futures ppt

7/28/2019 Futures PPT

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FUTURES PRICING

THEORIES &CHARACTERISTICS


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Futures Trading is animportant economicactivityfor the development of any Economy. It isthefirst formof Derivatives Trading.

Being aspecialized field, to be a successful marketoperator (Speculator, Arbitrageur, Trader, Investor orHedger) one must haveprofessional expertise and

sound knowledgeof the functioning of the FuturesMarkets.


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Futures Prices

In this chapter, we discuss how futurescontracts are priced. This chapter is organizedinto the following sections:

1. Reading Futures Prices2. The Basis and Spreads

3. Models of Futures Prices


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READING THE

FUTURES PRICES


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Futures prices are published inall important Magazines, NewsPapers and Journals.

These prices are reported

in Standardized Format.


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FUTURES NEWSPAPER QUOTES(sample)

Open High Low Settle Change High Low OpenInterest

GOLD

Aug 293 294 292.45 Xxxxxx Xxxxx xxxxx Xxxxx XxxxxxSep 296 297 296 Xxxxxx Xxxxx xxxxx Xxxxx Xxxxxx

Oct 300 302.5 299.5 Xxxxxx Xxxxx xxxxx xxxxx Xxxxxx

Nov 304 306.55 303.55 Xxxxxx Xxxxx xxxxx xxxxx Xxxxxx

Dec 307 309.55 306 xxxxxx Xxxxx xxxxx xxxxx Xxxxxx


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Terminology

Expiry Cycle: This appears in the first column on

the left side of the table. Every contract is given anexpiry cycle by the Exchange on the Contract that istraded. When the delivery date is reached, theContract is dropped from the table.

Open: The Open Column refers to the price at whichthe first contract of the day was transacted or in otherwords the price for the days first trade which

occurs during the designated time period is theOpen Price.

High: The Highest price of the contract recordedduring the day.

Low: The Lowest Price of the contract recorded

during the day.


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TERMINOLOGY

Settlement Price :Settlement price is theprice that contracts are traded at the end ofthe trading day.

Trading Session Settlement Price :New

term used to reflect round-the-clock trading.

Open Interest :Open interest is the numberof futures contracts for which delivery is

currently obligated.


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BASIS

The Basis is an important term in Futures Trading.The Basis is the difference between theCurrent/Cash/Spot Price and the Futures Price of aparticular asset at a Specified Location.

The Futures prices are different from places to

places. Therefore Basis refers to the differencebetween the Cash Price and the nearby Futures priceof the Contract.

When the Futures Contract is at Expiration, theFutures Price and the Spot Price of an Asset becomesthe SAME. This behaviour of the Basis over the time isknown as CONVERGENCE.


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Spreads

Where

F0,t = The current futures price for delivery of the productat time t.

This might be the price of a futures contracton wheat for delivery in 3 months.

F0,t+k= The current futures price for delivery of theproduct at time t +k.

This might be the price of a futures contractfor wheat for delivery in 6 months.

Spread relationships are important to speculators.

tkt FFSpread ,0,0

Spread

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


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Spreads

Suppose that the price of a futures contract on wheat fordelivery in 3 months is Rs. 4000 per QuintalSuppose further that the price of a futures contract onwheat for delivery in 6 months is Rs.4500 per Quintal.What is the spread?

tFktFSpread ,0,0

500.4000.4500. RsRsRsSpread


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Repo Rate

Repo Rate

The repo rate is the finance charges faced bytraders. The repo rate is the interest rate onrepurchase agreements.

A Repurchase Agreement

An agreement where a person sells securitiesat one point in time with the understanding

that he/she will repurchase the security at acertain price at a later time.

Example: Pawn Shop.


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Models of Futures Prices

Cost-of-Carry Model

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 rateofinterest.


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CARRYING COSTS

Storage Costs

Insurance Costs

Transportation Costs

Financing Costs.


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Cash-and-Carry Arbitrage

A cash-and-carry arbitrage occurs when atrader borrows money, buys the goods todayfor cash and carries the goods to the expirationof the futures contract. Then, delivers the

commodity against a futures contract andpays off the loan. Any profit from this strategywould be an arbitrage profit.

0 1

1.Borrow money2. Sell futures contract3. Buy commodity

4. Deliver the commodityagainst the futures contract

5. Recover money & payoff

loan


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Reverse Cash-and-Carry Arbitrage

A reverse cash-and-carry arbitrage occurs when a

trader sells short a physical asset. The traderpurchases a futures contract, which will be used tohonor the short sale commitment. Then the traderlends the proceeds at an established rate of interest.

In the future, the trader accepts delivery against thefutures contract and uses the commodity received tocover the short position. Any profit from this strategywould be an arbitrage profit.

0 1

1. Sell short the commodity

2. Lend money received

from short sale

3. Buy futures contract

4. Accept delivery from futures

contract

5. Use commodity received

to cover the short sale


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Arbitrage StrategiesTable 3.5

Transactions for Arbitrage Strategies

Market Cash-and-Carry Reverse Cash-and-

Carry

Debt Borrow funds Lend short sale

proceedsPhysical Buy asset and

store; deliver

against futures

Sell asset short;

secure

proceeds from

short saleFutures Sell futures Buy futures; accept

delivery; return

physical asset to

honor short sale

commitment


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Cost-of-Carry Model

),01(0,0 tCStF

Where:

S0 = the current spot price

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

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

The cost of carrying or storing includes:

1. Storage costs

2. Insurance costs

3. Transportation costs

4. Financing costs

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


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Cost-of-Carry Rule 1The futures price must be less than or equal to the spot price ofthe commodity plus the carrying charges necessary to carry the

spot commodity forward to delivery.

Cash-and-Carry Gold Arbitrage TransactionsPrices for the Analysis:

Spot price of gold$400

Future price of gold (for delivery in one year) $450Interest 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 deliv-ery 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 futu-rescontract.

Repay loan, including interest.

$0+450

-440

Total Cash Flow+$10

)1( ,00,0 tt CSF


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Cost-of-Carry Rule 1

0 1

1. Borrow $4002. Buy 1 oz gold3. Sell futures contract

4. Deliver gold againstfutures contract5. Repay loan


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The Cost-of-Carry Rule 2Since the futures price must be either less than or equal to the

spot price plus the cost of carrying the commodity forward by ruleAnd the futures price must be greater than or equal to the spot

price plus the cost of carrying the commodity forward by rule .

The only way that these two rules can reconciled so there is noarbitrage opportunity is by the cost of carry rule .

Rule #2: the futures price must be equal to the spot price plus thecost of carrying the commodity forward to the delivery date of the

futures contract.)1( ,00,0 tt CSF

If prices were not to conform to cost of carry rule #2, a cash-and carryarbitrage profit could be earned.

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


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Spreads and The Cost-of-Carry

As we have just seen, there must be a relationshipbetween the futures price and the spot price on thesame commodity.

Similarly, there must be a relationship between the

futures prices on the same commodity with differingtimes to maturity.

The following rules address these relationships:

Cost-of-Carry Rule 3Cost-of-Carry Rule 4



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The Cost-of-Carry Rule 3The distant futures price must be less than or equal to the nearbyfutures price plus the cost of carrying the commodity from thenearby delivery date to the distant delivery date.

)1( ,,0,0 dnnd CFF

where d > n

F0,d= the futures price at t=0 for the distant deliverycontract 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=nto t=d.

If prices were not to conform to cost of carry rule # 3, a cash-and-carry

arbitrage profit could be earned.


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Spreads and the Cost-of-Carry

Table 3.6Gold 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 $450Interest rate (to cover from year 1 to year 2) 10%


t = 0 Buy the futures expiring in 1 year.Sell the futures expiring in 2 years.Contract to borrow $400 at 10% for year1 to year 2.

+$000

Total Cash Flow$0

t = 1 Borrow $400 for 1 year at 10% ascontracted att = 0.Take delivery on the futures contract.Begin to store gold for one year.

+$400

- 4000

Total Cash Flow$0

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

+$450- 440

Total Cash Flow +$10

Table 3.6 shows that the spread between two futures contracts

can not exceed the cost of carrying the good from one deliverydate forward to the next, as required by the cost-of-carry rule #3.


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The Cost-of-Carry Rule 3

0 1

1. Buy futures contract w/expin 1 yrs.2. Sell futures contract w/exp

in 2 years3. 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 $4005. Take delivery on 1 yr to exp

futures contract.6. Place the gold in storage for oneyr.


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

Or alternatively, the distant futures price must be greaterthan or equal to the nearby futures price plus the cost ofcarrying the commodity from the nearby futures date to

the distant futures date.

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

dnnd CFF ,,0,0 1


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The Cost-of-Carry Rule 4Table 3.7 illustrates what happens if the nearby futures

price is too high relative to the distant futures price. When

this is the case, a forward reverse cash-and-carry arbitrageis possible.

Table 3.7Gold Forward Reverse Cash-and-Carry Arbitrage

Prices for the Analysis:

Futures price for gold expiring in 1 year $440Futures 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.Buy the futures expiring in two years.Contract to lend $440 at 10% from year 1toyear 2.

+$000

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 oneyear.

$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.

- $4500

+ 484

Total Cash Flow +$34


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0 1

1. Sell futures contractw/exp in 1 yrs.

2. Buy futures contractw/exp in 2 years3. Contract to lend$400 from yr 1-2

7. Accept deliveryon exp 2 yr

futures contract

8. Repay 1 oz.borrowed gold.

9. Collect $400loan

2

4. Borrow 1 oz. gold5. Deliver gold on 1

yr to exp futurescontract.6. Invest proceeds

from delivery forone yr.


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Since the distant futures price must be either less than or equal tothe nearby futures price plus the cost of carrying the commodityfrom the nearby delivery date to the distant delivery date by rule#3.

And the nearby futures price plus the cost of carrying thecommodity from the nearby delivery date to the distant deliverydate can not exceed the distant futures price by rule #4.

The only way that rules 3 and 4 can be reconciled so there is noarbitrage opportunity is by cost of carry rule #5.


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The distant futures price must equal the nearbyfutures price plus the cost of carrying thecommodity from the nearby to the distantdelivery date.

If prices were not to conform to cost of carry rule#5, a cash-and-carry arbitrage profit or reversecash-and-carry arbitrage profit could be earned.

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

)1( ,,0,0 dnnd CFF


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Implied Repo RatesIf we solve for C0,tin the above equation, and assume that

financing costs are the only costs associated with holding anasset, the implied cost of carrying the asset from one time pointto another can be estimated. This rate is called the implied reporate.

The Cost-of-Carry model gives us:

tC ,0Solving for

And

)1( ,00,0 tt CSF

)1( ,00

,0t

tC

S

F

tt

CS

F,0

0

,01


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Implied Repo Rates

Example: cash price is $3.45 and the futures price is$3.75. The implied repo rate is?

086956.0145.3$

75.3$

That is, the cost of carrying the asset from today until the expirationof the futures contract is 8.6956%.

tt

CS

F,0

0

,01


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The Cost-of-Carry Model inImperfect Markets

In real markets, no less than four factorscomplicate the Cost-of-Carry Model:

1. Direct transactions costs

2. Unequal borrowing and lending rates3. Margin and restrictions on short selling

4. Limitations to storage


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Transaction Costs

Transaction Costs

Traders generally are faced with transaction costs whenthey trade. In this case, the profit on arbitragetransactions might be reduced or disappear altogether.

Types of Transaction Costs:

Brokerage fees to have their orders executed

A bid ask spread

A market maker on the floor of the exchange needsto make a profit. He/She does so by paying oneprice (the bid price) for a product and selling it for ahigher price (the ask price).


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Unequal Borrowing & LendingRates

Thus far we have assumed that investors canborrow and lend at the same rate of interest.Anyone going to a bank knows that thispossibility generally does not exist.

Incorporating differential borrowing and lendingrates into the Cost-of-Carry Model gives us:

Where:CL= lending rateCB= borrowing rate

)1)(1()1)(1( 0,00 BtL CTSFCTS


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Unequal Borrowing & Lending RatesTable 3.11

Illustration of No-Arbitrage Boundswith Differential Borrowing and Lending Rates


Spot price of gold

$400Interest rate (borrowing)

12%Interest rate (lending)

8%Transaction costs (T)

3%

Upper No-Arbitrage Bound with Transaction Costs and a Borrowing Rate

F0,t < S0(1 +T)(1 + CB ) = $400(1.03)(1.12) = $461.44

Lower No-Arbitrage Bound with Transaction Costs and a Lending Rate

F0,t> S0(1 BT)(1 + CL ) = $400(.97)(1.08) = $419.04


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Restrictions on Short Selling

Thus far we have assumed that arbitrageurs can sell shortcommodities and have unlimited use of the proceeds.

There are two limitations to this in the real world:

It is difficult to sell some commodities short.

Investors are generally not allowed to use allproceeds from the short sale.

How do limitations on the use of funds from a short saleaffect the Cost-of-Carry Model?

We can examine this by editing our transaction cost anddifferential borrowing Cost-of-Carry Model as follows:


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Restrictions on Short Selling

The transaction cost and differential cost of borrowingmodel is as follows:

We modify this by recognizing that you will not get all ofthe proceeds from the short sale. You will get some

portion of the proceeds.

)1)(1()1)(1( 0,00 BtL CTSFfCTS

)1)(1()1)(1( 0,00 BtL CTSFCTS

Where:

= the proportion of funds received


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Restrictions on Short SellingTable 3.12 illustrates the effect of limitations on the use of short

sale proceeds.Table 3.12

Illustration of No-Arbitrage Boundswith Various Short Selling Restrictions


Spot price of gold$400

Interest rate (borrowing)

12%

Interest rate (lending)

8%Transaction costs (T)

3%

Upper No-Arbitrage Bound with Transaction Costs and a Borrowing Rate

F0,t < S0(1 +T)(1 + CB ) = $400(1.03)(1.12) = $461.44

Lower No-Arbitrage Bound with Transaction Costs and a Lending Rate, f= 1.0

F0,t > S0(1 BT)(1 + fCL ) = $400(.97)[1 + (1.0)(.08)] = $419.04


F0,t > S0(1 BT)(1 + fCL) = $400(.97)[1 + (.75)(.08)] = $411.28


F0,t> S0(1 BT)(1 + f CL ) = $400(.97)[1 + (0.5)(.08)] = $403.52


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Restrictions on Short SellingThe effect of the proceed use limitation is towiden the no-arbitrage trading bands.

Futures Price

Time

$403.52

$461.44


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Limitations on Storage

The ability to undertake certain arbitrage transactionsrequires storing the product. Some items are easier tostore than others.

Gold is very easy to store. You simply rent a safe depositbox at the bank and place your gold there for safekeeping.

Wheat is moderately easy to store.

How about milk or eggs?

They can be stored, but not for long periods of time.

To the extent that a commodity can not be stored, or haslimited storage life, the Cost-of-Carry Model may not hold.


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How Traders Deal with Market Imperfections

The costs associated with carrying commodities forwardvary widely among traders.

If you are a floor trader, your transaction costs will be verylow. If you are a farmer with unused grain storage on your

farm, your cost of storage will be very low.

Individuals with lowest trading costs (storage costs, andcost of borrowing) will have the most profitable arbitrageopportunities.

The ability to sell short varies between traders.


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Convenience Yield

When there is a return for holding aphysical asset, we say there is aconvenience yield.

A convenience yield can cause futuresprices to be below full carry.

In extreme cases, the cash price canexceed the futures price.

When the cash price exceeds the futuresprice, the market is said to be inbackwardation.

F t P i d


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Futures Prices andExpectations

If futures contracts are priced appropriately, the current futuresprice should tell us something about what the spot price will beat some point in the future.

There are four theories about futures prices and future spotprices:

Expectations or Risk Neutral Theory

Normal Backwardation

Contango

Capital Asset Pricing Model (CAPM)

Speculators play an important role in the futures market, theyensure that futures prices approximately equal the expectedfuture spot price.


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Expectations or Risk NeutralTheory

The Expectations Theory says that the futures price equalsthe expected future spot price.

Where

=the expected future spot price

)( 0,0 SEF t

)( 0SE

N l B k d ti


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Normal Backwardation

The Normal Backwardation Theory says that futures markets areprimarily driven by hedgers who hold short positions. Forexample, farmers who have sold futures contracts to reduce theirprice risk.

The hedgers must pay speculators a premium in order to assumethe price risk that the farmer wishes to get rid of.

So speculators take long positions to assume this price risk.They are rewarded for assuming this price risk when the futures

price increases to match the spot price at maturity.

So this theory implies that the futures price is less than theexpected future spot price.

)( 0,0 SEF t

C t


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Contango

The Contango Theory says that futures markets are

primarily driven by hedgers who hold long positions. Forexample, grain millers who have purchased futurescontracts to reduce their price risk.

The hedgers must pay speculators a premium in order toassume the price risk that the grain miller wishes to getrid of.

So speculators take short positions to assume this pricerisk. They are rewarded for assuming this price risk whenthe futures price declines to match the spot price at

maturity.So this theory implies that the futures price is greaterthan the expected future spot price.

)( 0,0 SEF t

C it l A t P i i M d l


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Capital Asset Pricing Model(CAPM)

The CAPM Theory is consistent with the NormalBackwardation Theory, the Contango Theory, and theExpectations Theories.

This model is applied to all kinds of financialinstruments. In general Higher the Risk, Higher will be theexpected return.

The CAPM model leads to the conclusion that there are twotypes of RisksSYSTEMATIC & UNSYSTEMATIC

Unsystematic Risk can be eliminated by holding a welldiversified Portfolio. Systematic Risk cannot be diversifiedaway.

So as per this model, the investors should be compensatedonly for Systematic Risk.

futures ppt

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