derrivatives

2

1875 •Setting up of Bombay Cotton Trade Association Ltd.

1883 •A separate association called “The Bombay Cotton Exchange Ltd.” was
constituted

1900 •Futures trading in oilseeds was started with the setting up of Gujarati
Vyapari Mandali

1926 •Seeds Traders’ Association Ltd was set up in Mumbai

1920 •Futures market in bullion began at Mumbai

1952 •Government passed the Forward Contract Regulation Act, which controls
all transferable forward contracts and futures.

1960/70 •Central govt suspended trading in several commodities like
cotton, jute, edible oilseeds, etc.

1966/1980 •Datwala Committee/ Khusro Committee recommended reintroduction of
commodities

1993 •The Kabra committee recommended futures trading in many
commodities and upgradation of futures market

3

December 14, 1995 •The NSE sought SEBI’s permission to trade index futures.

November 18, 1996 •The LC Gupta Committee set up to draft a policy framework for index futures.

May 11, 1998 •The LC Gupta Committee submitted a report on the policy framework for index
futures.

July 7, 1999 •Reserve Bank of India gave permission for OTC forward rate agreements and
interest rate swaps.

May 25, 2000 •SEBI allowed the NSE and the BSE to trade in index futures.

June 9, 2000 •Trading of the BSE Sensex futures commenced on the BSE.

June 12, 2000 •Trading of Nifty futures commenced on the NSE.

September 25, 2000 •Nifty futures trading commenced

July, 2001 •Trading on equity futures commenced at NSE on 31 securities

June, 2003 •Trading on interest rate futures commenced at NSE

5

Interest rate • Treasury bills, notes, bonds, debentures,
futures euro-dollar deposits etc.

Foreign • USD, Pound Sterling, Yen, etc.
currencies futures

Stock index • Based on indices of stocks
futures

Bond index • Indices of bond prices
futures

Cost of living • Aka inflation futures; CPI, WPI, etc.
index futures

6

Forward contracts were useful, but only up to a point. They didn’t
eliminate the risk of default among the parties involved in the trade.

For example, merchants might default on the forward agreements if they
found the same product cheaper elsewhere, leaving farmers with the
goods and no buyers.

Conversely, farmers could also default if prices went up dramatically
before the forward contract delivery date, and they could sell to someone
else at a much higher price.

Therefore, a standardized contract was required to address this issue.

12

A legally binding, standardized agreement to buy or sell a
standardized commodity, specifying quantity and quality at a
set price on a future date.

A great advantage of standardized contracts was that they were
easy to trade.

As a result, the contracts usually changed hands many times
before their specified delivery dates.

Many people who never intended to make or take delivery of a
commodity began to actively engage in buying and selling
futures contracts.

13

Why? They were ―speculating‖ — taking a
chance that as market conditions changed
they would be able to buy or sell the
contracts at a profit.

The ability to eliminate a ―position‖ on a
contract by buying or selling it before the
delivery date — called ―offsetting‖ — is a
key feature of futures trading.

15

Promise to pay $20,000

Buyer Seller

Promise to deliver 5, 000 bushels

16

Promise to pay $20,000 Promise to pay $20,000

Buyer Seller
Clearinghouse


18

Delivery or cash settlement
• Most commodity futures contracts are written for completion of the futures
contract through the physical delivery of a particular good.
• Most financial futures contracts allow completion through cash settlement. In
cash settlement, traders make payments at the expiration of the contract to
settle any gains or losses, instead of making physical delivery.
Offset or reversing trade
• If you previously sold a futures contract, you can close out your position by
purchasing an identical futures contract. The exchange will cancel out your
two positions.
Exchange-for-physicals (EFP) or ex-pit transaction
• Two traders agree to a simultaneous exchange of a cash commodity and
futures contracts based on that cash commodity.

19

Suppose today the price of the futures is $3.95 and next
day, the buyer finds that people are paying $4.15 per
bushel for wheat. If B believes that the price of wheat
will not go any higher, then B might sell a wheat
futures contract for $4.15 to someone else.

In this situation, B has made a reversing trade.

20
Day Price of wheat Event Amount Equity in account

If maintenance margin were not required

1 4 Deposit initial margin 1000 1000

2 4.10 Mark to market 500 1500

3 3.95 Mark to market -750 750

4 4.15 Mark to market 1000 1750

With required maintenance margin

1 4 Deposit initial margin 1000 1000

2 4.10 Mark to market 500 1500

Buyer withdraws cash -500 1000

3 3.95 Mark to market -750 250

Buyer deposits cash 750 1000

4 4.15 Mark to market 1000 2000

Reversing trade and withdrawal of cash -2000 0

21

Since B is involved in two wheat contracts, one as a
seller and one as a buyer, B is obligated to deliver
5000 bushels to clearing house and clearing house
in turn is required to deliver it back to B.

The moment B offsets his positions, clearing house
will immediately cancel both of them, and B will be
able to withdraw $2000 from his account.

22

An Exchange-for-Physicals Transaction
Before the EFP
Trader A Trader B
Long 1 wheat futures Short 1 wheat futures
Wants to acquire actual wheat Owns wheat and wishes to sell
EFP Transaction
Trader A Trader B
Agrees with Trader B to purchase Agrees with Trader A to sell wheat and
wheat and cancel futures cancel futures
Receives wheat; pays Trader B Delivers wheat; receives payment from
Trader A
Reports EFP to exchange; exchange a- Reports EFP to exchange; exchange
djusts books to show that Trader A is adjusts books to show that Trader B is
out of the market out of the market

24

The procedures that protect clearinghouse
from potential losses due to non-
compliance of the buyer or seller are:
• Impose initial margin requirements on both
buyers and sellers
• Mark to market the accounts of buyers and
sellers every day
• Impose daily maintenance margin
requirements on both buyers and sellers.

25

A performance bond is a deposit to cover losses you may
incur on a futures contract as it is marked-to-market.

A maintenance performance bond is a minimum amount
of money (a lesser amount than the initial performance bond)
that must be maintained on deposit in your account.

A performance bond call is a demand for an additional
deposit to bring your account up to the initial performance
bond level.

26

In stock trading, margin refers to a partial
deposit you put up with your broker to
purchase securities, while borrowing the
remaining amount (typically half) from the
broker (expecting to pay interest).

In futures, this ―down payment‖ is actually a
good faith deposit you pay to indicate that
you will be able to ensure fulfillment of the
contract.

27

Futures contracts require an initial performance bond in
an amount determined by the exchange itself.

This amount is roughly 5% to 15% of the total purchase price
of the futures contract. This margin covers only a part of the
protection against the total loss in the case of default.

Therefore, the use of marking to market coupled with a
maintenance margin requirement provides the requisite
amount of additional protection.

28

At the end of the trading day your position is marked-to-the-
market. That is, the clearing house will settle your account on a
cash basis.

Money will be added to your performance bond balance if your
position has made a profit that day.

If you’ve sustained a loss that day, money is deducted from your
performance bond account.

This rebalancing occurs each day after the close of trading.

29

If your position has lost money and the
balance in the performance bond account
has fallen below the maintenance level, a
performance bond call will be issued.

That means you have to put in more money
to bring the account up to the initial
performance bond level.

32

How Trading Affects Open Interest
Time Action Open Interest
t=0 Trading opens for the popular widget contract. 0
t=1 Trader A buys and Trader B sells 1 widget contract. 1
t=2 Trader C buys and Trader D sells 3 widget contracts. 4
t=3 Trader A sells and Trader D buys 1 widget contract. 3
(Trader A has offset 1 contract and is out of the mar-
ket. Trader D has offset 1 contract and is now short
2 contracts.)
t=4 Trader C sells and Trader E buys 1 widget contract. 3
Ending Trader Long Position Short Position
Posi- B 1
tions C 2
D 2
E 1
All Traders 3 3

34

Spot Spot Market Futures Market
Price Gain or Loss % Return Gain or Loss % Return

$420 $2,000 5% $2,000 100%
$410 $1,000 2.5% $1,000 50%
$400 0 0% 0 0%
$390 -$1,000 -2.5% -$1,000 -50%
$380 -$2,000 -5% -$2,000 -100%

36

Table 3.2
Gold Prices and the Basis
(July 11)
Contract Prices The Basis
CASH 353.70
JUL (this year) 354.10 -.40
AUG 355.60 -1.90
OCT 359.80 -6.10
DEC 364.20 -10.50
FEB (next year) 368.70 -15.00
APR 373.00 -19.30
JUN 377.50 -23.80
AUG 381.90 -28.20
OCT 386.70 -33.00
DEC 391.50 -37.80

38

Prices

Cash

Basis Futures

Time
Present Maturity

40

Basis = current spot price – corresponding future price
• Future price here is the purchase price stated in the futures contract.
• Spot price is the price of a good for immediate delivery.
• Open interest is the number of futures contracts for which delivery is currently obligated.

Repo Rate
• The repo rate is the finance charges faced by traders. The repo rate is the interest rate on
repurchase agreements.
• ―Repo‖ is the name commonly used to refer to a repurchase agreement. Under a repurchase
agreement, one party to the transaction, referred to as the repo side, borrows money by posting
government securities as collateral. The counterparty, referred to as the reverse repo side,
lends money secured by the collateral. The reverse repo party has use of the collateral for the
term of the repo while the repo party retains claim to any coupon payments or price
appreciation. (Ref. Randall Dodd Director, Financial Policy Forum, March 20, 2006)

A Repurchase Agreement
• An agreement where a person sells securities at one point in time with the understanding that
he/she will repurchase the security at a certain price at a later time.

41

An Arbitrageur attempts to exploit any discrepancies in price between the futures
and cash markets.

An academic arbitrage is a risk-free transaction consisting of purchasing an asset
at one price and simultaneously selling it that same asset at a higher price,
generating a profit on the difference.

Example: riskless arbitrage scenario for INFOSYS stock trading on the NSE and
BSE.

Assumptions:

• Perfect futures market
• No taxes
• No transactions costs
• Commodity can be sold short

42

Price Exchange

Arbitrageur Buys INFY (1105) BSE
Arbitrageur Sells INFY 1110 NSE
Riskless Profit 5

44

Since the futures or forwards
don’t require front-end from
either the long or short
transaction; therefore, the
contract’s initial market
value is usually zero.

45

There are three main
theories of future pricing
• The expectations hypothesis
• Normal backwardation
• A full carrying charge market

46

Hypothesis: The futures price for a commodity is
what the marketplace expects the cash price to be
when the delivery month arrives.

The expectation hypothesis is a good predictor
because it provides an important source of
information about what the future price is likely
to be. It works like a price discovery mechanism.

50

Normally, the futures price exceeds the spot
price; this market is called contango.

If the futures price is less than the spot price,
this is called backwardation, or an
inverted market.

As the gap between the futures price and spot
narrows, we say that the basis is strengthened.

A hedger (for example, a farmer) who is selling a futures contract is
trying to lock in the price of the commodity in future. i.e. the hedger is
trying to reduce the risk, but this risk has to be borne by somebody i.e.
speculators.

Now question is if the future price equals the spot price + storage costs +
other costs exactly, what the speculator will earn by bearing the risk?

Therefore, the speculator will agree to that future price where he expects
that the spot price on the delivery date will be higher than futures price.

This is called normal backwardation.

53

A full carrying charge market occurs when
futures prices reflect the cost of storing and
financing (borrowing) the commodity until
the delivery month.

In the world of certainty, the futures price
is equal to the current spot price plus the
carrying charges until the delivery month.

54

To the extent that markets adhere to the following equations
markets are said to be at ―full carry‖:

F 0, t S 0(1 C 0, t )

F 0, d F 0, n(1 Cn, d )
If the futures price is higher than that specified by above
equations, the market is said to be above full carry.

If the futures price is below that specified by the above
equations, the market is said to be below full carry.

55

To determine if a market is at full carry, consider the
following example:

Suppose that:

September Gold $410.20
December Gold $417.90
Bankers Rate 7.8%

56

Step 1: compute the annualized percentage
difference between two futures contracts.
12
AD (F )
F
0, d

0. N
M 1

Where
• AD = Annualized percentage difference
• M = Number of months between the maturity of the
futures contracts.

57

12
$417.90 3
AD ( )
$410.20
1

AD 0.0772

Step 2: compare the annualized difference to the
interest rate in the market.

The gold market is almost always at full carry. Other
markets can diverge substantially from full carry.

58
A spread is the difference in price between two futures contracts
on the same commodity for two different maturity dates:

Spread F 0, t k F 0, t
F0,t = The current futures price for delivery of the product at time t.
• This might be the price of a futures contract on wheat for delivery in 3 months.

F0,t+k = The current futures price for delivery of the product at time
t +k.
• This might be the price of a futures contract for wheat for delivery in 6 months.

Spread relationships are important to speculators.

We know that there is a relationship between the price of the
commodity in the cash market and price of that commodity in the
futures market. 59

The futures market price should reflect the storage cost of
that commodity unto that future date plus the cash price of that
commodity today and any other costs.

If futures price is more than this price (= cash price + storage cost
+ other costs) then there is a possibility of arbitrage.

One will purchase the commodity today, store it and at the same
time short a futures contract to deliver it on the futures date.

Since there is a difference in prices, there is a scope for arbitrage.

60

The common way to value a futures contract is by using
the Cost-of-Carry Model. The Cost-of-Carry Model says
that the futures price should depend upon two things:
• The current spot price.
• The cost of carrying or storing the underlying good from now until
the futures contract matures.

Assumptions:

• There are no transaction costs or margin requirements.
• There are no restrictions on short selling.
• Investors can borrow and lend at the same rate of interest.

Suppose you buy the corn now for the current cash price of S0 per bushel
61
and store it until you have to deliver it at date T, the forward price you
would be willing to commit would have to be high enough to cover
• The present cost of the corn and
• The cost of storing the corn until contract maturity

These storage costs involve

• Commission paid to the warehouse for storing
• Cost of financing the initial purchase
• LESS cash flows received by owing the asset.

F0,T = S0 + SC0,T

= S0 + (PC0, T + i 0, T – D0, T)

64
The Cost-of-Carry Model can be expressed as:

F 0, t S 0(1 C 0, t )
S0 = the current spot price

F0,t = the current futures price for delivery of
the product at time t.

C0,t = the percentage cost required to store (or carry) the
commodity from today until time t.

The cost of carrying or storing includes:
• Storage costs
• Insurance costs
• Transportation costs
• Financing costs

66

Cash-and-carry arbitrage
• When futures are overpriced

Reverse cash-and-carry arbitrage
• When futures are underpriced

67

A cash-and-carry arbitrage occurs when a trader borrows
money, buys the goods today for cash and carries the goods
to the expiration of the futures contract. Then, delivers the
commodity against a futures contract and pays off the loan.
Any profit from this strategy would be an arbitrage profit.
0 1

1. Borrow money 4. Deliver the commodity
2. Sell futures contract against the futures contract
3. Buy commodity 5. Recover money & payoff
loan

68

The futures price must be greater than or
equal to the spot price of the commodity
plus the carrying charges necessary to carry
the spot commodity forward to delivery.
F 0, t S 0(1 C 0, t )
0 1

1. Borrow $400 4. Deliver gold against
2. Buy 1 oz gold futures contract
3. Sell futures contract 5. Repay loan

69

Cash-and-Carry Gold Arbitrage Transactions
Prices for the Analysis:

Spot price of gold $400
Future price of gold (for delivery in one year) $450
Interest rate 10%
Transaction Cash Flow
t=0 Borrow $400 for one year at 10%. +$400
Buy 1 ounce of gold in the spot market for $400. - 400
Sell a futures contract for $450 for delivery of 0
one ounce in one year.
Total Cash Flow $0
t=1 Remove the gold from storage. $0
Deliver the ounce of gold against the futures +450
contract.
Repay loan, including interest. -440
Total Cash Flow
+$10

71

A reverse cash-and-carry arbitrage occurs when a trader sells short a
physical asset. The trader purchases a futures contract, which will be
used to honor the short sale commitment. Then the trader lends the
proceeds at an established rate of interest. In the future, the trader
accepts delivery against the futures contract and uses the commodity
received to cover the short position. Any profit from this strategy would
be an arbitrage profit.

0 1

1. Sell short the commodity 4. Accept delivery from futures
2. Lend money received contract
from short sale 5. Use commodity received
3. Buy futures contract to cover the short sale

72

The futures price must be equal to or less
than the spot price of the commodity plus
the carrying charges necessary to carry
the spot commodity forward to delivery.

0 F 0, t S 0(1 C 0, t ) 1

1. Sell short 1 oz. gold 4. Collect proceeds
2. Lend $420 at 10% from loan
interest 5. Accept delivery on
3. Buy a futures contract futures contract
6. Use gold from futures
contract to repay the
short sale

73

Reverse Cash-and-Carry Gold Arbitrage Transactions
Prices for the Analysis

Spot price of gold $420
Future price of gold (for delivery in one year) $450
Interest rate 10%
t=0 Sell 1 ounce of gold short. +$420
Lend the $420 for one year at 10%. - 420
Buy 1 ounce of gold futures for delivery in 1 0
year.
Total Cash Flow $0
t=1 Collect proceeds from the loan ($420 x 1.1). +$462
Accept delivery on the futures contract. -450
Use gold from futures delivery to repay short 0
sale.
Total Cash Flow +$12

75

Transactions for Arbitrage Strategies
Market Cash-and-Carry Reverse Cash-and-Carry
Debt Borrow funds Lend short sale proceeds
Physical Buy asset and store; deliver Sell asset short; secure
against futures proceeds from short sale
Futures Sell futures Buy futures; accept delivery;
return physical asset to honor
short sale commitment

Since the futures price must be76 either greater than or equal to
the spot price plus the cost of carrying the commodity
forward by rule #1.
And the futures price must be less than or equal to the spot
price plus the cost of carrying the commodity forward by rule
#2.

The only way that these two rules can reconciled so there is
no arbitrage opportunity is by the cost of carry rule #3.

Rule #3: the futures price must be equal to the spot price plus
the cost of carrying the commodity forward to the delivery
date of the futures contract.

F 0, t S 0(1 C 0, t )

77

If prices were not to conform to cost of
carry rule #3, a cash-and carry arbitrage
profit could be earned.

Recall that we have assumed away
transaction costs, margin requirements,
and restrictions against short selling.

78

As we have just seen, there must be a relationship between the futures price
and the spot price on the same commodity.

Similarly, there must be a relationship between the futures prices on the same
commodity with differing times to maturity.

The following rules address these relationships:

Cost-of-Carry Rule 4



The distant futures price must be greater than or equal to the nearby futures price plus
79
the cost of carrying the commodity from the nearby delivery date to the distant
delivery date.

F 0, d F 0, n(1 Cn, d )
F0,d = the futures price at t=0 for the distant delivery contract maturing at t=d.

Fo,n = the futures price at t=0 for the nearby delivery contract maturing at t=n.

Cn,d = the percentage cost of carrying the good from t=n to t=d.

If prices were not to conform to cost of carry rule # 4, a cash-and-carry arbitrage profit
could be earned.

80

0 1 2

7. Remove gold
1. Buy futures 4. Borrow $400 from storage
contract w/exp 5. Take delivery on 1 8. Deliver gold
in 1 yrs. yr to exp futures against 2 yr.
2. Sell futures contract. futures contract
contract w/exp 6. Place the gold in 9. Pay back loan
in 2 years storage for one yr.
3. Contract to
borrow $400
from yr 1-2

81

0 1 2

7. Remove gold
1. Buy futures 4. Borrow $400 from storage
contract w/exp 5. Take delivery on 1 8. Deliver gold
in 1 yrs. yr to exp futures against 2 yr.
2. Sell futures contract. futures contract
contract w/exp 6. Place the gold in 9. Pay back loan
in 2 years storage for one yr.
3. Contract to
borrow $400
from yr 1-2

82

Gold Forward Cash-and-Carry Arbitrage
Prices for the Analysis

Futures price for gold expiring in 1 year $400
Futures price for gold expiring in 2 years $450
Interest rate (to cover from year 1 to year 2) 10%
t=0 Buy the futures expiring in 1 year. +$0
Sell the futures expiring in 2 years. 0
Contract to borrow $400 at 10% for year 1 to 0
year 2.
Total Cash Flow $0

t=1 Borrow $400 for 1 year at 10% as contracted at +$400
t = 0.
Take delivery on the futures contract. - 400
Begin to store gold for one year. 0
Total Cash Flow $0

t=2 Deliver gold to honor futures contract. +$450
Repay loan ($400 x 1.1) - 440

Total Cash Flow + $10

83

The nearby futures price plus the cost of carrying the commodity from
the nearby delivery date to the distant delivery date cannot exceed the
distant futures price.

Or alternatively, the distant futures price must be less than or equal to
the nearby futures price plus the cost of carrying the commodity from the
nearby futures date to the distant futures date.

F0,d F0,n 1 Cn,d
If prices were not to conform to cost of carry rule # 5, a reverse cash-
and-carry arbitrage profit could be earned.

84

0 1 2

1. Sell futures 7. Accept delivery
contract w/exp 4. Borrow 1 oz. gold on exp 2 yr
in 1 yrs. 5. Deliver gold on 1 futures contract
2. Buy futures yr to exp futures 8. Repay 1 oz.
contract w/exp contract. borrowed gold.
in 2 years 6. Invest proceeds 9. Collect $400
3. Contract to from delivery for loan
lend $400 one yr.
from yr 1-2

85

Gold Forward Reverse Cash-and-Carry Arbitrage
Prices for the Analysis:

Futures price for gold expiring in 1 year $440
Futures price for gold expiring in 2 years $450
Interest rate (to cover from year 1 to year 2) 10%


t=0 Sell the futures expiring in one year. +$0
Buy the futures expiring in two years. 0
Contract to lend $440 at 10% from year 1 to 0
year 2.
Total Cash Flow $0

t=1 Borrow 1 ounce of gold for one year. $0
Deliver gold against the expiring futures. + 440
Invest proceeds from delivery for one year. - 440

Total Cash Flow $0

t=2 Accept delivery on expiring futures. - $450
Repay 1 ounce of borrowed gold. 0
Collect on loan of $440 made at t = 1. + 484

Total Cash Flow + $34

86

Since the distant futures price must be either greater than or equal
to the nearby futures price plus the cost of carrying the
commodity from the nearby delivery date to the distant delivery
date by rule #4.

And the nearby futures price plus the cost of carrying the
commodity from the nearby delivery date to the distant delivery
date can not exceed the distant futures price by rule #5.

The only way that rules 4 and 5 can be reconciled so there is no
arbitrage opportunity is by cost of carry rule #6.

87

The distant futures price must equal the nearby futures price plus the
cost of carrying the commodity from the nearby to the distant delivery
date.

F 0, d F 0, n(1 Cn, d )
If prices were not to conform to cost of carry rule #6, a cash-and-carry
arbitrage profit or reverse cash-and-carry arbitrage profit could be
earned.

Recall that we have assumed away transaction costs, margin
requirements, and restrictions against short selling.

88

Ease of Short Selling
• To the extent that it is easy to short sell a commodity, the market will
become closer to full carry.
• Difficulties in short selling will move a market away from full carry.
• Selling short of physical goods like wheat is more difficult, while
selling short of financial assets like Eurodollars is much easier. For
this reason, markets for financial assets tend to be closer to full carry
than markets for physical assets.

Large Supply
• If the supply of an asset is large relative to its consumption, the
market will tend to be closer to full carry. If the supply of an asset is
low relative to its consumption, the market will tend to be further
away from full carry.

89

Non-Seasonal Production
• To the extent that production of a crop is seasonal, temporary imbalances between
supply and demand can occur. In this case, prices can vary widely.
• Example: in North America, wheat harvest occurs between May and September.
Non-Seasonal Consumption
• To the extent that consumption of commodity is seasonal, temporary imbalances
between supply and demand can occur.
• Example: propane gas during winter Turkeys during thanksgiving
High Storability
• A market moves closer to full carry if its underline commodity can be stored easily.
• The Cost-of-Carry Model is not likely to apply to commodities that have poor
storage characteristics.
• Example: eggs

Hedging with futures
90

92

Cash market Futures market

May 10 Anticipate the sale of 20, 000 Sell four contracts, 5000 ounces
ounces in two months and each July futures contract at
receive Rs.1052 per ounce Rs.1068 per ounce

July 5 Cash price of silver is Rs.1071 Buy four contracts at Rs.1087
per ounce; mfg sales 20, 000
ounces at that rate

Results Profit of Rs. 19 per ounce However, he loses Rs.19 per ounce
when he buys the futures contract.

93


May 10 If he had sold today: 1052 x Sell : 4x5000x1068 = 2,13,60,000
20,000 = 2,10,40,000

July 5 1071 x 20, 000 = 2,14,20,000 Buy: 4x5000x 1087 = 2,17,40,000

Results Profit of Rs. 3, 80, 000 He loses Rs.3, 80, 000 in the futures
contract.

96

Suppose on June 1, Ms. Deepa realizes she needs to purchase
110,000 pieces of wood planks on September 1.

Today’s cash price for wood planks is $300 per 1000 board feet
($300/MBF). She observes that September Lumber futures are
currently trading at $305/MBF.

She also knows that historically the futures price in September
tends to be about $5/MBF higher than the cash price. So Deepa
figures that by buying a September Lumber futures contract in
June at $305, she is locking in a price of about $300.

97


June 1 Needs to buy wood planks in Buys (goes long) one September
September for $300/MBF Lumber futures contract at
to make desired profit. $305/MBF.

Sep 1 Cash price rises to $315/MBF. Deepa sells her September
Deepa buys lumber for Lumber contract at $320/MBF.
$315/MBF.

Results Deepa pays $15/MBF more However, she gains $15/MBF when
for lumber than she wanted she sells the futures contract.
to.

98


June 1 $300/MBF X 110 = $33,000 $305/MBF X 110 = $33,550

Sep 1 $315/MBF X 110 = $34,650 $320/MBF X 110 = $35,200

Results Higher cost in cash market: Net profit in futures market:
Spent $1,650 more Gained $1,650

99

The difference between the cash price and the
futures price is called basis.

The basis changes during the life of the futures
contract.

It tends to narrow as contract maturity approaches.

That is, the futures price moves closer to the cash
price during the delivery month.

100

At any date t, the basis is the spot price minus the
forward price for a contract maturing at date T,
• Bt,T = St – Ft,T (spot price of the asset to be hedged – futures price of contract used)

Initial basis at date 0 (B0,T) will always be known
since both the current spot and forward contract
prices can be observed.

Consider an investor who hedges her long position in
a commodity by taking a short position in a forward
contract(delivering the commodity at maturity).

At date 1, B1= S1 – F1
101

At date 2, B2 = S2 – F2

For the hedger who takes a short position in futures at
time 1, the price realized for the asset is S2 and the
profit on the futures position is (F1 – F2)

Therefore the effective price is = S2 + (F1 – F2) = F1 +
(S2 – F2) = F1 + B2

102

Suppose, an investor wishes in March to hedge a long position of
100, 000 pounds of cotton she is planning to sell in June.

However, each futures contract is requiring only 50, 000 pounds
of cotton. Therefore, she decides to short two of the July contracts
(intending to liquidate her position before the maturity)

Suppose, in the beginning, the spot cotton price was $0.4834 per
pound and the July futures contract was $0.5305 per pound.

Calculate initial basis. B1= S1 – F1= 0.4834 – 0.5305 = - 0.0471

Suppose, cotton prices have declined so that cash price in June are
104
$0.4660 and futures are trading at $0.4753.

Calculate basis for June. B2 = S2 – F2 = 0.4660 – 0.4753 = -
0.0093

Basis has increased in value or strengthened, which is to the short
hedger’s advantage.

Now, she sells cotton in cash market for $0.4660

At the same time she also sells the futures for its contract value i.e.
$0.5305 whereas the market future price is $0.4753; it means that
she has made a profit of (0.5305 – 0..4753) = $0.0552

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