Chp02 Futures Markets

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    Copyright K.Cuthbertson and D.Nitzsche1

    Version 1/9/2001

    FINANCIAL ENGINEERING:

    DERIVATIVES AND RISK MANAGEMENT(J. Wiley, 2001)

    K. Cuthbertson and D. Nitzsche

    LECTURE

    Futures Contracts

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    Basic Concepts

    Speculation

    Arbitrage

    Hedging

    Marking to Market (Margin Account)

    Topics

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    Basic Concepts

    Topics

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    Spot and Futures Markets

    Futures contract is an agreement to buy or sell something in the future at a

    price agreed today.

    There is a spot/cash asset underlying the futures contract

    (eg. can have a futures written on live hogs/oil/stocks)

    Let S = Spot/Cash price

    S = price for delivery today(in cattle market)

    Futures prices F are continuously quoted and change from second tosecond (and moves almost one-for-one with movements in S)

    But it is the futures contract you are buying and selling not the underlyingasset itself (e.g. they are traded on different exchanges - e.g. NYSE andCBOT)

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    FUTURES CONTRACT

    Futures Price F0=$100 on live hogs, quoted today (1st Jan) with DeliveryMonth in say September

    Buy = Long Futures

    -Agreed a (legal) contract to buy the underlying (eg, 1-live hog) inthe delivery month at F0 = $100

    (IF the contract is held to maturity)

    Sell = Short Futures

    -Agree to sell the underlying (1-live hog) in the delivery month at, F0=100 ( IF the short contract is held to maturity)

    (You will be notified by the exchange a few days before the maturity date ofthe contract, that on your particular contract delivery is going to takeplace

    - in order that you can have your hogs ready and looking good.

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    FUTURES CONTRACT

    No payment made today ( only a deposit to guarantee youwill not quit on the deal - this is know as a margin payment

    AND IS NOT THE FUTURES PRICE - see later).

    This means that futures provide LEVERAGE, in that aspeculator can enter into a futures contract whose valuechanges with that of the underlying stocks, but she does nothave to spend any of her own money at t=0 !

    The clearing house/futures exchange acts as an intermediarybetween buyers and sellers (and keeps a record of alltransactions)

    Analytically: Care must be taken to state whether youranalysis involves holding the futures to maturity or buyingthen selling prior to maturity

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    Why does F change between 1st Jan and 1st Feb ?

    As we see later arbitrageurs ensure that F changes as theprice of hogs changes in the spot market S.

    If S increases (falls) then F will increase (fall)- almost $1 for $1 over short horizons (e.g. 1 - 3 months)

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    Table 2 : Forward and Futures Contracts

    FORWARDS

    Private (non-marketable)contract between twoparties

    Delivery or cashsettlement at expiry

    Usually one delivery date

    No cash paid until expiry

    Negotiable choice ofdelivery dates, size ofcontract

    FUTURES

    Traded on an exchange

    Contract is usually closed outprior to maturity

    Range of delivery dates

    Cash payments into (out of)margin account, daily

    Standardised Contract

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    FINANCIAL FUTURES MARKETS

    Money market instruments:

    3-mth Euro$ Deposits90-day US T-bills

    3-mth Sterling, DM, deposits

    Bonds

    US T-bond, UK Gilt, German

    Bund. Stock Indexes

    S&P 500, FTSE100

    Currencies

    DM, Sterling, Yen,

    Mortgage pools (GNMA)

    LIFFE

    CBOT(IMM) CMEN.Y. Futures Exch.

    Phil. Exch.

    Singapore Int Exch.

    Hong Kong

    Tokyo\Osaka

    Pacific St. Ex. (San F.)

    Sydney Fut. Exch.

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    FUTURES CONTRACT

    Most contracts are closed out prior to thematurity/delivery date ( -see also hedging, later)

    Note that if on 1st Jan you bought a Sept-futures contractat F0then

    you can get out of this contract before maturity simply byselling this Sept-futures contract on say 1st Feb

    at whatever price F1is being quoted for the Sept-contracton 1st Feb. Then nobody delivers anything at maturity.

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    Who Uses Futures ?

    Speculation with futures

    Buy low, sell high - risky ( naked/open position)

    Hedging with futures

    eg.In Jan, farmer wants to lock in sale price of his hogs which willbe fat by Sept

    - In Jan he sells hog futures at F0=$100 with maturity date of Sept - ifhe holds contract to maturity he delivers his hog in Sept andreceives the $100 (for certain) - ie. even if hogs in (spot) cattle marketare selling for $10 .

    Arbitrage

    Spot and futures prices are linked by the actions of arbitrageurs andS and F move almost one-for-one - latter is useful for hedgers (seelater)

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    Table 2.4: Futures: Price Quotes

    CORN (CBT) 5,000 bu (cents per bu.)

    (1) (2) (3) (4) (5) Lifetime Open

    Open High Low Settle Change High Low Interest

    Sept 1821

    2 1831

    4 1791

    4 1801

    2 - 21

    4 2651

    2 1781

    4 132,493

    Dec 19412 195 191

    14 192

    14 - 2 1/2 279 190 176,843

    Mar 01 20612 206 203 204

    14 - 2

    14 279 202 37,875

    Source : Wall Street Journal Thursday 27thJuly 2000.

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    Speculation With Futures

    Purchase at F0 = 100Hope to sell at higher price later F1= 110

    Close-out position before delivery date.

    Obtain Leverage (ie. initial margin is low)

    Example:Leeson: Feb 95, Long 61,000 Nikkei-225index futures (underlying value = $7bn). Nikkei felland he lost money (lots of it) - he was supposed to be

    doing riskless index arbitrage not speculating

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    Figure 2.3 : Speculation with futures

    Futures price

    Profit/Loss per contract

    $10

    -$10

    0

    Long future

    Short future

    F2= 110

    F2= 90

    F1=

    100

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    Payoffs: Direction Vectors

    Long Futures

    or, Long Spot

    Short Futures

    or, Short Spot

    +1

    -1

    -1

    +1

    F increase

    then profit increasesF increase

    then profit decrease

    Underlying,S

    Profit/Loss Profit/Loss

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    ARBITRAGEwith

    FUTURES

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    ARBITRAGE AT MATURITY

    At expiry (T) we must have FT= ST

    otherwise riskless arbitrage profits could be made

    EG. Suppose 1-day before maturity

    FT = 100 > ST =98

    Then buy low at S=98 in cattle market , and at same timesell one future contract at F = 100.

    One day later deliver the hog in the futures contract and collectF=$100 (at maturity).

    This is (virtually) riskless.

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    Figure 2.7 : Backwardation and Contango

    Stock price, St

    For simplicity we assume that the spot price remains constant. In practise, Sandhence Fwill fluctuate as you approach Tbut with Ft> Stif the market is in contanand F

    t

    < St

    if the market is in backwardation.

    T

    Forward price in contango : F> S

    Forward price in backwardation : F< S

    0

    At T, ST= FT

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    ARBITRAGE(at t

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    ARBITRAGE: Pricing a Futures Contract

    Borrow and purchase stock today is

    equivalent to having the stock in 3-mnths

    = SYNTHETIC FUTURE

    ( Note: No own funds used to create the synthetic )

    Cost of synthetic future, SF = S ( 1 + r.T ) = $101

    Arbitrage ensures quoted futures price equals SF

    F = S ( 1 + r .T ) = $101

    Futures Price = Spot price + cost of carry

    Cost of Carry = S rT = $1

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    Hedging with Futures

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    Hedging with Futures

    Arbitrageurs ensure F and S are nearly perfectlypositively correlated and move $1 for $1.

    F = S ( 1 + r .T ) = S (1.01)

    so approx:

    (F1- F0) = (S1- S0) ie. dollar for dollar

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    Hedging with Futures

    F and S are positively correlated

    Create a negative correlation If you are long spot( ie. own 1-share) then short the futures

    contract ( on the share) to offset the risk in spot/cash market

    1) Hope that the loss in the cash/spot market is (partly) offset bygain on the futures (dollar for dollar)

    or,

    2) Final Value = Cash Market Value + gain on futures, locks in aknown price

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    Hedge = Long Underlying + Short Futures

    LongUnderlying

    Stock+

    Short

    Futures

    Hedge=0 0

    +1

    +1

    -1

    -1

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    Own (long) 1-share Spot price S0= $100Fear price fall over next 3-mths

    3-month futures contract has current price, F0= $101

    AIMS:

    1) To offset some of the loss in S by profit on F or,

    2) To lock in a final value of F0= $101

    Assume: F and S are perfectly (positively) correlated

    Strategy: Long share + short one futures contract

    Simple Hedging

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    Simple Hedging (S0 = $100, F0 = $101)

    1) Loss in spot market offset by gain on the futures

    3 MONTHS LATER(Spot Price has fallen)

    Spot Price S1= $90 Futures Price F1= $90

    Note that we have assumed the contract is closed outjust before maturity so that S

    1

    = F1

    Gain on Futures = (101 - 90) = ( F0- F1) = $11

    Loss on the spot = (100 - 90) = (S0- S1) = $10

    Net Profit = ( F0- F1 ) - ( S0- S1) = 11 - 10 = $1

    Note that you cannot guarantee that the hedge will give a net profitof zero, only that the net profit in the hedge will be less uncertain

    than simply holding the stocks (ie. here a loss of $10).

    Si l H d i (S $100 F $101)

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    Simple Hedging (S0 = $100, F0 = $101)

    2) Can we lock in a price of F0= 101 ?

    3 MONTHS LATER(Spot Price has fallen)

    Spot Price S1= $90 Futures Price F1= $90

    Spot asset is worth S1= 90 and we close out futuresposition

    Profit on Futures = (101 - 90) = F0- F1= $11

    Final Value = Final Value of stocks + profit from futures

    = 90 + 11 = (S1) + F0 - F1= $101

    Hence we have locked in a final value of F0= 101

    Si l H d i (S

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    Simple Hedging (S0 =$100, F0 = $101)

    Some Algebra:

    Final Value = S1+ (F0 - F1) = $101

    = (S1- F1 ) + F0

    = b1 + F0

    where Final basis = b1= S1- F1

    Note: At maturity of the futures contract the basis is zero(since S1= F1 . In general, when the contract is closed out

    prior to maturity b1= S1- F1 may not be zero. This is calledBASIS RISK. However b1will usually be small in relation toF0.

    Source of basis risk is changes in r : F = S (1+r.T)

    Wh d th h d l t b f t it ?

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    Even though you close out the contract, you still lock in a price whichis close to the initial futures (delivery) price of F

    0= 101.

    But why not just take delivery at F0= 101 ?

    Easiest to see if you are a farmer in New Orleans who wants to sell his

    live hogs in 3-months time when they have been fattened up.

    If he delivers them in the futures contract he will have to send the hogsto Chicago (the delivery point). This is expensive, so instead he sellsthem in the local cattle market in New Orleans for S

    1

    =90

    But he also makes $11 cash profit on the futures, giving an effectiveprice of $101, which EQUALS the F-price had he taken delivery

    Why does the hedger close out before maturity ?

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    MARKING TO MARKET

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    MARKING TO MARKET:CONTRACT SPECIFICATION

    One contract is for z = $100,000 of the underlying asset (eg. US T-Bond Future).

    F= price per $100 nominal

    Let 1-tick = change in F of 1 unit(eg. 98.0 to 99.0 )

    Tick Value (set by the CBOT) = $1000 (= 1.0 /100) x $100,000

    Initial Margin = $5000 Maintenance Margin=$4,000

    If balance in margin account falls below $4,000 at market close,then it must be made up to $5,000 by the next morning.

    Buy one contract at F0= 98 (noon, day-1) [ Value = $98,000]

    Close out contract at F3= 98.5 (after 3-days)

    Table 2 3 : Marking to Market

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    Table 2.3 : Marking to Market

    Day Settlement

    (Price)

    Mark to

    Market

    Margin

    Pa ment

    Balance

    1. 94,000(94.0) -4000 5000 $1000

    2. 93,500(93.5) -500 4000 $4500

    3. 98,500(98.5) +5000 $9500

    Tick value (=1unit) = $1,000

    Initial margin = $5000, (Maintenance margin = $4000)

    Buy at F0= 98 (noon, day-1)

    TEXT BOOK:

    Total Profit =(F3

    - F0

    ) 1,000

    = (98.5 - 98) $1,000 = +$500

    Marking to Market

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    Buy at F0= 98 (noon, day-1)

    End of Day-1, contract is worth F1= 94.0

    Change on the day = - 4 x $1000 = -$4000

    New balance = $5,000 - $4,000 = $1000

    Balance is below maintenance margin, hence must pay in 4,000 tomake opening balance on day-2 = 5,000 (ie. the initial margin)

    End of Day-2, contract is worth F2= 93.5 (ie. Lost 500)

    Closing balance = 5,000 - 500 = 4,500 (above, maintenance margin)

    End of Day-3, contract is worth F2= 98.5 (ie. +5 ticks)

    Closing balance = 4,000+5000 = $9,500 (send cheque)

    Total Profit using Margin Account

    Final balance received = $9,500

    less what you paid in $5,000+$4000 = $9,000

    So f inal prof i t= + $500

    Marking to Market

    MARKING TO MARKET

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    MARKING TO MARKET

    Futures contract is like a forward contract that is closed out

    every day and your daily cash gains/losses are noted by theClearing House (CH). Then you enter a new forward contract atthe beginning of the next day at the new futures price. Any cashgain/loss alters the balance in your margin account, daily.

    The initial margin of $5000 is equivalent to 5 ticks. If the marketfalls less than 5 ticks in a day, the long (and the ClearingHouse) can always honour the contract. Trading halts aresometimes used to prevent a fall of more than 5 ticks in one day,

    so that margin payments can take place before the next daystrading.

    This is why futures contract involve no credit(default) risk

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