This document provides an overview of futures markets and contracts. Key points include: - Futures contracts are standardized agreements to buy or sell an asset at a predetermined price on a future date. This allows hedging of price risk. - Margin deposits are required as security and daily gains/losses are settled, allowing high leverage from low margins. - Speculators take on risk from hedgers for potential profit from price movements. Hedgers use futures to lock in prices and eliminate risk. - Examples demonstrate how farmers can hedge crop prices and processors can lock in input costs using long and short futures positions.

1. 1
FuturesFutures

2. 2
Futures TradingFutures Trading
• Continuous auctions marketsContinuous auctions markets
• Clearing houses for the latest info. aboutClearing houses for the latest info. about
supply and demandsupply and demand
• Futures markets eliminate extremeFutures markets eliminate extreme
seasonal price fluctuations in farmseasonal price fluctuations in farm
commodities (excess SS at harvest andcommodities (excess SS at harvest and
excess DD off season)excess DD off season)
• Hedgers and speculatorsHedgers and speculators

3. 3
Brief HistoryBrief History
• Japan (18Japan (18thth
century) – rice and silkcentury) – rice and silk
• Holland (18Holland (18thth
century) – tulip bulbscentury) – tulip bulbs
• U.S. (19U.S. (19thth
century) – grain marketscentury) – grain markets
• Chicago Mercantile Exchange (CME) (1970s) –Chicago Mercantile Exchange (CME) (1970s) –
financial instrumentsfinancial instruments
• London Int’l Fin. Fut. & Options Ex. (nowLondon Int’l Fin. Fut. & Options Ex. (now
Euronext.liffe) (1982)Euronext.liffe) (1982)
• Today worldwide there are more than 75Today worldwide there are more than 75
exchangesexchanges

4. 4
The Futures ContractThe Futures Contract
• A standardized agreement, traded in aA standardized agreement, traded in a
centralized futures exchange, that obligescentralized futures exchange, that obliges
traders to purchase or sell an asset at antraders to purchase or sell an asset at an
agreed-upon price on a specified futureagreed-upon price on a specified future
date.date.
Today Delivery (Maturity) date
S0 ST
F0
Spot (actual) Prices
Futures PricesFt
FT
St
Cash Flow 0 Ft - F0 ST - F0 CF if contract is closed (reversed) at time
t
CF if contract is closed at
maturity
ConvergenceConvergence
Property:Property:
Arbitrage ensuresArbitrage ensures
SSTT = F= FTT

5. 5
Futures vs. OptionsFutures vs. Options
• FuturesFutures
– Holder has obligation to buy (long) or sellHolder has obligation to buy (long) or sell
(short)(short)
– Both parties must fulfill contractBoth parties must fulfill contract
• OptionsOptions
– Holder has the right, but not the obligation, toHolder has the right, but not the obligation, to
buy (call) or sell (put)buy (call) or sell (put)
– Holder may or may not exerciseHolder may or may not exercise

6. 6
Profits: Futures Buyers and Call BuyersProfits: Futures Buyers and Call Buyers
ProfitProfit
PricePrice
0
Call BuyerCall Buyer
FuturesFutures
BuyerBuyer
Fo

7. 7
Profits: Futures Sellers and Put BuyersProfits: Futures Sellers and Put Buyers
0
ProfitsProfits
PricePrice
Futures SellerFutures Seller
Put BuyerPut Buyer
Fo

8. 8
Futures Listings (Agriculture)Futures Listings (Agriculture)
Tuesday, March 25, 2003Tuesday, March 25, 2003
ExpiryExpiry OpenOpen HighHigh LowLow SettleSettle CHGCHG LifetimeLifetime
HighHigh
LifetimeLifetime
LowLow
OpenOpen
InterestInterest
Corn (CBT) -5,000 bu; cents per buCorn (CBT) -5,000 bu; cents per bu
MayMay 229.00229.00 229.50229.50 227.25227.25 228.25228.25 -.75-.75 301.00301.00 227.25227.25 171,705171,705
Pork Bellies (CME)-40,000 lbs.; cents per lbPork Bellies (CME)-40,000 lbs.; cents per lb
MarMar 89.2589.25 89.7089.70 89.2589.25 89.7089.70 -.05-.05 91.4091.40 57.8757.87 2323
Representative trading price duringRepresentative trading price during
the last few minutes of tradingthe last few minutes of trading
before exchange close, $2.2825/bubefore exchange close, $2.2825/bu
Each contract is 5,000 bu,Each contract is 5,000 bu,
or 5,000 x $2.2825 =or 5,000 x $2.2825 =
$11,412.50 at today’s close$11,412.50 at today’s close
TradedTraded
at theat the
ChicagoChicago
Board ofBoard of
TradeTrade
Number ofNumber of
outstandingoutstanding
contractscontracts
Pricing unitPricing unit
Few contractsFew contracts
stay open asstay open as
expiry approachesexpiry approaches

9. 9
Futures Listings (Financial)Futures Listings (Financial)
Tuesday, March 25, 2003Tuesday, March 25, 2003
ExpiryExpiry OpenOpen HighHigh LowLow SettleSettle CHGCHG LifetimeLifetime
HighHigh
LifetimeLifetime
LowLow
OpenOpen
InterestInterest
Treasury Bonds (CBT)-$100,000; pts. 32Treasury Bonds (CBT)-$100,000; pts. 32ndnd
of 100%of 100%
JuneJune 111-03111-03 111-23111-23 110-14110-14 111-02111-02 11 115-27115-27 105-00105-00 416,150416,150
Canadian Dollar (CME)-CAD 100,000; $ per CADCanadian Dollar (CME)-CAD 100,000; $ per CAD
JuneJune .6722.6722 .6757.6757 .6720.6720 .6742.6742 .0016.0016 .6818.6818 .6197.6197 87,08787,087
S&P 500 Index (CME)-$250 x indexS&P 500 Index (CME)-$250 x index
JuneJune 8638086380 8793087930 8560085600 8722087220 870870 133280133280 7705077050 609,138609,138
Each contractEach contract
is worth $250 xis worth $250 x
872.20 at close872.20 at close
=$218,050=$218,050
1111110202
/32 = 111.0625% of/32 = 111.0625% of
par or $111,062.50 perpar or $111,062.50 per
contractcontract
Each contractEach contract
calls for deliverycalls for delivery
of $100,000 parof $100,000 par
value of bondsvalue of bonds
Decimal pt isDecimal pt is
omitted: 872.20omitted: 872.20

10. 10
Types of Futures ContractTypes of Futures Contract
• Delivery Type ContractsDelivery Type Contracts
– Call for physical delivery of a particular commodityCall for physical delivery of a particular commodity
– The vast majority of holders choose to realize theirThe vast majority of holders choose to realize their
gains or losses by buying or selling an offsettinggains or losses by buying or selling an offsetting
futures contract prior to the delivery datefutures contract prior to the delivery date
• Cash Settlement Type ContractsCash Settlement Type Contracts
– Settled in cash rather than by deliverySettled in cash rather than by delivery
– Example: Stock Index Futures. If FExample: Stock Index Futures. If F00 = 900 and S= 900 and STT ==
905, then holder’s profit = $250 x (905-900) = $1,250.905, then holder’s profit = $250 x (905-900) = $1,250.

11. 11
MarginsMargins
• A deposit of good faith money (security) that canA deposit of good faith money (security) that can
be drawn on by the brokerage firm to cover anybe drawn on by the brokerage firm to cover any
day-to-day losses that may be incurred (how isday-to-day losses that may be incurred (how is
this different from stock trades?)this different from stock trades?)
• Initial marginInitial margin
– Amount to be deposited at the start of each contractAmount to be deposited at the start of each contract
– Typically 5%-15% of contract valueTypically 5%-15% of contract value
– Could use cash or near cash securities, e.g., T-billsCould use cash or near cash securities, e.g., T-bills
– Required of both parties b/c both exposed to lossesRequired of both parties b/c both exposed to losses
• Maintenance margin – the minimal value of theMaintenance margin – the minimal value of the
margin balance before a margin call is issuedmargin balance before a margin call is issued

12. 12
Marking to MarketMarking to Market
Example: Corn futuresExample: Corn futures
Tuesday, March 25, 2003Tuesday, March 25, 2003
DayDay FFtt P/LP/L ProceedsProceeds
= P/L x 5K= P/L x 5K
Acct.Acct.
BalanceBalance
Initial margin = 10% or $2.28x5000x.1Initial margin = 10% or $2.28x5000x.1 $1,140$1,140
11 2.302.30 .02.02 $100$100 1,2401,240
22 2.252.25 -.05-.05 -250-250 990990
33 2.162.16 -.09-.09 -450-450 540540
44 2.192.19 .03.03 150150 720720
Margin call is issued if maintenance margin = 5% orMargin call is issued if maintenance margin = 5% or
$570. The min. is reached with a 11c drop since 1c$570. The min. is reached with a 11c drop since 1c
costs $50
Total =-$450,Total =-$450,
same assame as
(S(STT -F-F00 ) x 5K) x 5KFF00

13. 13
LeverageLeverage
• In above example, on Day 1, FIn above example, on Day 1, Ftt has movedhas moved
(2.30-2.28)/2.28 = 0.88%, but profit as %(2.30-2.28)/2.28 = 0.88%, but profit as %
of initial margin (ROM) = 100/1140 =of initial margin (ROM) = 100/1140 =
8.8%, or 10X the change in F8.8%, or 10X the change in Ftt since initialsince initial
margin is only 10% of contract value.margin is only 10% of contract value.
• High leverage results from low marginHigh leverage results from low margin
requirement.requirement.

14. 14
SpeculationSpeculation
• Enables profit from movement in FEnables profit from movement in Ftt
• Enables shifting of market risk to speculatorEnables shifting of market risk to speculator
– Price volatility (risk) is inherent in all commodities andPrice volatility (risk) is inherent in all commodities and
financial marketsfinancial markets
– Futures contracts allow such risk to be shifted to aFutures contracts allow such risk to be shifted to a
risk takerrisk taker
– This differs from gambling which involves the creationThis differs from gambling which involves the creation
of a risk for the sole purpose of it being takenof a risk for the sole purpose of it being taken
• Why speculators buy futures and not the asset?Why speculators buy futures and not the asset?
– Lower transaction costsLower transaction costs
– LeverageLeverage

15. 15
HedgingHedging
• Short (long) hedge – the sale (purchase) ofShort (long) hedge – the sale (purchase) of
futures contract [commit to selling (buying) assetfutures contract [commit to selling (buying) asset
at current futures price (Fat current futures price (F00)] to reduce the)] to reduce the
possible decline (rise) in value of an assetpossible decline (rise) in value of an asset
already held (not yet owned).already held (not yet owned).
• Convergence property (FConvergence property (FTT=S=STT)) ⇒⇒ hedger bearshedger bears
no risk if asset and contract held until maturityno risk if asset and contract held until maturity
• Basis (FBasis (Ftt-S-Stt) risk) risk
– if contract or asset liquidated before maturity.if contract or asset liquidated before maturity.
– If basis narrows (widens), SIf basis narrows (widens), Stt rises more (less) than Frises more (less) than Ftt,,
a long spot-short future (short spot-long future)a long spot-short future (short spot-long future)
position will benefit.position will benefit.

16. 16
Example – Short HedgeExample – Short Hedge
• Owns 200 bonds @$1,000 par value. Total portfolio =Owns 200 bonds @$1,000 par value. Total portfolio =
$200,000$200,000
• Want to insulate bonds from price changeWant to insulate bonds from price change
• FF00 = $111 per $100 par value.= $111 per $100 par value.
• Since each T-bond futures contract is $100,000, itSince each T-bond futures contract is $100,000, it
needs to sell (short) 2 contracts to fully hedgeneeds to sell (short) 2 contracts to fully hedge
T-bond Price at Contract MaturityT-bond Price at Contract Maturity
$110$110 $111$111 $112$112
Bond holdingsBond holdings $220,000$220,000 $222,000$222,000 $224,000$224,000
Futures P/LFutures P/L 2,0002,000 00 -2,000-2,000
TotalTotal $222,000$222,000 $222,000$222,000 $222,000$222,000
2 x (110-111)% of par (100,000)

17. 17
Example – Long HedgeExample – Long Hedge
• Corn mill processor expects to receive cashCorn mill processor expects to receive cash
inflow of $12,500 at time T (maturity date)inflow of $12,500 at time T (maturity date)
• Wants to lock in current price at $2.50 (FWants to lock in current price at $2.50 (F00))
• Buy (long) 1 corn futures contract (5,000 bu)Buy (long) 1 corn futures contract (5,000 bu)
Corn Price at Contract MaturityCorn Price at Contract Maturity
$2.40$2.40 $2.50$2.50 $2.60$2.60
Buy corn at marketBuy corn at market 12,00012,000 12,50012,500 $13,000$13,000
Futures contractFutures contract
Loss/(Gain)Loss/(Gain)
500500 00 (500)(500)
Net costNet cost $12,500$12,500 $12,500$12,500 $12,500$12,500
1 x (2.40-2.50) x 5,000

18. 18
ProblemProblem
• Farmer Brown grows #1 red corn andFarmer Brown grows #1 red corn and
would like to hedge the value of thewould like to hedge the value of the
coming harvest. However, the futurescoming harvest. However, the futures
contract is on the #2 yellow grade of corn.contract is on the #2 yellow grade of corn.
Suppose that yellow corn typically sells forSuppose that yellow corn typically sells for
90% of the price of red corn. If he grows90% of the price of red corn. If he grows
100,000 bushels and each futures100,000 bushels and each futures
contract calls for delivery of 5,000 bushels,contract calls for delivery of 5,000 bushels,
how many contracts should he buy or sellhow many contracts should he buy or sell
to hedge his position?to hedge his position?

19. 19
Pricing commodity futuresPricing commodity futures
• Two equivalent strategies –Two equivalent strategies –
1.1. Buy futures contract today; take delivery of commodity atBuy futures contract today; take delivery of commodity at
maturity and pay Fmaturity and pay F00 at maturity.at maturity.
– Cash flow = FCash flow = F00
2.2. Borrow the spot price (SBorrow the spot price (S00) and buy the commodity today;) and buy the commodity today;
incur storage cost ofincur storage cost of cc per period (as % of spot price) untilper period (as % of spot price) until
maturity. Assume maturity is t period out, thenmaturity. Assume maturity is t period out, then
– Cash flow = Purchase cost (SCash flow = Purchase cost (S00) + interest cost (S) + interest cost (S00rrff) +) +
storage cost (Sstorage cost (S00cc) = S) = S00 (1+r(1+rff++cc))tt
where rwhere rff = periodic risk-= periodic risk-
free ratefree rate
• Arbitrage opportunityArbitrage opportunity ⇒⇒ both strategies have the sameboth strategies have the same
value, thusvalue, thus
FF00 == SS00 (1 + r(1 + rff ++ cc))tt
• Why rWhy rff? Let t=1. A total upfront investment of S? Let t=1. A total upfront investment of S00, net of, net of
storage cost of Sstorage cost of S00cc, grows to a final value of F, grows to a final value of F00 atat
maturity: the rate of return is (Fmaturity: the rate of return is (F00 – S– S00 – S– S00cc)/S)/S00..
Since all values in this expression are known at time 0,Since all values in this expression are known at time 0,
the return is risk-free, thus rthe return is risk-free, thus r ..

20. 20
Pricing commodity futuresPricing commodity futures
• If the asset is not storable forIf the asset is not storable for
technological (electricity) or economictechnological (electricity) or economic
(crops with seasonal harvest cycles)(crops with seasonal harvest cycles)
reasons, thenreasons, then cc = 0= 0
• SpreadsSpreads
– Relationship between futures prices forRelationship between futures prices for
contracts of different maturity datescontracts of different maturity dates
– Since FSince F11==SS00 (1 + r(1 + rff ++ cc))t1t1
and Fand F22==SS00 (1 + r(1 + rff ++ cc))t2,t2,
thus Fthus F22==FF11 (1 + r(1 + rff ++ cc))t2-t1t2-t1

21. 21
Spread tradingSpread trading
• The simultaneous purchase and sale ofThe simultaneous purchase and sale of
the same or similar commodity in thethe same or similar commodity in the
same or different contract months.same or different contract months.
– Intra-commodity spread – same commodityIntra-commodity spread – same commodity
– Inter-commodity spread – two relatedInter-commodity spread – two related
commodities (long one and short the other)commodities (long one and short the other)
• Advantages of spreadsAdvantages of spreads
1. typically require smaller margin deposits1. typically require smaller margin deposits
2. underlying market direction isn't important2. underlying market direction isn't important
3. seasonal patterns exist among spreads3. seasonal patterns exist among spreads

22. 22
Example of spread tradingExample of spread trading
• July Soybeans were trading at $5.10/bushel andJuly Soybeans were trading at $5.10/bushel and
November Soybeans were at $5.35November Soybeans were at $5.35 ⇒⇒ the spread is saidthe spread is said
to be at .25 to the November side.to be at .25 to the November side.
• Enter a July/November bean spread (buy a July and sellEnter a July/November bean spread (buy a July and sell
a November contract)a November contract)
• If soybeans rallied and July settled one day at $5.70 andIf soybeans rallied and July settled one day at $5.70 and
November settled at $5.75, the spread would now be .November settled at $5.75, the spread would now be .
05.05.
• The July contract will make 60 cents and NovemberThe July contract will make 60 cents and November
contract will lose 40 cents, leaving a net gain of 20 centscontract will lose 40 cents, leaving a net gain of 20 cents
on the spread.on the spread.
• Since each contract is 5000 bushels, the profit will be 20Since each contract is 5000 bushels, the profit will be 20
cents/bushel * 5000 bushels = $1,000.cents/bushel * 5000 bushels = $1,000.
• If you had entered the spread in the other direction youIf you had entered the spread in the other direction you
would be losing $1,000.would be losing $1,000.

23. 23
Stock index futuresStock index futures
• ContractContract
– cash settlement onlycash settlement only
– S&P500 (x$250), DJIA (x$10), Russell 2000 (x$500),S&P500 (x$250), DJIA (x$10), Russell 2000 (x$500),
Nasdaq 100 (x$100), S&P Mid-Cap (x$500), FT-SENasdaq 100 (x$100), S&P Mid-Cap (x$500), FT-SE
100 (x10 pound), Nikkei (x$5)100 (x10 pound), Nikkei (x$5)
• PricingPricing
– FF00 == SS00 (1 + r(1 + rff --dd ))tt
wherewhere dd = dividend accruing to= dividend accruing to
holder of portfolio (as % of spot price Sholder of portfolio (as % of spot price S00))
– Net cost of long position (buy portfolio now and carryNet cost of long position (buy portfolio now and carry
to maturity) = cost of purchase (Sto maturity) = cost of purchase (S00) + interest cost of) + interest cost of
funds (Sfunds (S00 x rx rff) - dividend received (S) - dividend received (S00 xx dd).).
– Net cost of short position = buying the portfolio withNet cost of short position = buying the portfolio with
deferred delivery and pay Fdeferred delivery and pay F00 at that timeat that time
– Arbitrage opportunityArbitrage opportunity ⇒⇒ both strategies have theboth strategies have the
same valuesame value

24. 24
ProblemProblem
• Assume the S&P500 index is at 1,000 and isAssume the S&P500 index is at 1,000 and is
expected to be at 1,020 in one month.expected to be at 1,020 in one month.
• rrff=0.5% and=0.5% and dd=0.2% per month=0.2% per month
• If you go long on a 12-month index contract,If you go long on a 12-month index contract,
what will bewhat will be
(a) the cash flow from the mark-to-market(a) the cash flow from the mark-to-market
proceeds in one month (assume the parityproceeds in one month (assume the parity
condition holds)?condition holds)?
(b) the holding period return if the initial margin(b) the holding period return if the initial margin
on the contract is $15,000?on the contract is $15,000?

25. 25
Creating synthetic stock positions withCreating synthetic stock positions with
stock index futuresstock index futures
• Index futures allow participation in broadIndex futures allow participation in broad
market movements without actually buyingmarket movements without actually buying
or selling large amounts of stockor selling large amounts of stock
• Market timers shift between stocks andMarket timers shift between stocks and
bills frequently (an expensive strategy).bills frequently (an expensive strategy).
• A cheaper strategy is to buy and hold T-A cheaper strategy is to buy and hold T-
bills and adjust only futures positions.bills and adjust only futures positions.

26. 26
Synthetic stock positionSynthetic stock position
exampleexample• Wants to invest $90M in market for 1 mo. (short)Wants to invest $90M in market for 1 mo. (short)
• S&P Index SS&P Index S00 = 900 and F= 900 and F00 = 915= 915
• T-bill one month yield = 1%T-bill one month yield = 1%
• Since each contract controls $250 x 900 = $225,000Since each contract controls $250 x 900 = $225,000
worth of stocks, it needs $90M/225K = 400 contractsworth of stocks, it needs $90M/225K = 400 contracts
• To pay for 400 contracts @915 in one month, we needTo pay for 400 contracts @915 in one month, we need
400 x 250 x 915/1.01 = $90.59M in T-bills400 x 250 x 915/1.01 = $90.59M in T-bills
• At maturity,At maturity,
– T-bills are worth $90.59 x 1.01 = $91.5MT-bills are worth $90.59 x 1.01 = $91.5M
– P/L from contract = 400 x 250 x (SP/L from contract = 400 x 250 x (S11 – 915) = 100,000S– 915) = 100,000S11 - $91.5M- $91.5M
– Net = 100,000SNet = 100,000S11 = proportional to stock index value= proportional to stock index value
• Strategy is thus equivalent to holding the stock index,Strategy is thus equivalent to holding the stock index,
minus the huge transaction costs.minus the huge transaction costs.

27. 27
Hedging market risk with index futuresHedging market risk with index futures
• You own a $30M diversified stock portfolio withYou own a $30M diversified stock portfolio with
ββ=0.8. The current S&P 500 index is 1,000.=0.8. The current S&P 500 index is 1,000.
What should you do if you want to protect theWhat should you do if you want to protect the
portfolio from price declines in the next 2portfolio from price declines in the next 2
months?months?
– You are long on asset, so you need to short (sell) theYou are long on asset, so you need to short (sell) the
futures contracts with 2 month expiryfutures contracts with 2 month expiry
– For every 1 pt. drop in the S&P, the portfolio incurs aFor every 1 pt. drop in the S&P, the portfolio incurs a
loss of 0.8 x (1/1000) = 0.08%. In dollar terms, 0.08%loss of 0.8 x (1/1000) = 0.08%. In dollar terms, 0.08%
x $30M = $24,000.x $30M = $24,000.
– A 1 pt. drop on the index, however, will generate profitA 1 pt. drop on the index, however, will generate profit
of 1 x $250 =$250 on the futures contract.of 1 x $250 =$250 on the futures contract.
– To hedge, you need (24,000/250) = 96 contracts.To hedge, you need (24,000/250) = 96 contracts.
– Alternatively, one contract controls $250 x 1000 =Alternatively, one contract controls $250 x 1000 =
250K worth of stocks, thus to cover $30M you need250K worth of stocks, thus to cover $30M you need
(30/0.25)x0.8 = 96 contracts.(30/0.25)x0.8 = 96 contracts.

28. 28
ProblemProblem
• You manage a $13.5M stock portfolio withYou manage a $13.5M stock portfolio with
ββ = 0.6. You believe the market is about to= 0.6. You believe the market is about to
drop temporarily, but you don’t want todrop temporarily, but you don’t want to
move your portfolio into T-bills because ofmove your portfolio into T-bills because of
the transaction cost. The S&P 500 index isthe transaction cost. The S&P 500 index is
currently at 1,350. What should you docurrently at 1,350. What should you do
using futures contracts to hedge theusing futures contracts to hedge the
downside risk?downside risk?

29. 29
Foreign Exchange FuturesForeign Exchange Futures
• Interest rate parity theoremInterest rate parity theorem
– an investor must earn the same rate of return byan investor must earn the same rate of return by
investing in risk-free money market securities atinvesting in risk-free money market securities at
home as could be earned from a hedged investmenthome as could be earned from a hedged investment
in risk-free foreign money market securities.in risk-free foreign money market securities.
1.1. Proceeds in 1 year by investing in risk-free money marketProceeds in 1 year by investing in risk-free money market
securities at home = $1 x (1+rsecurities at home = $1 x (1+rusus))
2.2. (a) Proceeds in 1 year by investing in foreign money market(a) Proceeds in 1 year by investing in foreign money market
securities = $1/Ssecurities = $1/S00 x (1+rx (1+rforeignforeign))
(b) Hedging the foreign investment to guarantee current(b) Hedging the foreign investment to guarantee current
exchange rate = $1/Sexchange rate = $1/S00 x (1+rx (1+rforeignforeign) x F) x F00
• Since these two strategies are equivalent,Since these two strategies are equivalent,
(1+r(1+rusus )/(1+r)/(1+rforeignforeign ) = F) = F00 /S/S00

30. 30
Covered interest arbitrageCovered interest arbitrage
• Violation of interest rate parity theoremViolation of interest rate parity theorem
⇒⇒ arbitrage opportunityarbitrage opportunity
• If rIf rUSUS = 5%, r= 5%, rUKUK = 6%, S= 6%, S00 = $1.40, then F= $1.40, then F00
should be [(1.05)/(1.06)] x $1.40 =should be [(1.05)/(1.06)] x $1.40 =
$1.387/pound$1.387/pound
• If FIf F00 = $1.37 instead, it is under-priced.= $1.37 instead, it is under-priced.
Profit is to be had if this favorable rate isProfit is to be had if this favorable rate is
hedged forward.hedged forward.
• If the parity condition holds, rIf the parity condition holds, rUKUK = (1+r= (1+rusus) x) x
(S(S00/F/F00) = (1.05)x(1.40/1.37)-1 =) = (1.05)x(1.40/1.37)-1 =
7.3%>6%. We’ll borrow in the U.K.7.3%>6%. We’ll borrow in the U.K.

31. 31
Covered interest arbitrageCovered interest arbitrage
ActionAction Initial CF ($)Initial CF ($) CF in 1 yr ($)CF in 1 yr ($)
1.1. Borrow 1 U.K. pound.Borrow 1 U.K. pound.
Convert to $. RepayConvert to $. Repay
1.06 pound at year end1.06 pound at year end
$1.37$1.37 -S-S11 x (1.06)x (1.06)
2.2. Lend $1.40 in the U.S.Lend $1.40 in the U.S. -$1.37-$1.37 $1.40 x (1.05)$1.40 x (1.05)
3.3. Enter futures contractEnter futures contract
to buy 1.06 pound at Fto buy 1.06 pound at F00
= $1.37= $1.37
$0$0 1.06 x1.06 x
(S(S11-$1.37)-$1.37)
TotalTotal $0$0 $.0178$.0178
Gain = (1.40 x 1.05 – 1.37 x 1.06)
Long hedge
Short asset

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Interest rate futuresInterest rate futures
• A great tool to hedge against uncertaintyA great tool to hedge against uncertainty
in interest rates forin interest rates for
– Bond portfolio managersBond portfolio managers
– Companies planning to issue bondsCompanies planning to issue bonds
– Investment funds (e.g., pension funds)Investment funds (e.g., pension funds)
• Key bond concept –Key bond concept –
– Modified duration (D*): %Modified duration (D*): % ∆∆ P = -D* xP = -D* x ∆∆YTMYTM
(e.g., a 1% change in the YTM of the bond will(e.g., a 1% change in the YTM of the bond will
reduce bond price by D* %.). Note that D* =reduce bond price by D* %.). Note that D* =
D/(1+YTM) where D=duration.D/(1+YTM) where D=duration.

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Interest rate risk hedge exampleInterest rate risk hedge example
• You manage (long position) a $10M bondYou manage (long position) a $10M bond
portfolio with D*= 9 yrs.portfolio with D*= 9 yrs.
• A 1% rise in interest rate will result in D* x 1% =A 1% rise in interest rate will result in D* x 1% =
9% (or 9% x 10M = $900K) loss in bond value9% (or 9% x 10M = $900K) loss in bond value ⇒⇒
900K/100 basis pt = $9,000/basis pt = Price900K/100 basis pt = $9,000/basis pt = Price
Value of a Basis Point (PVBP)Value of a Basis Point (PVBP)
• Assume T-bond FAssume T-bond F00 = 90 with D*=10 yrs. A 1%= 90 with D*=10 yrs. A 1%
rise in interest rate will result in D* x 1% = 10%rise in interest rate will result in D* x 1% = 10%
(or 10% x bond value per contract = 10% x $90(or 10% x bond value per contract = 10% x $90
x $1,000 = $9K) loss in a futures contractx $1,000 = $9K) loss in a futures contract ⇒⇒
PVBP = 9K/100 basis pt = $90/basis pt.PVBP = 9K/100 basis pt = $90/basis pt.
• Number of contracts needed to hedge = H =Number of contracts needed to hedge = H =
PVBP Portfolio/PVBP hedge vehicle = 9K/90 =PVBP Portfolio/PVBP hedge vehicle = 9K/90 =
100 contracts.100 contracts.

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Interest rate swapsInterest rate swaps
• Obligate two counterparties to exchange cashObligate two counterparties to exchange cash
flows at one or more future datesflows at one or more future dates
• Example: Firm with $10M fixed 8% LTD desiresExample: Firm with $10M fixed 8% LTD desires
to convert into floating rate.to convert into floating rate.
• Strategy: use swap agreement with notionalStrategy: use swap agreement with notional
principal of $10M that exchanges LIBOR for anprincipal of $10M that exchanges LIBOR for an
8% fixed rate. Firm will pay counterparty $10M x8% fixed rate. Firm will pay counterparty $10M x
LIBOR and receive $10M x 8% which offsets theLIBOR and receive $10M x 8% which offsets the
fixed obligation on the LTD.fixed obligation on the LTD.
• Net cash flow = -LIBOR x $10M instead of -8% xNet cash flow = -LIBOR x $10M instead of -8% x
$10M.$10M.

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Futures vs. ForwardsFutures vs. Forwards
FuturesFutures ForwardForward
ContractContract Highly standardizedHighly standardized CustomCustom
ExchangeExchange EstablishedEstablished OTCOTC
Mark toMark to
MktMkt
YesYes NoNo
Settled @Settled @ Ending price (PEnding price (PTT)) Contract price (FContract price (F00))
Credit riskCredit risk No (counter party isNo (counter party is
clearinghouse)clearinghouse)
YesYes
DurationDuration Traded continuouslyTraded continuously Held until maturityHeld until maturity
Cash flowCash flow Daily + Margin Req.Daily + Margin Req. At deliveryAt delivery