FUTURES

DefinitionDefinition

• Futures are marketable forward contracts.

• Forward Contracts are agreements to buy or sell a specified asset (commodities, indices, debt securities, currencies, etc.) at an agreed-upon price (f) for purchase or delivery on a specified date (delivery date: T).

• Futures are marketable forward contracts.

• Forward Contracts are agreements to buy or sell a specified asset (commodities, indices, debt securities, currencies, etc.) at an agreed-upon price (f) for purchase or delivery on a specified date (delivery date: T).

Futures ExchangesFutures Exchanges

• Futures are traded on organized exchanges:– CBOT

– CME

– NYFE

• The exchanges provide marketability:

• Listings– Standardization

– Position Traders

– Clearinghouse

• Futures are traded on organized exchanges:– CBOT

– CME

– NYFE

• The exchanges provide marketability:

• Listings– Standardization

– Position Traders

– Clearinghouse

Futures PositionsFutures Positions

• Long Position: Agreement to buy.

• Short Position: Agreement to sell.

• Long Hedge: Taking a long position in futures to protect against a price increase.

• Short Hedge: Taking a short position in a futures to protect against a price decrease.

• Long Position: Agreement to buy.

• Short Position: Agreement to sell.

• Long Hedge: Taking a long position in futures to protect against a price increase.

• Short Hedge: Taking a short position in a futures to protect against a price decrease.

ClearinghouseClearinghouse

Like the OCC, the futures clearinghouse guarantees each contract (both long and short positions) and acts as an intermediary, breaking up each contract after it has been established.

Like the OCC, the futures clearinghouse guarantees each contract (both long and short positions) and acts as an intermediary, breaking up each contract after it has been established.

ExampleExample

• Suppose A buys a September Wheat Futures contract (5,000 bu.) from B for fo = $2.50/bu.– A is long; B is Short

• After the contract is established, the CH steps in and breaks up the contract.

• Suppose A buys a September Wheat Futures contract (5,000 bu.) from B for fo = $2.50/bu.– A is long; B is Short

• After the contract is established, the CH steps in and breaks up the contract.

CH RecordsCH Records

• A agrees to buy at $2.50.

• B agrees to sell at $2.50.

• A agrees to buy at $2.50.

• B agrees to sell at $2.50.

Example Continued

• Suppose the price of wheat increases, causing the September futures price to increase to ft = $3.00.

• Suppose A decides to close by going short.

• New Contract: A agrees to sell September Wheat futures at $3.00 to C.

– A is short; C is long.

• After the contract is established, the CH breaks it up.

CH Records

• A agrees to buy at $2.50.

• B agrees to sell at $2.50.

• A agrees to sell at $3.00.

• C agrees to buy at $3.00.

CH owes A$0.50

At Expiration

• In the absence of arbitrage, the price on an expiring futures contract must be equal to the spot price.

f ST T

Example Continued

• At the September expiration, suppose the spot price of wheat is at $3.50/bu.

• B is short and needs to close by going long (B is not a farmer).

• C is long and needs to close by going short (C does not need 5000 bu of wheat).– New Contract: B agrees to buy September Wheat (that is

expiring) from C for $3.50.• CH breaks up the contract.

CH RecordsCH Records

• B agrees to sell at $2.50.

• C agrees to buy at $3.00.

• B agrees to buy at $3.50.

• C agrees to sell at $3.50.

B owes CH $0.50

CH owes C $.50

Long Futures Hedge

• Take long position in futures to protect against an increase in the spot price.

• EXAMPLE:– OJ distributor plans to buy 15,000 lbs of frozen OJ in September.

To protect against an increase in the spot price of OJ, the distributor goes long in one OJ futures contract (size = 15,000 lbs) at fo = $0.96/lb.

– At delivery, the distributor buys OJ on the spot market at the spot price and closes the futures position by going short in the expiring futures at a futures price equal to the spot price.

Cost at T

S fT T $ 0 . 9 0 $ 0 . 9 6 $ 1 . 0 0

O J C o s t = S ( 1 5 , 0 0 0 ) 1 3 5 0 0 1 4 4 0 0 1 5 0 0 0

F Tf [ $ . ]9 6 1 5 0 0 0 - 9 0 0 0 6 0 0

C o s t = R o w 2 - R o w 3 1 4 4 0 0 1 4 4 0 0 1 4 4 0 0

Short Futures Hedge

• Take short position in futures to protect against a decrease in the spot price.

• EXAMPLE:– Wheat farmer plans to sell 5000 bu. of wheat in September. To

protect against a decrease in the spot price, the farmer goes short in a September wheat futures at fo = $2.40

– At delivery, the farmer sells wheat on the spot market at the spot price and closes the futures position by going long in the expiring futures at a futures price equal to the spot price.

Revenue at T

S fT T $ 2 . 0 0 $ 2 . 4 0 $ 3 . 0 0

O J R e v . = S ( 5 0 0 0 ) 1 0 0 0 0 1 2 0 0 0 1 5 0 0 0

F Tf [ $ 2 . ]4 0 5 0 0 0 2 0 0 0 0 - 3 0 0 0

R e v = R o w 2 + R o w 3 1 2 0 0 0 1 2 0 0 0 1 2 0 0 0

Hedging Risk

Quantity Risk

Quality Risk

Timing Risk

Speculative Positions

• Pure Outright Position: – Long Position (Bullish)

– Short Position (bearish)

• Spread– Intracommodity Spread: long and short in futures on the

same underlying asset but with different expirations.– Intercommodity Spread: Long and short in futures with

different underlying assets but the same expiration.

Initial Margin Requirements

• Initial Margin: Cash or RF securities that must be deposited with the broker to secure the position. Initial margin (Mo) is equal to a porportion (m) times the contract value.

• Example: September wheat contract at fo = $2.40 (long or short) with m = .10:

M0 10 40 . [($2. )(5000)] $1200

Maintenance Margin Requirements

• Maintenance Margin: Keep the equity value of the commodity account (Eq) equal to a proportion (90% to 100%) of initial margin.

Eq M position Value 0 ( .. )

Example• September wheat prices increase from $2.40 to

$2.42. With a 100% maintenance margin requirement, a long position would be overmargined and a short position would be undermargined:

LONG Eq

Eq Overm ined

SHORT Eq

Eq Underm ined

: $1200 ($2. . )(5000)

$1300 arg

: $1200 ($2. $2. )(5000)

$1100 arg

42 2 40

40 42

Undermargined Positions

• If an account is undermargined, the investor must deposit additional funds to satisfy the maintenance margin requirement. If the investor does not do this, then she will receive a margin call from the broker instructing her that her account will be closed unless she deposits the requisite funds.

• When the equity value of the account meets the maintenance margin requirement, the account is said to be marked to market.

Other Points

• Equity accounts are adjusted daily.

• Futures Funds are often set up where the funds of investors are used to buy RF securities which the fund uses to satisfy the margin requirements for the futures. Such funds can be viewed as overmargined futures positions.

Financial Futures• Stock Index Futures

• Futures on Debt Securities

• Foreign Currency Futures

Stock Index Futures

• Types:– SP 500 (CME, Multiplier = 500)– MMI (CBT, Multiplier = 250)– SP OTC (CME, Multiplier = 500)

• Cash Settlement Feature• Multiplier • Use: Speculation, hedging, and portfolio

management.

Hedging Portfolio Future Value

Example:• Portfolio manager plans to liquidate a $50M portfolio in

September. The portfolio is well-diversified with a beta of 1.25. The current S&P 500 is at 1250 and there is a September S&P 500 futures index trading at fo = 1250. (Note futures and spot prices are usually not equal.)

• Hedging Strategy: Go short in 100 September index futures contracts:

nV

f

Mf

0

0

125

1250100

( . )$50

( )(500)

Hedged Value at TST 1.25g V g MT( . )501125 f 3+2

1000 -.25 $37.50M $12.5M$50M

1125 -.125 $43.75M 6.25M50M

1250 0 $50.00M 0 50M

1375 .125 $56.25M -6.25M50M

1500 .25 $62.5M -12.5M50M

gST

1250

1250 f TS ( )(500)[ ]100 1250

Portfolio Uses

• Speculating on Unsystematic Risk

• Market Timing

nV

ff TR 0

00[ ]

nV

ff

S

0

0

Futures on Debt Securities• Types

–T-Bills (IMM)

–T-Bonds and Notes (CBT)

–Eurodollar Deposits (IMM)

–Municipal Bond Index (CBT)

T-Bill Futures

• T-Bill futures call for the delivery or purchase of a T-bill with a maturity of 91 days and a face value of $1M. Used for speculating on S-T rates and hedging.

• Prices on T-Bill futures are quoted in terms of the IMM index or discount yield (Rd):

• Formula to Convert:

Index RD 100

fR

MD0

100 25

100

(. )($1 )

Eurodollar Futures

Eurodollar Futures are similar to T-Bill futures. They call for delivery or purchase of Eurodollar deposits with a maturity of 90 days and F = $1M. They are quoted in terms of the IMM index. They differ from T-Bill futures in that there is a cash settlement feature. The cash settlement is based on the LIBOR. Used for speculating on ST rates and for hedging bank positions ( correlated with CD rates).

T-Bond Futures• T-Bond Futures contracts call for the delivery or

purchase of a T-Bond with a face value of $100,000. The contract allows for the delivery of a number of T-Bonds; there is a conversion factor used to determine the actual price of the futures given the bond that is delivered.

• T-Bond futures are quoted in terms of a T-Bond with an 8% coupon, semiannual payments, maturity of 15 years, and face value of $100.

Long Hedging with Debt Futures

• Bond manager expecting an inflow of cash in the future which he plans to invest in T-Bills for 90 days (or long term). To hedge the manager would go long in T-Bill futures (T-Bond Futures).

r P nTB

f

Short Hedging with Debt Futures

Short Hedging Strategies:

• Bond manager expecting to liquidate a bond portfolio in the future.

• A company planning to issue bonds or borrow.

• A bank or financial institution managing its maturity gap.

• A company wanting to fix a variable-rate loan.

Speculation • Outright Positions

– Long: Expect rates to decrease. ST Rates: use T-Bills or Eurodollar futures; LT: use T-Bonds or Notes.

– Short: Expect rates to increase. ST: use T-Bills or Eurodollars; LT: use T-Bonds or Notes.

• Spread:– Intracommodity

– Intercommodity: • Expect Recession: Short MBI, Long T-Bond or Short Eurodollar, long T-

Bill.

• Expect Upward Twist of YC: Short T-B0nd, Long T-Bill.

Cross Hedging

• Cross Hedging is hedging a position with a futures contract in which the asset underlying the futures is different than the asset to be hedged.

• Example: Future CP sale hedged with T-Bill futures; AA Bond portfolio hedged with T-Bond futures.

• For bond positions, the following formula can be used:

nDur

Dur

S

f

YTM

YTMfS

f

f

S

0

0

1

1

Foreign Currency Futures

• Traded on the IMM.

• Futures on major currencies:– DM (125,000)– BP (25,000)– FF (250,000)

• Use: Hedging and speculation.

Hedging Example

• Expecting a receipt of 625,000 DM in September.

• September DM futures is trading at fo = $0.40/DM.

• Hedging Strategy: Go short in 5 September DM futures:– nf = 625000DM/125000DM

Hedged Dollar Revenue at T

ET E DMT( )625000 f C2+C3

$.35/DM $218,750 $31,250$250,000

$.40/DM $250,000 0 $250,000

$.45/DM $281,250 -31,250$250,000 f TDM DM E (5)( , )[$. / ]125 000 40

Futures Pricing

• Basis (B):

• Carrying Cost Model: Equilibrium futures price is equal to the net cost of carrying the underlyning asset to expiration. This relation is governed by arbitrage.

B f S

B Normal

B Inverted

t t t

t

t

0

0

Pricing T-Bill Futures

• Let So = spot price of T-Bill with maturity of 91 days + T; Rf = RF rate or repo rate with maturity of T; fo = price of T-bill future expiring at T.

f S R fT

0 0 1 ( )

Example

• Price on spot T-Bill maturing in 161 days is So = 97.5844; 70-day RF rate is 6.38%.

• Equilibrium price of T-Bill futures with expiration of 70 days (or T= 70/365):

f070 36597 5844 10638 98 74875 . ( . ) ./

Arbitrage

• Overpriced:• If the market price of T-bill futures is at 99, an arbitrageur

could earn a riskless profit of 99-.98.74875 = 0.25125 (times a $1M) by:– Borrowing $97.5844 at Rf = 6.38% , then buying 161-day T-Bill

at So = 97.5844;

– taking short position in a T-bill futures expiring in 70 days at fm = 99.

• At T, the arbitrageur would sell the spot T-bill on the futures (it would now have a maturity of 91 days) and pay off her loan.

Arbitrage

• Underpriced:• If the market price of T-bill futures is at 98, an investor

holding 161-day bills could earn a riskless profit of 98.74875-98 = 0.74875 (times a $1M) by:– Selling the bills for $97.5844, then investing the proceeds in RF

security for 91 days at Rf = 6.38%;

– taking long position in a T-bill futures expiring in 70 days at fm = 98.

• At T, the arbitrageur would buy the spot T-bill on the futures (it would now have a maturity of 91 days) for 98 and receive 98.74875 from her investment.

Pricing Stock Index Futures

• Let So = spot price of stock index (S&P 500); Rf = RF rate or repo rate with maturity of T; D = dividend per share on portfolio underlying the index which can be estimated from a proxy portfolio; fo = price of T-bill future expiring at T.

f S R DfT

0 0 1 ( )

Proxy Portfolio

• Stock Index futures are often priced in terms of a proxy portfolio. A Proxy portfolio is a portfolio which is highly correlated with the index (could be 30-stock portfolio or a MF). This portfolio can be viewed as equivalent to holding hypothetical shares in the index.

• For example, if the S&P 500 is at 1200, a $10M well-diversified portfolio with a beta of 1 and expected dividends at T worth $250,000 could be viewed as owning 8333.333 hypothetical index shares that are selling at $1200 per share and paying a dividend per share of $30.

Example

• Spot index (S&P 500) is at 1200 and RF rate is 8% for RF securities maturing in 180 days.

• Using the proxy portfolio, the equilibrium price S&P 500 futures with expiration of 180 days (or T= .5 per year:

07.121730$)08.1(1200 5.0 f

Index Arbitrage

• Overpriced:

• If the futures were priced at fm = 1245, an arbitrageur could earn a riskless profit by going long in the proxy portfolio and short in the futures:– Borrow $10M and buy portfolio.– Go short in 8333.333/500 = 16.6667 futures.

CF at TC l o s i n gP o s i t i o n s

g = - . 1 0S = 1 0 8 0

g = + . 1 0S = 1 3 2 0

D e b t :$ 1 0 ( . ) .M 1 0 8 5

- $ 1 0 . 3 9 2 M - $ 1 0 . 3 9 2 M

P o r t f o l i o : $ 1 0 M ( 1 + g )

$ 9 M $ 1 1 M

F u t u r e s :( . ) ( 5 0 0 ) [ ]1 6 6 6 6 7 1 2 4 5 f T

$ 1 . 3 7 5 M - $ . 6 2 5 M

D i v i d e n d s $ . 2 3 3 M $ . 2 3 3 M

C F $ . 1 9 1 3 M $ . 1 9 1 3 M

Pricing Currency Futures

• Carrying cost for currency futures is the interest rate parity model discussed in many international text:

f ER

R

where

R Foreign RF Rate

US

F

T

F

0 0

1

1

:

.. ..