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FUTURES MARKET: MEANING, PARTIES, TRADING PROCEDURE, HEDGING STRATEGIES, VALUATION, SEBI GUIDELINES DM – Module 2 1
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FUTURES MARKET: MEANING, PARTIES, TRADING PROCEDURE, HEDGING STRATEGIES, VALUATION,
SEBI GUIDELINES
DM – Module 21
Evolution of futures market in India
•Setting up of Bombay Cotton Trade Association Ltd.1875
•A separate association called “The Bombay Cotton Exchange Ltd.” was constituted1883
•Futures trading in oilseeds was started with the setting up of Gujarati Vyapari Mandali1900
•Seeds Traders’ Association Ltd was set up in Mumbai1926
•Futures market in bullion began at Mumbai1920•Government passed the Forward Contract Regulation Act, which controls all transferable forward contracts and futures.1952•Central govt suspended trading in several commodities like cotton, jute, edible oilseeds, etc.1960/70
•Datwala Committee/ Khusro Committee recommended reintroduction of commodities 1966/1980•The Kabra committee recommended futures trading in many commodities and upgradation of futures market1993
2
Chronology in India
•The NSE sought SEBI’s permission to trade index futures.December 14, 1995
•The LC Gupta Committee set up to draft a policy framework for index futures.November 18, 1996
•The LC Gupta Committee submitted a report on the policy framework for index futures.May 11, 1998
•Reserve Bank of India gave permission for OTC forward rate agreements and interest rate swaps.July 7, 1999
•SEBI allowed the NSE and the BSE to trade in index futures.May 25, 2000
•Trading of the BSE Sensex futures commenced on the BSE.June 9, 2000
•Trading of Nifty futures commenced on the NSE.June 12, 2000
•Nifty futures trading commenced September 25, 2000
•Trading on equity futures commenced at NSE on 31 securitiesJuly, 2001
•Trading on interest rate futures commenced at NSEJune, 2003
3
Regulation in financial derivatives in India
Regulated by SEBI, Forward Markets Commission (FMC), and RBI
FMC holds the overall charge of all forwards in commodities specifically.
SEBI regulates the carry forward trading in equity stock, stock index, options etc.
RBI regulates OTC forward contracts and options on foreign currencies.
4
Types of financial futures contracts
•Treasury bills, notes, bonds, debentures, euro-dollar deposits etc.
Interest rate futures
•USD, Pound Sterling, Yen, etc.Foreign currencies futures
•Based on indices of stocksStock index futures
•Indices of bond pricesBond index futures
•Aka inflation futures; CPI, WPI, etc.Cost of living index futures
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Birth of futures
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.
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The concept of futures contract
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.
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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.
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The clearinghouse
Clearing house becomes seller’s buyer and buyer’s seller.
Let us say, buyer and seller agree on a $4 per bushel (min 5000 bushels) contract wheat futures contract
Buyer Seller
Promise to pay $20,000
Promise to deliver 5, 000 bushels
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The house becomes an intermediary to the futures contract
ClearinghouseBuyer Seller
Promise to pay $20,000
Promise to deliver 5, 000 bushelsPromise to deliver 5, 000 bushels
Promise to pay $20,000
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Closing a futures Position (Settlement)
Physical deliveryCash settlement/deliveryOffsettingExchange of futures for physicals (EFP)
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There are 3 ways to close a futures position
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.
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Reversing trades (offsetting)
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.
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Margin requirements for a futures contract (buyer)
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
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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.
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An Exchange-for-Physicals Transaction
Before the EFP
Trader A
Trader B Long 1 wheat futures Wants to acquire actual wheat
Short 1 wheat futures Owns wheat and wishes to sell
EFP Transaction Trader A
Trader B
Agrees with Trader B to purchase wheat and cancel futures Receives wheat; pays Trader B Reports EFP to exchange; exchange a-djusts books to show that Trader A is out of the market
Agrees with Trader A to sell wheat and cancel futures Delivers wheat; receives payment from Trader A Reports EFP to exchange; exchange adjusts books to show that Trader B is out of the market
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Methods to protect clearinghouse against default of buyers/sellers
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.
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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.
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Initial margin (initial performance bond)
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.
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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.
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Marked-to-the-market
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.
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Performance bond call
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.
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How Trading affects open interest
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. (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.)
3
t = 4
Trader C sells and Trader E buys 1 widget contract.
3
Ending Posi-tions
Trader
Long Position
Short Position
B C D E All Traders
2
1 3
1
2
3
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Leverage with Futures
On futures trading, the only out-of-pocket payment is the margin deposited as a security performance bond. No payments are required for the contract, nor for the underlying assets until the settlement of the contract. This provides an opportunity for leverage. The gold futures buyer is leveraging his/her
$2,000 initial margin into a contract to buy 100 oz of gold in the future, which amounts to $40,000 in today's value. This provides 20 times leverage as compare to buying gold in the spot market. This leverage, however, increases the return volatility. It only takes a small change on the gold price to wipe out the $2,000 initial investment.
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Leverage with Futures
Example : Initial investment required on the gold futures = $2,000
Initial investment required for a spot market purchase
= $40,000
Spot Price
Spot MarketGain or Loss % Return
Futures MarketGain or Loss % Return
$420$410$400$390$380
$2,000 5% $1,000 2.5%0 0%-$1,000 -2.5%-$2,000 -5%
$2,000 100%$1,000 50%0 0%-$1,000 -50%-$2,000 -100%
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The Basis
...is the current cash price of a particular commodity minus the price of a futures contract for the same commodity.
BASIS = CURRENT CASH PRICE - FP
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The Basis (continued)
Table 3.2
Gold Prices and the Basis (July 11)
Contract
Prices
The Basis
CASH JUL (this year) AUG OCT DEC FEB (next year) APR JUN AUG OCT DEC
353.70 354.10 355.60 359.80 364.20 368.70 373.00 377.50 381.90 386.70 391.50
-.40 -1.90 -6.10
-10.50 -15.00 -19.30 -23.80 -28.20 -33.00 -37.80
If the current price of gold in the cash market is $353.70 (July 11) and a futures contract with delivery in December is $364.20. How much is the basis?
-10.50
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The Basis (continued)
Basis
Prices
Present MaturityTime
Futures
Cash
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The Basis (continued)
1. Relation between Cash & Futures
2. SpreadsThe difference between two futures prices (same type of contract) at two different points in time
Basis, Repo rate
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.
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Arbitrage
An Arbitrageur attempts to exploit any discrepancies in price between the futures and cash markets.
• Perfect futures market • No taxes• No transactions costs• Commodity can be sold short
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:
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Price Exchange
Arbitrageur Buys INFY (1105) BSEArbitrageur Sells INFY 1110 NSERiskless Profit 5
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Futures Pricing43
Forwards and Futures: Basic Evaluation Concepts
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.
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Principles of futures contract pricing
There are three main theories of future pricing
• The expectations hypothesis• Normal backwardation• A full carrying charge market
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1. The expectations hypothesis
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.
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Futures Prices and Expected Futures Spot Prices
The expectation model states that the current futures price is equal to the market's expected value of the spot price at period T:
Ft = E(PT)If this model is correct, a speculator can
expect neither to gain nor to lose from a position in the futures market:
E(Profit)= E(PT)- FT= 0
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EX: Suppose that at time period 0, a speculator purchases a futures contract at a price of F, and posts 100% margin in the form of riskless securities.
At contract maturity T, the value of the
margin account will have grown to F0* (1+rf)
At maturity, the value of the futures contract itself will be: (PT - F0).
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The actual rate of return the speculator will earn is
(1+rf)F0 + (PT - F0) (PT - F0)r = --------------------------- -1 = rf + -------- F0 F0
The expected rate of return r is
E(PT) - F0
E(R) = rf + ------------- = rf
F0
If the expectation model is correct.
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Contango and Backwardation
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.
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2. Normal Backwardation
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.
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backwardation in commodity forward markets.avi
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3. A full carrying charge market
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.
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The concept of full-carry market
To the extent that markets adhere to the following equations markets are said to be at “full carry”:
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.
)1( ,00,0 tt CSF
)1( ,,0,0 dnnd CFF
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To determine if a market is at full carry, consider the following example:
Suppose that:
September Gold $410.20December Gold $417.90Bankers Rate 7.8%
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Annualized percentage difference
Step 1: compute the annualized percentage difference between two futures contracts.
• AD = Annualized percentage difference• M = Number of months between the maturity of the futures contracts.
Where
1
12
)(.0
,0 M
F
FAD
N
d
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Step 2: compare the annualized difference to the interest rate in the market.
The gold market is almost always at full carry. Other markets can diverge substantially from full carry.
13
12
20.410$
90.417$ )( AD
0772.0AD
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Spread
A spread is the difference in price between two futures contracts on the same commodity for two different maturity dates:
• This might be the price of a futures contract on wheat for delivery in 3 months.
• This might be the price of a futures contract for wheat for delivery in 6 months.
F0,t = The current futures price for delivery of the product at time t.
F0,t+k = The current futures price for delivery of the product at time t +k.
Spread relationships are important to speculators.
tkt FFSpread ,0,0
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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.
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.
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Cost-of-carry model of futures prices
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.
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The relationship between spot and forward prices
Suppose you buy the corn now for the current cash price of S0 per bushel 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)
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FINANCIAL FUTURES PRICING
Ex: Suppose that the spot price of No. 2 Wheat in a Chicago warehouse is 300 cents per bushel, the yield a one-month T-bill is 6%, and the cost of storing and insuring one bushel of wheat is 4 cents per month. What is the price of a futures contract that has one-month to maturity?
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FINANCIAL FUTURES PRICING Two ways to have wheat in one month:
1. Purchase a one-month wheat futures contract at $F/bushel:
Costs in one month = $F
2. Purchase in spot today and carry it over for one month:
Costs in one month = (300¢ + 4¢)*(1 + 6%/12) = 305.5¢
For the two alternatives to be indifferent, two costs would have to be the same, i.e.,
$F = 305.5¢ or
F = P + C
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To summarize
The Cost-of-Carry Model can be expressed as:
• Storage costs• Insurance costs• Transportation costs• Financing costs
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:
)1( ,00,0 tt CSF
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FINANCIAL FUTURES PRICING
This is an equilibrium condition. If this is not true, then market adjustments will bring back the equilibrium. If F > P+C, a trader could make a riskless
profit by taking a long position in the asset and a short position in the futures contract. Cash and carry arbitrage
If F < P+C, the arbitrage strategy would be to buy the futures and sell the commodity short. Reverse cash and carry arbitrage
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Two arbitrage strategies with Cost-of carry model
Cash-and-carry arbitrage
• When futures are overpriced
Reverse cash-and-carry arbitrage
• When futures are underpriced
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A cash-and-carry arbitrage
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 money2. Sell futures contract3. Buy commodity
4. Deliver the commodity against the futures contract5. Recover money & payoff loan
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Cost of carry Rule 1
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.
)1( ,00,0 tt CSF 0 1
1. Borrow $4002. Buy 1 oz gold3. Sell futures contract
4. Deliver gold against futures contract5. Repay loan
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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%. Buy 1 ounce of gold in the spot market for $400. Sell a futures contract for $450 for delivery of one ounce in one year.
+$400 - 400
0
Total Cash Flow $0 t = 1 Remove the gold from storage.
Deliver the ounce of gold against the futures contract. Repay loan, including interest.
$0
+450
-440 Total Cash Flow
+$10
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Another example
Suppose the stock is trading today at 120 when the risk-free rate of interest is 5%
What should be the forward price of the stock at the end of one year?
120 x 1.05 = 126Now, if the forward/futures price is 128. Is
there any arbitrage possibility? If yes, calculate the arbitrage profit.
Assume The stock is not paying any dividend during the period. Storage cost is NIL No benefit can be derived holding the stock
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A reverse cash-and-carry arbitrage
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 commodity2. Lend money received from short sale3. Buy futures contract
4. Accept delivery from futures contract5. Use commodity received to cover the short sale
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Cost of carry Rule 2
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.
)1( ,00,0 tt CSF 0 1
1. Sell short 1 oz. gold2. Lend $420 at 10% interest3. Buy a futures contract
4. Collect proceeds from loan5. Accept delivery on futures contract6. Use gold from futures contract to repay the short sale
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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%
Transaction Cash Flow
t = 0 Sell 1 ounce of gold short. Lend the $420 for one year at 10%. Buy 1 ounce of gold futures for delivery in 1 year.
+$420 - 420
0
Total Cash Flow $0 t = 1 Collect proceeds from the loan ($420 x 1.1).
Accept delivery on the futures contract. Use gold from futures delivery to repay short sale.
+$462
-450 0
Total Cash Flow +$12
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Another example
Suppose the stock is trading today at 120 when the risk-free rate of interest is 5%
What should be the forward price of the stock at the end of one year?
120 x 1.05 = 126Now, if the forward/futures price is 123. Is
there any arbitrage possibility? If yes, calculate the arbitrage profit.
Assume The stock is not paying any dividend during the period. Storage cost is NIL No benefit can be derived holding the stock
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Summary
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 against futures
Sell asset short; secure proceeds from short sale
Futures Sell futures
Buy futures; accept delivery; return physical asset to honor short sale commitment
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Cost of carry Rule 3Since the futures price must be 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.
)1( ,00,0 tt CSF
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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.
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Spreads and the cost-of-carry
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
Cost-of-Carry Rule 5
Cost-of-Carry Rule 6
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Cost-of-carry rule no 4The distant futures price must be 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.
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.
)1( ,,0,0 dnnd CFF
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Rule No 4
0 1
1. Buy futures contract w/exp
in 1 yrs. 2. Sell futures
contract w/exp in 2 years
3. Contract to borrow $400 from yr 1-2
7. Remove gold from storage8. Deliver gold against 2 yr. futures contract9. Pay back loan
2
4. Borrow $400 5. Take delivery on 1
yr to exp futures contract.
6. Place the gold in storage for one yr.
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Rule No 4
0 1
1. Buy futures contract w/exp
in 1 yrs. 2. Sell futures
contract w/exp in 2 years
3. Contract to borrow $400 from yr 1-2
7. Remove gold from storage8. Deliver gold against 2 yr. futures contract9. Pay back loan
2
4. Borrow $400 5. Take delivery on 1
yr to exp futures contract.
6. Place the gold in storage for one yr.
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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%
Transaction Cash Flow
t = 0 Buy the futures expiring in 1 year. Sell the futures expiring in 2 years. Contract to borrow $400 at 10% for year 1 to year 2.
+$0
0 0
Total Cash Flow $0
t = 1 Borrow $400 for 1 year at 10% as contracted at
t = 0. Take delivery on the futures contract. Begin to store gold for one year.
+$400
- 400
0 Total Cash Flow $0
t = 2 Deliver gold to honor futures contract.
Repay loan ($400 x 1.1)
+$450 - 440
Total Cash Flow + $10
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Rule No 5
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.
If prices were not to conform to cost of carry rule # 5, a reverse cash-and-carry arbitrage profit could be earned.
dnnd CFF ,,0,0 1
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Rule N0 5
0 1
1. Sell futures contract w/exp
in 1 yrs. 2. Buy futures
contract w/exp in 2 years
3. Contract to lend $400 from yr 1-2
7. Accept delivery on exp 2 yr
futures contract 8. Repay 1 oz.
borrowed gold. 9. Collect $400
loan
2
4. Borrow 1 oz. gold 5. Deliver gold on 1
yr to exp futures contract.
6. Invest proceeds from delivery for one yr.
84
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%
Transaction
Cash Flow
t = 0 Sell the futures expiring in one year.
Buy the futures expiring in two years. Contract to lend $440 at 10% from year 1 to year 2.
+$0
0 0
Total Cash Flow $0
t = 1 Borrow 1 ounce of gold for one year.
Deliver gold against the expiring futures. Invest proceeds from delivery for one year.
$0
+ 440 - 440
Total Cash Flow $0
t = 2 Accept delivery on expiring futures.
Repay 1 ounce of borrowed gold. Collect on loan of $440 made at t = 1.
- $450
0 + 484
Total Cash Flow + $34
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What does this all mean?
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.
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Rule No 6
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.
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.
)1( ,,0,0 dnnd CFF
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Market features that promote full-carry market
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.
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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
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Hedging with futures90
Perfect Hedging using futures
A silver manufacturer is concerned about the price of silver. Given the current level of production, he expects to have about 20, 000 ounces of silver ready in next two months.
The current price of silver on May 10 is Rs.1052.5 per ounce, and July futures price is Rs.1068 per ounce, which he believes to be satisfactory price.
But he fears that prices in futures may go down. So he will enter into futures contract. He will sell four futures contracts at MCX where each contract is of 5000 ounces at Rs.1068 for delivery in July.
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Short hedge
Cash market Futures market
May 10 Anticipate the sale of 20, 000 ounces in two months and receive Rs.1052 per ounce
Sell four contracts, 5000 ounces each July futures contract at Rs.1068 per ounce
July 5 Cash price of silver is Rs.1071 per ounce; mfg sales 20, 000 ounces at that rate
Buy four contracts at Rs.1087
Results Profit of Rs. 19 per ounce However, he loses Rs.19 per ounce when he buys the futures contract.
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Cash market Futures market
May 10 If he had sold today: 1052 x 20,000 = 2,10,40,000
Sell : 4x5000x1068 = 2,13,60,000
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.
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A short hedge (situation 1)94
A short hedge (situation 2)95
Long Hedge
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.
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Cash market Futures market
June 1 Needs to buy wood planks inSeptember for $300/MBFto make desired profit.
Buys (goes long) one SeptemberLumber futures contract at $305/MBF.
Sep 1 Cash price rises to $315/MBF. Deepa buys lumber for $315/MBF.
Deepa sells her SeptemberLumber contract at $320/MBF.
Results Deepa pays $15/MBF more for lumber than she wanted to.
However, she gains $15/MBF whenshe sells the futures contract.
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Cash market Futures market
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:Spent $1,650 more
Net profit in futures market:Gained $1,650
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Hedging with futures
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.
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Hedging with futures: Hedging and Basis
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).
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At date 1, B1= S1 – F1
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
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Example on Basis Risk
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
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Hedging in the context of Basis
Calculation using excel
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Suppose, cotton prices have declined so that cash price in June are $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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Hedge ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure.
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Optimal hedge ratio
The number of futures contract per unit of spot contract is not straight forward i.e. it does not match exactly.
In such situation, approach is to choose the number of contracts that minimizes the variance of net profit from a hedged commodity position.
Consider the position of a short hedger who is long one of a particular commodity and short N forward contracts on that commodity.
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Profit from short hedge = (S2-S1)–(F2 – F1) (N) = ∆S - ∆ F * NThe variance of this value is then given asVariance of profit = σ2
∆S + N2 σ2∆F -2N Cov
∆S ∆F
Solving for N,N = (σ∆S/ σ∆F)ρ
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