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8/13/2019 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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SLIDES END HERE