Futures1

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Forward Contract

Forward Contracts Definition: a contract between two parties for

one party to buy something from the other at

a later date at a price agreed upon today Exclusively over-the-counter

Example: A corn flakes manufacturer(company) and a corn producer (farmer)agreeing to trade in corn produced at a futuredate at a price agreed upon today.

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Futures Contracts

Forward Contract traded in an exchange

Definition: a contract between two parties for oneparty to buy something from the other at a later date

at a price agreed upon today; subject to a daily

settlement of gains and losses and guaranteed

against the risk that either party might default

Exclusively traded on a futures exchange

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Organized Futures Trading

Contract Terms and Conditions contract size

quotation unit

minimum price fluctuation

contract grade

trading hours

Delivery Terms delivery date and time

delivery or cash settlement

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Difference between Futures and

ForwardsFutures Market Forward Market

Location Futures Exchange No fixed Location

Size of Contract Fixed (standard) Depends on Contract

Maturity Fixed (standard) Depends on Contract

Counterparty Clearing House Known Bank or Client

Valuation Marked-to-Market Everyday No unique Method

Variation Margin Daily None

Regulations Regulated by Exchange Self Regulated

Credit Risk Almost Non Existent Depends on Counterparty

Settlement Through Clearing House Depends on Contract

Liquidation Mostly by Offsetting the positions Mostly settled by actual delivery

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Open Interest And Volume

Ex-1Period 1

Trader A Sells one Option Contract and Trader

B buys one Options contractPeriod 2Trader A buys one option contract and trader Csells one

Period 3Trader C Buys one option contract and Trader Bsells one Option Contract.

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Time A B C VolumeOpen

interest

1 Sells 1 Buys 1 1 1

2 Buys 1 Sells 1 1 1

3 Sells 1 Buys 1 1 0

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Ex-2

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Open Interest is a measure of how many Futurescontract exist at any particular time.

It shows the number of long positions not squared off ornumber of short positions not squared off at anyparticular point of time.

Futures contracts are created and destroyed depending

on how trades are matched up

Volume Simply measures how many trades occurred.

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Newspaper

Futures

Ex: Reliance-September

Delivery Month

All contracts of a month expire on the last Thursday ofthe month.

Open high low close

Value No of contracts

Open Interest and Volume

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Problem

On October 1st

Reliance Spot Price is Rs. 1000 Reliance (December Futures/Forward price) = 1050

On November 10th

reliance spot price is 1200 and futures price is 1275

In December at expiration date Reliance trades at 1100

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Forward Market

Date Spot Forward( December contract)

1-Oct 1000 1050 ( Mutually Agreed Price)

November 10th 1200 SO what ?

December (Maturity) 1100 Honor the contract

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Pay Off in Forward Market at

MaturityPayoff of Long futures (if you buy Reliance Forward contract)=Sell price Buy price= Spot price at expiration forward price=1100-1050 =50

Pay off of short futures ( if you sell Reliance Forward contract)=Sell price Buy price= Forward Price Spot price at expiration=1050-1100= -50

Because One contract is for 600 shares. Your profit or loss getsmultiplied by 600 times.

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Futures Market

Date Spot

Futures( December

contract)

1-Oct 1000 1050

November 10th 1200 1275

December

(Maturity) 1100 1100

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Payoff on Futures Contract at

expirationPayoff of Long futures (if you buy Reliance Forwardcontract)

=Sell price Buy price

= Spot price at expiration forward price

=1100-1050 =50

Pay off of short futures ( if you sell Reliance Forwardcontract)

=Sell price Buy price= Forward Price spot price at expiration

=1050-1100= -50

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Payoff of Futures Contract on

November 10

th

Payoff of Long futures = Sell price Buy price

= 1275-1050 =225

Pay off of short futures = Sell price Buy price

= 1050 1275= -225

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Futures Contracts (contd)

A futures contract involves a processknown as marking to market

Money actually moves between accounts

each day as prices move up and down

A forward contractis functionally

similar to a futures contract, however: There is no marking to market Forward contracts are not marketable

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DaySettlement

Price

1 4700

2 4500

3 4650

4 4750

5 4700

The initial margin is set at Rs. 10,000 per contract, while the maintenancemargin is Set at Rs. 8000 per contract. The multiple of each contract is 50.

Calculate the mark-to-market cash flows and the daily closing balances inAccounts of.A) An investor who has gone long at 4600 on day 0.B) An investor who has gone short at 4600 on day 0.C) Calculate the net profit/loss on each of the contracts.

Problem

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Investor Who has gone long at 4600 (initial margin =10,000 and Maintenance margin = 8,000)

Day Settlement Price

Opening

Balance

Mark-to-

Market

Is the balance

< 8000

Margin

Call

Closing

Balance

0 Bought 50 @4600 10000 - - - 10000

1 4700 10000 5000 NO 15000

2 4500 15000 -10000 YES 5000 10000

3 4650 10000 7500 NO 17500

4 4750 17500 5000 NO 22500

5 4700 22500 -2500 NO 20000

Total Profit/Loss 5000

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Investor Who has gone Short at 4600 (Initial margin =10,000 and Maintenance margin = 8,000)

Day

Settlement

Price

Opening

Balance

Mark-to-

Mar

ket

Is the

balance

< 8000

Margin

Call

Closing

Bala

nce

0

Sold 50 @

4600 10000 - - - 10000

1 4700 10000 -5000 Yes 5000 10000

2 4500 10000 10000 NO 20000

3 4650 20000 -7500 NO 12500

4 4750 12500 -5000 Yes 2500 10000

5 4700 10000 2500 NO 12500

Total

Profit/Loss -5000

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BASIS

The difference between spot price andfutures price is called Basis.

Basis= Spot Price - Futures Price

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Reliance Spot and Futures Prices

Futures a t Pr ce

500

520

540

560

580

600

620

28 27 24 23 22 21 20 17 16 15 14 13 10 9 8 7 6 2 1

e to Maturty

Futures_Price

S O PR

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Behavior of Basis

When the futures price is at expiration, thefutures price of reliance and spot price ofreliance must be same.

That is the basis must be zero.

This behavior of basis over time is calledconvergence

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When basis is constant you get perfecthedge

Hedge 1; Long in spot and sell in futures

Spot Price Futures Price Basis

before maturity 10 15 -5

before Maturity 20 25 -5

Profit/Loss 10 -10

Hedge 2; Short in spot and buy in futures

Spot Price Futures Price BasisSome time Bef. Mat 10 15 -5

Before Maturity 20 25 -5

Profit/Loss -10 10

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Basis Risk

Basis risk arises because basis does not remain constant

We know that Basis at maturity is always equal to ZERO.

At the time of purchase of futures contract the basis is eithernegative or positive

You have either positive or negative basis at start and if you hold thecontract until maturity basis will become zero

Implies Basis rarely will be constant during the holding period of thecontract.

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Basis Risk

Nature Ofhedge Basis At the start

Positive Negative

BUY (Futures)and Hold until

maturity Favorable AdverseSELL (Futures)

Hold UntilMaturity Adverse Favorable

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When Basis is negative at start


Spot PriceFuturesPrice Basis Total P/L

before mat. 10 15 -5

At maturity 20 20 0

Profit/Loss 10 -5 5


Spot PriceFuturesPrice Basis

Before Mat. 10 15 -5

At Maturity 20 20 0

Profit/Loss -10 5 -5

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When Basis is Positive at start


Spot PriceFutures

Price Basis Total P/L

20 15 5

At maturity 20 20 0

Profit/Loss 0 -5 -5


Spot PriceFutures

Price Basis

20 15 5

At maturity 20 20 0

Profit/Loss 0 5 5

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Basis Risk

Nature Ofhedge Basis At the start

Positive Negative

BUY (Futures) Favorable Adverse

SELL (Futures) Adverse Favorable

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How are Futures PricesDetermined

How to determine Futures Prices.

How are Futures prices related to Spot

Price.

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Models of Futures Prices

Model No 1

Cost of Carry Model

According to this model futures pricedepend on the cash price of a commodityand the cost of storing the underlying

goods from the present to the deliverydate of the futures contract.

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Cost of Carry Model

The cost of carry model in perfect markets.

The cost of carry or carrying charge is the total cost tocarry a good forward in time.

For example, wheat on hand in June can be carriedforward to, or stored until, December

Carrying charges fall into four basic categories.

Storage Costs Insurance Costs

Transportation Costs

Financing Costs

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Cost of Carry Model

The carrying charge reflects only the charges involved in carrying acommodity from one time or one place to another.

The carrying charges do not include the value of commodity itself.

So, if gold costs $400 per ounce and the financing rate is 1 percentper month (ignoring other costs),

the financing charge for carrying the gold forward is $ 4 per month(1%X$400)

According to cost of carry model

Forward Price( maturing in 1 month) = 400 +4 = $404

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Cost of Carry Model

If FP > spot price + cost of carry

Investors will indulge in cash and carry arbitrage

Buy underlying now and sell futures and reverse thetrades at maturity

IF FP < spot price + cost of carry

Investors will indulge in reverse cash and carryarbitrage

Short Sell underlying asset and buy futures now andreverse the trades at maturity

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Cost of Carry Model

Assuming Perfect markets and no arbitrageconditions

FP = spot price + cost to carry

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Cost of Carry Model

If futures price follow cost of carry model then basis is negative.

FP = Spot + cost of carry.

Since Futures price is always more than spot price: Basis is alwaysnegative according to cost of carry model.

Given FP = Spot price (SP) + Cost to carry (X)

Basis = Spot price Futures price= Spot price (spot price + x)

= -x

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Contango Market

When futures price is higher than cashprice then the market is said to be inContango.

Orwhen Basis is negative then Market is said

to be in Contango.

OrWhen the market follows Full cost of carry

model then it is called Contango Market.

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Can the Basis be Positive?

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Convenience Yield The benefit or premium associated with holding an underlying product or

physical good, rather than the contract or derivative product.

An example would be purchasing physical bales of wheat rather than futurecontracts. Should their be a sudden drought and the demand for wheatincreases, the difference between the first purchase price of the wheatversus the price after the shock would be the convenience yield.

When an asset has convenience yield then full cost of carry model does nothold.

Convenience Yield is a return on holding an Asset

Anybody who has use of an asset for consumption can derive ConvenienceYield.

Ex: Food processor might Derive a convenience yield by holding on tocommodity.

When Futures price is below cash price or spot price then you need to doreverse cash and carry arbitrage to exploit it.

But because (say soya beans) has convenience yield there will be no onewilling to lend. Hence short selling of beans will not be possible.

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Backwardation

When basis is positive then the market is said to be inbackwardation.

Backwardation is the opposite of contango.

Backwardation says that as the contract approachesexpiration, the futures contract will trade at a higher pricecompared to when the contract was further away fromexpiration. This is said to occur due to the convenienceyield being higher than the prevailing risk free rate.

Expectation Model

The price of the Futures price is the expected FuturesSpot Price.

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Role of Speculators andExpectation Model

If the Futures price were $15 , exceedingthe expected Futures spot price of $10.Then speculators would sell futures at $

15 and on maturity they would buy backthe futures at $10 and make a profit.

In effect speculators would make sure thatFutures price is equal to expected FutureSpot Price.

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Who would trade in Futures?

Futures trading will be of interest to those who wish to:

1) Price Risk Transfer - Hedging

2) Invest- Speculating

3) Arbitrage

4) Leverage

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Example Hedging (Futures)

Company A must Pay 1 Million in September for imports from Britain. Company B will receive 3 Million in September from exports to Britain

Current Exchange Rate Rs/ = 70.2039 September Futures Price Rs/ = 69.9147 in September at expiration spot price is 71

Size of Futures Contract 62500

Company As Hedging Strategy Positing in the SPOT (pay=SHORT) Buy (Long) Position in 16 Futures Contracts. This locks in the exchange rate of

69.9147 for the 1 Million it will pay

Company Bs Hedging Strategy Position in the spot (receive=LONG) Sell (Short) Position in 48 Futures Contracts. This locks in an exchange rate of

69.9147 for the 3 Million it will receive.

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Company A

Short position inCash Market

Long Position in Futuresmarket

Time Spot Futures Basis Profit/Loss

Right now 70.2039 69.9147 0.289

At maturity 71 71 0

Pay off -0.7961 1.0853 0.2892

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Company B

Long position inCash Market

Short Position in Futuresmarket


Right now 70.2039 69.9147 0.2892

At maturity 71 71 0

Pay off 0.7961 -1.0853 -0.2892

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Total profit in spot = .7961*3,000,000

=2,388,300

Total Loss in futures = -1.0853* 48*62500

=-3,255,900

Net Loss =867,600

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Hedge Ratio

Can I hedge the loss due to basis Risk ?

A ratio comparing the value of futures contracts purchased or sold tothe value of the cash commodity being hedged.

Say you are holding $10,000 in foreign equity, which exposes you tocurrency risk. If you hedge $5,000 worth of the equity with acurrency position, your hedge ratio is 0.5 (50 / 100). This means that50% of your equity position is sheltered from exchange rate risk.

The hedge ratio is important for investors in futures contracts, as it willhelp to identify and minimize basis risk.

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Company B

Long position in

Cash Market

Short Position in Futures

market


Right now 70.2039 69.9147 0.2892

At maturity 71 71 0

Pay off 0.7961 -1.0853 -0.2892

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Instead of 48 futures contracts If CompanyB had sold 35.20943 contracts then itwould have resulted in perfect hedge.

Loss in futures =35.20943*62500* (-1.0853)

=-2,388,300

Which is exactly equal to the profit in spot.

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Hedge Ratio = Futures position/UnderlyingAsset Position

Hedge Ratio =35.20944/48

=0.73353 (.7961/1.0853)

=(Change in Spot/Change in futures)

Hence: 35.209 = 0.73* 48 ;

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How to estimate Hedge ratio

Change (St)= alpha + beta *change (Ft) + error term

Change (St) = change in cash price on day t

Change (Ft) = change in futures price on day t

Beta gives the hedge ratio.

Beta = Covariance (S,F) /variance (F) orBeta = correlation coefficient (S,F)* standard deviation (S)/

Std. dev of (F)

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Speculators

Exploit the differences in own forecast andmarket expectations.

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Speculation Using Currency futures Problem

Rs/$ spot = 45.1 March futures = 45.30 June Futures = 45.34

September futures = 45.60

Mr. A, a forex dealer, holds the view that the market iswrong and the $ will actually depreciate.

Another speculator Mr. N agrees with the market thatthe dollar will appreciate but thinks that the market isover estimating the extent of appreciation

What strategy should they adopt

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Sell futures now and buy back futures later asthey expect the dollar to depreciate.

Calculate profit and loss if

if on September 10th

following rates prevail. Scenario 1

Spot Rs/$ = 45.5

September Future = 45.70

Scenario 2

Spot Rs /$ = 45.3 September Future = 45.4

Assume contract size to be 1 million dollars.

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Scenario 1

Pay off = Sell price buy price

=45.6-45.7 = - .1 * 1 million = Loss of 1 lakh

Scenario 2

Pay off = sell price buy price

=45.6-45.4 = .2 * 1 million = profit of 2 lakhs

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