Chg.
Life Life Open Int.
Hi Lo
Settle price change in
number of
(Average settle price
outstanding
of the day)
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 Futures
You 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)
0 924.5
0
1 926
2 x 500 x (-1.5)=
(1,500)
2 924 2 x 500 x 2= 2000
3 927
2 x 500 x (-3) =
(3,000)
4 930
(3,000)
4
5
6
930
929
925
0
1,000
4,000
Equity
46,225
44,725
Debt Position
878,275 924,500
878,275 923,000
Margin Call
0
Restricted
46,725
43,725
878,275 925,000
878,275 922,000
Over margined
Restricted
40,725 878,275 919,000 CALL: + $5,500 from
(<41,602.50)
your pocket to cover
the requirements
46,225 878,275
0
0
47,225 878,275 925,500
Over margined
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(“-”)
Speculating with futures
• 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.
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).
On the “spot” market
-$3.05/bushel or
-40,000 x 3.05 = -$122,000
August $3.00/bushel or
40,000 x 3.00 = $120,000
Time
June
Total
-2,000
Balance +16,000
On the futures market
$3.45/bushel or
40,000 x 3.45 = $138,000
-$3.00/bushel or
-40,000 x 3.00 = -$120,000
(notice: spot price =futures price at maturity)
+18,000
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 9608; 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
June 1st
Cash Market
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
Futures Market
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 The December T-bill futures is worth 95is worth 96-8. Sell your T-bonds at 96- 10. Close (buy) your short position at 958--i.e., +$96,250
10--i.e., -$95,312.5
You lost 96,250-98,312.5=-$2,062.5
You Gain 97,000-95,312.5=+$1,687.5 on
Bottom
on the Cash Market
the Futures Market
Line
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.
Solution
you 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
Today
2 month after
On the “spot” market
-$5,000,000
+$4,000,000
Total
Balance
-1,000,000
-250,000
On the futures market
200 x 500 x 50= $5,000,000
170 x 500 x 50= -$4,250,000
(notice: spot price =futures price at maturity)
+750,000
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
Imperfect hedges and bond portfolio
The objective of hedging is to select a hedge ratio (D) such as
(change in S) – hedge ratio X (change in F) = 0
or
hedge ratio =D = (change in S) / (change in F)
Imperfect hedges and bond portfolio
(continued)
S DS
S  hF  Constan t  h 

F DF
change in S
change in S
S
S
h


change in F F
change in F
F
 D mod ified for S
change in yield for S S



 D mod ified for F change in yield for F F
D mod ified for S
S


D mod ified for F F
Imperfect hedges and bond portfolio
(continued)
D modS S
Hedge Ratio  h =

D modF F
n  h
amount to hedge
value of 1 contract
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
Price
BOND
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)
D mod S
D mod F
8.52

 8.18
8.25%
(1 
)
2
10.05

 9.68
7.7%
(1 
)
2
8.18 100
Hedge Ratio  D =

 0.819
9.68 103.06
10,000,000
n  0.819
 82 contracts
100,000
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
BOND
7.48% 7.25% 2
26 11.45268584
T_BOND (FUT) 7.89%
8% 2
20 9.952213432
Price
97.375
101.125
Solution:
• You build a short hedge by selling 1,111 TBond futures:
D mod S
D mod F
11.45

 11.04
7.48%
(1 
)
2
9.95

 9.57
7.89%
(1 
)
2
11.04 97.375
Hedge rat io  D =

 1.111
9.57 101.125
100,000,000
n  1.111
 1111 cont ract s
100,000
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%
C
C 
1 
1  C 6X
1 

CF 

 

x 
2N 
2N 
(1.03) 6  2 0.06  (1.03)  (1.03)  2  6 
where
1
CF  conversionfactor
C  annualcouponin decimalform
N  number of whole years to maturity
X  the number of monthsin excess of the whole N
Hedging With Interest Rate Futures
• The hedge ratio is:
Pb D b (1  YTM ctd )
h  CFctd 
Pf D f (1  YTM b )
• The number of contracts necessary is given by:
portfoliopar value
# contracts
 hedge ratio
$100,000
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?
0.97  9.0 1.071
HR  1.1529 
 0.9898
0.906875 11.14 1.078
$10,000,00
0
# contracts
 0.9898 98.98
$100,000
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 welldiversified 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
Using Futures Contracts to Hedge Portfolios
You 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.
• 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
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:
 Value of P ort folio
N=


 Value of 1 cont ract
 $3,243,750/ $308,500 1.15
 12.09
Hedge Ratio example
Determining 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
Dollar value of theportfolio
 beta
Dollar value of theS & P futurescontract
$75,000,000

 0.9  177.96  178contracts
1,517.20 $250
HR 
The Market Falls
Using 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 Rises
Using 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 Unchanged
Using 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
Dm ,t arg et 
V portfolio,current
Vfutures
Vportfolio, t arg et
V portfolio,t arg et
 Dm ,current 
V futures
V portfolio,t arg et
 Dm , futures
1
number of contracts contractsize
CF , thus

Vportfolio,target


Vportfolio,current
 D m,current   Vportfolio,target
D m, target 
Vportfolio, t arg et


number of contracts
1
D m, futures  contractsize
CF
Example
A 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.


Vportfolio,current
 D m,current   Vportfolio,target
D m, target 
Vportfolio, t arg et


number of contracts
1
D m, futures  contractsize
CF


 9.7
10,000,000
4.85 

 10,000,000
 8.5% 

10,000,000 1  8.5% 
1 
2
2 

 55.77  56 contractslong
9.7
1
(
)  100,000
7.22%
1.1223
1
2
Speculation: Active management-- Adjust
Portfolio Beta
portfolio  %equity equity  %Futures futures
number of cont ract s cont ractsize x fut uresprice
, t hus
port foliovalue
 portfolio  %equit y equity  port foliovalue
number of cont ract s
cont ractsize  fut uresprice
%fut ures 


Example
• You have a $25 million equity portfolio
consisting of $22.5M in stocks and $2.5M in Tbills. 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).
Adjusting Market Risk: Example
Determining 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:
# contracts
$75 million (1.50  0.90)
 119
1517.20 $250
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 = 1020.0
Treasury 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
Desired Asset Allocation
Bonds
18%
Bonds
40%
Stock
60%
Stock
82%
Bond Adjustment


Vportfolio,current
 D m,current   Vportfolio,target
D m, target 
V
portfolio, t arg et


number of contracts 
D m, futures  contractsize / CF


 8.7
18%  175,000,000
8.7 


 8%
  175,000,000  40%
8
%
40%  175,000,000 1 
1 

2
2 

 520.98  521contractslong
8.6
1
(
)  100,000
9.59%
1.3275
1
2
Thus, the manager should buy 521 T-bond futures
Stock Adjustment
• For this portfolio, the hedge ratio is:

 portfolio  %equity  equity  portfoliovalue
numberof contracts
contractsize futuresprice
82%  175,000,000


1
.
1


1
.
1

  175,000,000  60%
60
%

175
,
000
,
000

numberof contracts 
 166
250 1020
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 futuresincrease 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