1. Copyright K.Cuthbertson and D.Nitzsche 1 Lecture Futures Contracts This version 11/9/2001 Copyright K.Cuthbertson and D.Nitzsche

2. 2 u Basic Concepts u Speculation u Pricing/Arbitrage u Hedging u Marking to Market (Margin Account) Topics

3. Copyright K.Cuthbertson and D.Nitzsche 3 Investments:Spot and Derivative Markets, K.Cuthbertson and D.Nitzsche u CHAPTER 19: Derivative Securities: An Overview Derivative Securities: An Overview u CHAPTER 20: Futures Markets READING

4. Copyright K.Cuthbertson and D.Nitzsche 4 Basic Concepts

5. Copyright K.Cuthbertson and D.Nitzsche 5 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 to second (and moves almost one-for-one with movements in S) But it is the futures contract you are buying and selling not the underlying asset itself (e.g. they are traded on different exchanges - e.g. NYSE and CBOT)

6. Copyright K.Cuthbertson and D.Nitzsche Futures Contract u Futures Price F 0 =$100 on live hogs, quoted today (1st Jan) with Delivery Month in say September u Buy = Long Futures ~ agree a (legal) contract to buy the “underlying” (eg, 1-live hog) in the delivery month at F 0 = $100 (IF the contract is held to maturity) u Sell = Short Futures ~ agree to sell the “underlying” (1-live hog) in the delivery month at, F 0 =100 ( IF the short contract is held to maturity) (You will be notified by the exchange a few days before the maturity date of the contract, that on your particular contract ‘delivery’ is going to take place ~ in order that you can have your hogs ready and ‘looking good’.

7. Copyright K.Cuthbertson and D.Nitzsche u No “payment” made today ( only a “deposit” to guarantee you will not “quit” on the deal - this is know as a “margin payment AND IS NOT THE FUTURES PRICE - see later). u This means that futures provide LEVERAGE, in that a speculator can enter into a futures contract whose value changes with that of the underlying stocks, but she does not have to spend any of her own money at t=0 ! u The clearing house/futures exchange acts as an intermediary between buyers and sellers (and keeps a record of all transactions) Futures Contract

8. Copyright K.Cuthbertson and D.Nitzsche Why does F change between 1st Jan and 1st Feb ? u As we see later ‘arbitrageurs’ ensure that F changes as the price of hogs changes in the spot market S. u If S increases (falls) then F will increase (fall) - almost $1 for $1 over short horizons (e.g. 1 - 3 months) u Analytically: Care must be taken to state whether your analysis involves holding the futures to maturity or “buying then selling “ prior to maturity

9. Copyright K.Cuthbertson and D.Nitzsche 9 Table 2 : Forward and Futures Contracts u FORWARDS u Private (non-marketable) contract between two parties u Delivery or cash settlement at expiry u Usually one delivery date u No cash paid until expiry u Negotiable choice of delivery dates, size of contract u FUTURES u Traded on an exchange u Contract is usually closed out prior to maturity u Range of delivery dates u Cash payments into (out of) margin account, daily u Standardised Contract

10. Copyright K.Cuthbertson and D.Nitzsche 10 FINANCIAL FUTURES MARKETS u Money market instruments: 3-mth Euro$ Deposits 90-day US T-bills 3-mth Sterling, DM, deposits u Bonds US T-bond, UK Gilt, German Bund. u Stock Indexes S&P 500, FTSE100 u Currencies DM, Sterling, Yen, u Mortgage pools (GNMA) LIFFE CBOT(IMM) CME N.Y. Futures Exch. Phil. Exch. Singapore Int Exch. Hong Kong Tokyo\Osaka Pacific St. Ex. (San F.) Sydney Fut. Exch.

11. Copyright K.Cuthbertson and D.Nitzsche u Most contracts are “closed out” prior to the maturity/delivery date ( -see also “hedging”, later) u Note that if on 1st Jan you bought a Sept-futures contract at F 0 then you can “get out” of this contract before maturity simply by selling this Sept-futures contract on say 1st Feb at whatever price F 1 is being quoted for the Sept-contract on 1st Feb. Then “nobody” delivers “anything” at maturity. Futures Contract

12. Copyright K.Cuthbertson and D.Nitzsche 12 Who Uses Futures ? u Speculation with futures Buy low, sell high - risky ( ‘naked/open’ position) u Hedging with futures eg.In Jan, farmer wants to “lock in” sale price of his hogs which will be ‘fat’ by Sept - In Jan he sells hog futures at F 0 =$100 with maturity date of Sept - if he holds contract to maturity he ‘delivers’ his hog in Sept and receives the $100 (for certain) - ie. even if hogs in (spot) cattle market are selling for $10. u Arbitrage Spot and futures prices are ‘linked’ by the actions of arbitrageurs and S and F move almost one-for-one - latter is useful for hedgers (see later)

13. Copyright K.Cuthbertson and D.Nitzsche 13 Table 2.4: Futures: Price Quotes CORN (CBT) 5,000 bu (cents per bu.)

14. Copyright K.Cuthbertson and D.Nitzsche 14 Speculation With Futures

15. Copyright K.Cuthbertson and D.Nitzsche 15 Speculation With Futures Purchase at F 0 = 100 Hope to sell at higher price later F 1 = 110 Close-out position before delivery date. Obtain Leverage (ie. initial margin is ‘low’) Example:Leeson: Feb 95, Long 61,000 Nikkei-225 index futures (underlying value = $7bn). Nikkei fell and he lost money (lots of it) - he was supposed to be doing riskless ‘index arbitrage’ not speculating

16. Copyright K.Cuthbertson and D.Nitzsche 16 Figure 2.3 : Speculation with futures Futures price Profit/Loss per contract $10 -$10 0 Long future Short future F 2 = 110 F 2 = 90 F 1 = 100

17. Copyright K.Cuthbertson and D.Nitzsche Payoffs: Direction Vectors Long Futures or, Long Spot Short Futures or, Short Spot +1 +1 F increase then profit increases F increase then profit decrease Underlying,S Profit/Loss

18. Copyright K.Cuthbertson and D.Nitzsche Pricing/Arbitrage with Futures

19. Copyright K.Cuthbertson and D.Nitzsche Arbitrage at Maturity At expiry (T) we must have F T = S T u otherwise riskless arbitrage profits could be made u EG. Suppose 1-day before maturity F T = 100 > S T =98 Then buy ‘low’ at S=98 in ‘cattle market’, and at same time sell one future contract at F = 100. One day later ‘deliver’ the hog in the futures contract and collect F=$100 (at maturity). This is (virtually) riskless.

20. Copyright K.Cuthbertson and D.Nitzsche 20 Figure 2.7 : Backwardation and Contango Stock price, S t For simplicity we assume that the spot price remains constant. In practise, S and hence F will fluctuate as you approach T but with F t > S t if the market is in contango and F t < S t if the market is in backwardation. T Forward price in contango : F > S Forward price in backwardation : F < S 0 At T, S T = F T

21. Copyright K.Cuthbertson and D.Nitzsche 21 Arbitrage (at t<T): Pricing a Futures Contract ‘Cash and Carry’ Arbitrage Stock price, S = $100 Safe rate r = 4% p.a. Quoted Futures Price F = $102 (for delivery in 3m ) Strategy Today Sell futures contract at $102 (receive nothing today) Borrow $100, buy stock ( = synthetic future) Use no “own funds” 3-Months Time ( T = 1/4 ) Loan Outstanding = $100( 1 + 0.04 / 4) = $101 Deliver stock and receipt from f.c. = $102 Riskless profit = $1

22. Copyright K.Cuthbertson and D.Nitzsche 22 u 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 u Arbitrage ensuresquoted futures price equals SF F = S ( 1 + r.T ) = $101 Futures Price = Spot price + cost of carry “Cost of Carry” = S rT = $1 Arbitrage (at t<T): Pricing a Futures Contract

23. Copyright K.Cuthbertson and D.Nitzsche 23 Hedging with Futures

24. Copyright K.Cuthbertson and D.Nitzsche 24 Hedging with Futures u Arbitrageurs ensure F and S are nearly perfectly positively correlated and move $1 for $1. F = S ( 1 + r.T ) = S (1.01) so approx: (F 1 - F 0 ) = (S 1 - S 0 )ie. ‘dollar for dollar’

25. Copyright K.Cuthbertson and D.Nitzsche 25 Hedging with Futures u F and S are positively correlated u To Hedge: 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 by gain on the futures (‘dollar for dollar’) or, 2) Final Value = Cash Market Value + gain on futures, “locks in” a known “price”

26. Copyright K.Cuthbertson and D.Nitzsche Hedge = Long Underlying + Short Futures Long Underlying Stock + Short Futures Hedge = 0 0 +1

27. Copyright K.Cuthbertson and D.Nitzsche 27 Own (long) 1-share Spot price S 0 = $100 Fear price fall over next 3-mths 3-month futures contract has current price, F 0 = $101 AIMS: 1) To offset some of the loss in S by profit on F or, 2) To “lock in” a “final value” of F 0 = $101 Assume: F and S are perfectly (positively) correlated Strategy: ‘Long’ share + ‘short’ one futures contract Simple Hedging

28. Copyright K.Cuthbertson and D.Nitzsche 28 Simple Hedging (S 0 = $100, F 0 = $101) 1) Loss in spot market offset by gain on the futures 3 MONTHS LATER(Spot Price has fallen) Spot Price S 1 = $90 Futures Price F 1 = $90 Note that we have assumed the contract is closed out just before maturity so that S 1 = F 1 Gain on Futures = (101 - 90) = ( F 0 - F 1 ) = $11 Loss on the spot = (100 - 90) = (S 0 - S 1 ) = $10 Net Profit = ( F 0 - F 1 ) - ( S 0 - S 1 ) = 11 - 10 = $1 Note that you cannot guarantee that the hedge will give a net profit of zero, only that the net profit in the hedge will be less uncertain than simply holding the stocks (ie. here a loss of $10).

29. Copyright K.Cuthbertson and D.Nitzsche 29 Simple Hedging (S 0 = $100, F 0 = $101) 2) Can we “lock in” a price of F 0 = 101 ? 3 MONTHS LATER(Spot Price has fallen) Spot Price S 1 = $90 Futures Price F 1 = $90 Spot asset is worth S 1 = 90 and we close out futures position Profit on Futures = (101 - 90) = F 0 - F 1 = $11 Final Value = Final Value of stocks + profit from futures = 90 + 11 = (S 1 ) + F 0 - F 1 = $101 Hence we have locked in a final value of F 0 = 101

30. Copyright K.Cuthbertson and D.Nitzsche 30 Simple Hedging (S 0 = $100, F 0 = $101) Some Algebra: Final Value = S 1 + (F 0 - F 1 ) = $101 = (S 1 - F 1 ) + F 0 = b 1 + F 0 where “Final basis” = b 1 = S 1 - F 1 Note: At maturity of the futures contract the basis is zero (since S 1 = F 1. In general, when the contract is closed out prior to maturity b 1 = S 1 - F 1 may not be zero. This is called BASIS RISK. However b 1 will usually be “small in relation to F 0. Source of basis risk is changes in r : F = S (1+r.T)

31. Copyright K.Cuthbertson and D.Nitzsche 31 Even though you close out the contract, you still “ lock in” a price which is close to the initial futures (delivery) price of F 0 = 101. But why not just take delivery at F 0 = 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 hogs to Chicago (the delivery point). This is expensive, so instead he sells them in the local cattle market in New Orleans for S 1 =90 But he also makes $11 cash profit on the futures, giving an effective price of $101, which EQUALS the F-price had he taken delivery Why does the hedger close out before maturity ?

32. Copyright K.Cuthbertson and D.Nitzsche 32 MARKING TO MARKET

33. Copyright K.Cuthbertson and D.Nitzsche 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 = $5000Maintenance 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 F 0 = 98 (noon, day-1) [ Value = $98,000] Close out contract at F 3 = 98.5 (after 3-days)

34. Copyright K.Cuthbertson and D.Nitzsche Tick value (=1unit) = $1,000 Initial margin = $5000, (Maintenance margin = $4000) Buy at F 0 = 98 (noon, day-1) TEXT BOOK: Total Profit = (F 3 - F 0 ) 1,000 = (98.5 - 98) $1,000 = +$500 Marking To Market

35. Copyright K.Cuthbertson and D.Nitzsche 35 Buy at F 0 = 98 (noon, day-1) u End of Day-1, contract is worth F 1 = 94.0 u Change on the day = - 4 x $1000 = -$4000 u New balance = $5,000 - $4,000 = $1000 Balance is below maintenance margin, hence must pay in 4,000 to make opening balance on day-2 = £5,000 (ie. the initial margin) u End of Day-2, contract is worth F 2 = 93.5 (ie. Lost 500) u Closing balance = 5,000 - 500 = 4,500 (above, maintenance margin) u End of Day-3, contract is worth F 2 = 98.5 (ie. +5 ticks) u 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 final profit = + $500 Marking To Market: Day-by-Day

36. Copyright K.Cuthbertson and D.Nitzsche 36 u Futures contract is like a forward contract that is closed out every day and your daily cash gains/losses are noted by the Clearing House (CH). Then you enter a new forward contract at the beginning of the next day at the new futures price. Any cash gain/loss alters the balance in your margin account, daily. u The initial margin of $5000 is equivalent to 5 ticks. If the market falls less than 5 ticks in a day, the “long” (and the Clearing House) can always honour the contract. Trading halts are sometimes used to prevent a fall of more than 5 ticks in one day, so that margin payments can take place before the next days trading. u This is why futures contract involve no credit(default) risk Marking To Market

37. Copyright K.Cuthbertson and D.Nitzsche 37 SLIDES END HERE