11

FuturesFutures

22

Futures TradingFutures Trading

• Continuous auctions marketsContinuous auctions markets

• Clearing houses for the latest info. Clearing houses for the latest info. about supply and demandabout supply and demand

• Futures markets eliminate extreme Futures markets eliminate extreme seasonal price fluctuations in farm seasonal price fluctuations in farm commodities (excess SS at harvest commodities (excess SS at harvest and excess DD off season)and excess DD off season)

• Hedgers and speculatorsHedgers and speculators

33

Brief HistoryBrief History

• Japan (18Japan (18thth century) – rice and silk century) – rice and silk• Holland (18Holland (18thth century) – tulip bulbs century) – tulip bulbs• U.S. (19U.S. (19thth century) – grain markets century) – grain markets• Chicago Mercantile Exchange (CME) Chicago Mercantile Exchange (CME)

(1970s) – financial instruments(1970s) – financial instruments• London Int’l Fin. Fut. & Options Ex. (now London Int’l Fin. Fut. & Options Ex. (now

Euronext.liffe) (1982)Euronext.liffe) (1982)• Today worldwide there are more than 75 Today worldwide there are more than 75

exchanges exchanges

44

The Futures ContractThe Futures Contract• A standardized agreement, traded in A standardized agreement, traded in

a centralized futures exchange, that a centralized futures exchange, that obliges traders to purchase or sell an obliges traders to purchase or sell an asset at an agreed-upon price on a asset at an agreed-upon price on a specified future date.specified future 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

Convergence Convergence Property: Property: Arbitrage Arbitrage ensures Sensures STT= F= FTT

55

Futures vs. OptionsFutures vs. Options

• FuturesFutures– Holder has obligation to buy (long) or Holder has obligation to buy (long) or

sell (short)sell (short)– Both parties must fulfill contractBoth parties must fulfill contract

• OptionsOptions– Holder has the right, but not the Holder has the right, but not the

obligation, to buy (call) or sell (put)obligation, to buy (call) or sell (put)– Holder may or may not exerciseHolder may or may not exercise

66

Profits: Futures Buyers and Call Profits: Futures Buyers and Call BuyersBuyers

ProfitProfit

PricePrice

0

Call BuyerCall Buyer

Futures Futures BuyerBuyer

Fo

77

Profits: Futures Sellers and Put Profits: Futures Sellers and Put BuyersBuyers

0

ProfitsProfits

PricePrice

Futures SellerFutures Seller

Put BuyerPut BuyerFo

88

Futures Listings Futures Listings (Agriculture)(Agriculture)

Tuesday, March 25, 2003Tuesday, March 25, 2003

ExpiryExpiry OpenOpen HighHigh LowLow SettleSettle CHGCHG LifetimeLifetime

HighHigh

LifetimeLifetime

LowLow

Open Open 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 during Representative trading price during the last few minutes of trading the 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

Traded Traded at the at the Chicago Chicago Board of Board of TradeTrade

Number of Number of outstanding outstanding contractscontracts

Pricing unitPricing unit

Few contracts Few contracts stay open as stay open as expiry approachesexpiry approaches

99

Futures Listings (Financial)Futures Listings (Financial)

Tuesday, March 25, 2003Tuesday, March 25, 2003

ExpiryExpiry OpenOpen HighHigh LowLow SettleSettle CHGCHG LifetimeLifetime

HighHigh

LifetimeLifetime

LowLow

Open Open 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 contract Each contract is worth $250 x is worth $250 x 872.20 at close 872.20 at close =$218,050=$218,050

1111110202/32 = 111.0625% of /32 = 111.0625% of par or $111,062.50 per par or $111,062.50 per contractcontract

Each contract Each contract calls for delivery calls for delivery of $100,000 par of $100,000 par value of bondsvalue of bonds

Decimal pt is Decimal pt is omitted: 872.20omitted: 872.20

1010

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 their The vast majority of holders choose to realize their

gains or losses by buying or selling an offsetting gains 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) = 905, then holder’s profit = $250 x (905-900) = $1,250.$1,250.

1111

MarginsMargins• A deposit of good faith money (security) that can A deposit of good faith money (security) that can

be drawn on by the brokerage firm to cover any be drawn on by the brokerage firm to cover any day-to-day losses that may be incurred (how is day-to-day losses that may be incurred (how is this different from stock trades?) this different from stock trades?)

• Initial margin Initial 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 the Maintenance margin – the minimal value of the margin balance before a margin call is issuedmargin balance before a margin call is issued

1212

Marking to MarketMarking to MarketExample: Corn futuresExample: Corn futures

Tuesday, March 25, 2003Tuesday, March 25, 2003

DayDay FFtt P/LP/L ProceedsProceeds

= P/L x = P/L x 5K5K

Acct. Acct. BalanceBalance

Initial margin = 10% or Initial margin = 10% or $2.28x5000x.1$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 720720Margin call is issued if maintenance margin = 5% or Margin 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 $50costs $50

Total =-Total =-$450, same $450, same as (Sas (STT-F-F00) ) x 5K x 5K

FF00

1313

LeverageLeverage

• In above example, on Day 1, FIn above example, on Day 1, Ft t has has moved (2.30-2.28)/2.28 = 0.88%, but moved (2.30-2.28)/2.28 = 0.88%, but profit as % of initial margin (ROM) = profit as % of initial margin (ROM) = 100/1140 = 8.8%, or 10X the change 100/1140 = 8.8%, or 10X the change in Fin Ft t since initial margin is only 10% since initial margin is only 10% of contract value.of contract value.

• High leverage results from low High leverage results from low margin requirement.margin requirement.

1414

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 Price volatility (risk) is inherent in all commodities

and financial marketsand financial markets– Futures contracts allow such risk to be shifted to a Futures contracts allow such risk to be shifted to a

risk takerrisk taker– This differs from gambling which involves the This differs from gambling which involves the

creation of a risk for the sole purpose of it being creation of a risk for the sole purpose of it being takentaken

• Why speculators buy futures and not the asset?Why speculators buy futures and not the asset?– Lower transaction costsLower transaction costs– LeverageLeverage

1515

HedgingHedging• Short (long) hedge – the sale (purchase) of Short (long) hedge – the sale (purchase) of

futures contract [commit to selling (buying) futures contract [commit to selling (buying) asset at current futures price (Fasset at current futures price (F00)] to reduce )] to reduce the possible decline (rise) in value of an asset the possible 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 bears hedger bears no risk if asset and contract held until no risk if asset and contract held until maturitymaturity

• 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 rises more (less) than

FFtt, a long spot-short future (short spot-long future) , a long spot-short future (short spot-long future) position will benefit.position will benefit.

1616

Example – Short HedgeExample – Short Hedge• Owns 200 bonds @$1,000 par value. Total Owns 200 bonds @$1,000 par value. Total

portfolio = $200,000portfolio = $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, Since each T-bond futures contract is $100,000,

it needs to sell (short) 2 contracts to fully hedgeit needs 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 Bond holdingsholdings

$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)

1717

Example – Long HedgeExample – Long Hedge• Corn mill processor expects to receive cash Corn 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 Buy corn at marketmarket

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

1818

ProblemProblem• Farmer Brown grows #1 red corn and Farmer Brown grows #1 red corn and

would like to hedge the value of the would like to hedge the value of the coming harvest. However, the futures coming harvest. However, the futures contract is on the #2 yellow grade of contract is on the #2 yellow grade of corn. Suppose that yellow corn corn. Suppose that yellow corn typically sells for 90% of the price of typically sells for 90% of the price of red corn. If he grows 100,000 bushels red corn. If he grows 100,000 bushels and each futures contract calls for and each futures contract calls for delivery of 5,000 bushels, how many delivery of 5,000 bushels, how many contracts should he buy or sell to contracts should he buy or sell to hedge his position?hedge his position?

1919

Pricing commodity futuresPricing commodity futures• Two equivalent strategies –Two equivalent strategies –

1.1. Buy futures contract today; take delivery of commodity Buy futures contract today; take delivery of commodity at maturity and pay Fat maturity and pay F0 0 at maturity. at maturity. – Cash flow = FCash flow = F0 0

2.2. Borrow the spot price (SBorrow the spot price (S00) and buy the commodity ) and buy the commodity today; incur storage cost of today; incur storage cost of cc per period (as % of spot per period (as % of spot price) until maturity. Assume maturity is t period out, price) until maturity. Assume maturity is t period out, thenthen– Cash flow = Purchase cost (SCash flow = Purchase cost (S00) + interest cost (S) + interest cost (S00rrff) )

+ storage cost (S+ storage cost (S00cc) = S) = S00 (1+r (1+rff++cc))t t where rwhere rf f = = periodic risk-free rateperiodic risk-free rate

• Arbitrage opportunity Arbitrage opportunity both strategies have the both strategies have the same value, thussame value, thus

FF0 0 == SS00 (1 + r (1 + rf f + + cc))t t

• Why rWhy rff? Let t=1. A total upfront investment of S? Let t=1. A total upfront investment of S00, , net of storage cost of Snet of storage cost of S00cc, grows to a final value of , grows to a final value of FF00 at maturity: the rate of return is (F at maturity: the rate of return is (F00 – S – S00 – S – S00cc)/S)/S00. . Since all values in this expression are known at Since all values in this expression are known at time 0, the return is risk-free, thus rtime 0, the return is risk-free, thus r ff..

2020

Pricing commodity futuresPricing commodity futures• If the asset is not storable for If the asset is not storable for

technological (electricity) or technological (electricity) or economic (crops with seasonal economic (crops with seasonal harvest cycles) reasons, then harvest cycles) reasons, then cc = 0 = 0

• SpreadsSpreads– Relationship between futures prices for Relationship between futures prices for

contracts of different maturity datescontracts of different maturity dates

– Since FSince F11== SS00 (1 + r (1 + rf f + + cc))t1t1 and F and F22== SS00 (1 + (1 + rrf f + + cc))t2, t2, thus Fthus F22== FF1 1 (1 + r(1 + rf f + + cc))t2-t1t2-t1

2121

Spread tradingSpread trading• The simultaneous purchase and sale of The simultaneous purchase and sale of

the same or similar commodity in the the 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 related Inter-commodity spread – two related

commodities (long one and short the other)commodities (long one and short the other)

• Advantages of spreads Advantages of spreads 1. typically require smaller margin deposits 1. typically require smaller margin deposits 2. underlying market direction isn't 2. underlying market direction isn't importantimportant3. seasonal patterns exist among spreads3. seasonal patterns exist among spreads

2222

Example of spread tradingExample of spread trading• July Soybeans were trading at $5.10/bushel and July Soybeans were trading at $5.10/bushel and

November Soybeans were at $5.35 November Soybeans were at $5.35 the spread the spread is said to be at .25 to the November side. is said to be at .25 to the November side.

• Enter a July/November bean spread (buy a July Enter a July/November bean spread (buy a July and sell a November contract)and sell a November contract)

• If soybeans rallied and July settled one day at If soybeans rallied and July settled one day at $5.70 and November settled at $5.75, the spread $5.70 and November settled at $5.75, the spread would now be .05. would now be .05.

• The July contract will make 60 cents and The July contract will make 60 cents and November contract will lose 40 cents, leaving a November contract will lose 40 cents, leaving a net gain of 20 cents on the spread. net gain of 20 cents on the spread.

• Since each contract is 5000 bushels, the profit Since each contract is 5000 bushels, the profit will be 20 cents/bushel * 5000 bushels = $1,000. will be 20 cents/bushel * 5000 bushels = $1,000.

• If you had entered the spread in the other If you had entered the spread in the other direction you would be losing $1,000. direction you would be losing $1,000.

2323

Stock index futuresStock index futures• Contract Contract

– cash settlement onlycash settlement only– S&P500 (x$250), DJIA (x$10), Russell 2000 S&P500 (x$250), DJIA (x$10), Russell 2000

(x$500), Nasdaq 100 (x$100), S&P Mid-Cap (x$500), Nasdaq 100 (x$100), S&P Mid-Cap (x$500), FT-SE 100 (x10 pound), Nikkei (x$5) (x$500), FT-SE 100 (x10 pound), Nikkei (x$5)

• PricingPricing– FF0 0 == SS00 (1 + r (1 + rf f --d d ))t t where where dd = dividend accruing = dividend accruing

to holder of portfolio (as % of spot price Sto holder of portfolio (as % of spot price S00))– Net cost of long position (buy portfolio now and Net cost of long position (buy portfolio now and

carry to maturity) = cost of purchase (Scarry to maturity) = cost of purchase (S00) + ) + interest cost of funds (Sinterest cost of funds (S00 x r x rff) - dividend received ) - dividend received (S(S00 x x dd).).

– Net cost of short position = buying the portfolio Net cost of short position = buying the portfolio with deferred delivery and pay Fwith deferred delivery and pay F00 at that time at that time

– Arbitrage opportunity Arbitrage opportunity both strategies have the both strategies have the same valuesame value

2424

ProblemProblem• Assume the S&P500 index is at 1,000 and Assume the S&P500 index is at 1,000 and

is expected to be at 1,020 in one month.is 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 If you go long on a 12-month index contract, what will be contract, what 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 parity proceeds in one month (assume the parity condition holds)? condition holds)?

(b) the holding period return if the initial (b) the holding period return if the initial margin on the contract is $15,000?margin on the contract is $15,000?

2525

Creating synthetic stock positions Creating synthetic stock positions with stock index futureswith stock index futures

• Index futures allow participation in broad Index futures allow participation in broad market movements without actually market movements without actually buying or selling large amounts of stockbuying or selling large amounts of stock

• Market timers shift between stocks and Market 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.

2626

Synthetic stock position Synthetic 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 = Since each contract controls $250 x 900 =

$225,000 worth of stocks, it needs $90M/225K = $225,000 worth of stocks, it needs $90M/225K = 400 contracts400 contracts

• To pay for 400 contracts @915 in one month, we To pay for 400 contracts @915 in one month, we need 400 x 250 x 915/1.01 = $90.59M in T-billsneed 400 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 Strategy is thus equivalent to holding the stock index, minus the huge transaction costs.index, minus the huge transaction costs.

2727

Hedging market risk with index Hedging market risk with index futuresfutures• You own a $30M diversified stock portfolio You own a $30M diversified stock portfolio

with with =0.8. The current S&P 500 index is =0.8. The current S&P 500 index is 1,000. What should you do if you want to 1,000. What should you do if you want to protect the portfolio from price declines in protect the portfolio from price declines in the next 2 months?the next 2 months?– You are long on asset, so you need to short (sell) You are long on asset, so you need to short (sell)

the futures contracts with 2 month expirythe futures contracts with 2 month expiry– For every 1 pt. drop in the S&P, the portfolio For every 1 pt. drop in the S&P, the portfolio

incurs a loss of 0.8 x (1/1000) = 0.08%. In dollar incurs a loss of 0.8 x (1/1000) = 0.08%. In dollar terms, 0.08% x $30M = $24,000. terms, 0.08% x $30M = $24,000.

– A 1 pt. drop on the index, however, will generate A 1 pt. drop on the index, however, will generate profit of 1 x $250 =$250 on the futures contract.profit of 1 x $250 =$250 on the futures contract.

– To hedge, you need (24,000/250) = 96 To hedge, you need (24,000/250) = 96 contracts.contracts.

– Alternatively, one contract controls $250 x 1000 Alternatively, one contract controls $250 x 1000 = 250K worth of stocks, thus to cover $30M you = 250K worth of stocks, thus to cover $30M you need (30/0.25)x0.8 = 96 contracts. need (30/0.25)x0.8 = 96 contracts.

2828

ProblemProblem• You manage a $13.5M stock portfolio You manage a $13.5M stock portfolio

with with = 0.6. You believe the market = 0.6. You believe the market is about to drop temporarily, but you is about to drop temporarily, but you don’t want to move your portfolio don’t want to move your portfolio into T-bills because of the transaction into T-bills because of the transaction cost. The S&P 500 index is currently cost. The S&P 500 index is currently at 1,350. What should you do using at 1,350. What should you do using futures contracts to hedge the futures contracts to hedge the downside risk? downside risk?

2929

Foreign Exchange FuturesForeign Exchange Futures• Interest rate parity theoremInterest rate parity theorem

– an investor must earn the same rate of return an investor must earn the same rate of return by investing in risk-free money market by investing in risk-free money market securities at home as could be earned from a securities at home as could be earned from a hedged investment in risk-free foreign money hedged investment in risk-free foreign money market securities. market securities. 1.1. Proceeds in 1 year by investing in risk-free money Proceeds in 1 year by investing in risk-free money

market securities at home = $1 x (1+rmarket securities at home = $1 x (1+rusus))2.2. (a) Proceeds in 1 year by investing in foreign money (a) Proceeds in 1 year by investing in foreign money

market securities = $1/Smarket securities = $1/S00 x (1+r x (1+rforeignforeign))(b) Hedging the foreign investment to guarantee (b) Hedging the foreign investment to guarantee current exchange rate = $1/Scurrent exchange rate = $1/S00 x (1+r x (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

3030

Covered interest arbitrageCovered interest arbitrage• Violation of interest rate parity theorem Violation of interest rate parity theorem

arbitrage opportunity arbitrage 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 is Profit 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 (Sx (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.

3131

Covered interest arbitrageCovered interest arbitrageActionAction 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 $. Repay Convert to $. Repay 1.06 pound at year 1.06 pound at year endend

$1.37$1.37 -S-S11 x (1.06) x (1.06)

2.2. Lend $1.40 in the Lend $1.40 in the U.S. U.S.

-$1.37-$1.37 $1.40 x $1.40 x (1.05)(1.05)

3.3. Enter futures Enter futures contract to buy 1.06 contract to buy 1.06 pound at Fpound at F00 = $1.37 = $1.37

$0$0 1.06 x 1.06 x

(S(S11-$1.37)-$1.37)

TotalTotal $0$0 $.0178$.0178Gain = (1.40 x 1.05 – 1.37 x 1.06)

Long hedgeShort asset

3232

Interest rate futuresInterest rate futures• A great tool to hedge against A great tool to hedge against

uncertainty in interest rates foruncertainty in 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* x P = -D* x

YTM (e.g., a 1% change in the YTM of YTM (e.g., a 1% change in the YTM of the bond will reduce bond price by D* the bond will reduce bond price by D* %.). Note that D* = D/(1+YTM) where %.). Note that D* = D/(1+YTM) where D=duration.D=duration.

3333

Interest rate risk hedge Interest rate risk hedge exampleexample• You manage (long position) a $10M bond You 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 A 1% rise in interest rate will result in D* x

1% = 9% (or 9% x 10M = $900K) loss in bond 1% = 9% (or 9% x 10M = $900K) loss in bond value value 900K/100 basis pt = $9,000/basis pt 900K/100 basis pt = $9,000/basis pt = Price Value of a Basis Point (PVBP)= Price 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% = rise in interest rate will result in D* x 1% = 10% (or 10% x bond value per contract = 10% (or 10% x bond value per contract = 10% x $90 x $1,000 = $9K) loss in a futures 10% x $90 x $1,000 = $9K) loss in a futures contract contract PVBP = 9K/100 basis pt = PVBP = 9K/100 basis pt = $90/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.

3434

Interest rate swapsInterest rate swaps• Obligate two counterparties to exchange Obligate two counterparties to exchange

cash flows at one or more future datescash flows at one or more future dates

• Example: Firm with $10M fixed 8% LTD Example: Firm with $10M fixed 8% LTD desires to convert into floating rate.desires to convert into floating rate.

• Strategy: use swap agreement with notional Strategy: use swap agreement with notional principal of $10M that exchanges LIBOR for principal of $10M that exchanges LIBOR for an 8% fixed rate. Firm will pay counterparty an 8% fixed rate. Firm will pay counterparty $10M x LIBOR and receive $10M x 8% which $10M x LIBOR and receive $10M x 8% which offsets the fixed obligation on the LTD.offsets the fixed obligation on the LTD.

• Net cash flow = -LIBOR x $10M instead of -Net cash flow = -LIBOR x $10M instead of -8% x $10M. 8% x $10M.

3535

Futures vs. ForwardsFutures vs. ForwardsFuturesFutures ForwardForward

ContractContract Highly Highly standardizedstandardized

CustomCustom

ExchangeExchange EstablishedEstablished OTCOTC

Mark to Mark to MktMkt

YesYes NoNo

Settled @Settled @ Ending price (PEnding price (PTT)) Contract price (FContract price (F00))

Credit riskCredit risk No (counter party No (counter party is clearinghouse)is clearinghouse)

YesYes

DurationDuration Traded Traded continuouslycontinuously

Held until maturityHeld until maturity

Cash flowCash flow Daily + Margin Daily + Margin Req.Req.

At deliveryAt delivery