10. Futures and Forwards(1) (1)

8/6/2019 10. Futures and Forwards(1) (1)

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Dr. E. BOUKRAMI09/05/11 1

v

Futures andFutures and

forwardsforwards


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Agenda

Futures and forwards

Pricing Trading mechanics

Trading strategies

Basis risk

Theories of futures prices

Foreign exchange futures and hedging FX risk

Index futures and index arbitrage

Hedging systematic risk Interest rate futures and IR hedging


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Futures and Forwards

Forward - an agreement calling for a future delivery of an

asset at an agreed-upon price (delivery price) Future- similar to a forward but with formalized andstandardized structure (and other peculiarities as we willsee)

Forward (or futures) price - agreed-upon price for thetransaction at maturity.

Underlying: the commodity or asset that is to be sold orbought.

Long position - agree to purchase at a future date Short position - agree to sell at a future date

Maturity date: day for the agreed transaction


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Payoff diagrams

S(T) = price of spot at maturity time TK = original forward price

S(T) - K K - S(T)

Spot price atmaturity

Spot price atmaturity

P/L P/L

Profits on positions at maturity:

Long position Short position

KK


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Determining the forward price

Cost of carry model:

No arbitrage hypothesis

K = S(0)(1+r)T

Short position in a

forward contract

with forward price K Receive K

Buy underlying

asset at today'sprice -S(0) Deliver asset

Borrow S(0) Payback loan -S(0)*(1+r)^T

Net investment: 0 P/L: K - S(0)*(1+r)^T

Initial time Maturity date

K = S(0)erT

Discrete time

Continuous time


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Profits and losses before maturityF(t) = forward price at time tK = F(0) = forward price at initial timeS(t) = spot price at time t

T = maturity time

t=0

Long positionforward price isset at F(0)=K

t t=T

New contractsprice is quoted atF(t)

P/L of my position is:Present value of F(t)- K

K

F(t)F(t)


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Convergence between forward and spot pricesF(t) = future (or forward) price at time tK = F(0) = futures price at initial time

S(t) = spot price at time tT = maturity time

t=0 t t=T

K

F(t)

S(t)

F(T)=S(T)

S(0)

F(t)=S(t)er(T-t)


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Futures contracts

Futures - similar to forwards but feature formalized and standardizedcharacteristics

Forwards Futures

OTC transactions Exchange traded

Non-standardized, tailored to

specific needs Standardized contracts

Single delivery date Range of delivery dates

Settled at maturity Daily marked-to-market

No margin requirement Margin requirements

Held until maturity Positions sclosed before maturity

Usuallly final delivery takes

place Contract settled before maturity

No secondary market Secondary market (+liquidity)


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Markets

http://www.biz.uiowa.edu/iem

CME Group

CME

CBOT

Eurex

Euronext.liffe

Euronext (merger of Amsterdam, Brussels and ParisExchanges)

Liffe

Pit + Electronic trading system GLOBEX

Non financial:

Financial:

(Deutsche Borse + Swiss Exchange)

NYSE-Euronext


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Futures trading

Investorin NYwants tobuy

Broker FloorTrader

FloorTrader

Broker

Investor inParis wantsto sell

Agreed price

Current futures price

Pricediscovery

process

ask

bid

Exchange pit (open outcry)

and/or electronic platform


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Margins

Investorin NYwants tobuy

Broker FloorTrader

FloorTrader

Broker

Investor inParis wantsto sell

ask

bid

Clearinghouse

Member

InitialMargin

InitialMargin


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Futures Trading Mechanics

Clearinghouse - acts as a party to all buyers and sellers

Obligated to deliver or supply delivery

Closing out positions Reversing the trade

Take or make delivery

Most trades are reversed and do not involve actual delivery

Open Interest

Physical delivery The actual commodity with certaincharacteristics is delivered at a specific time and location.

Cash Settlement some contracts are settled in cash ratherthan delivery of the underlying assets


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Margin and Trading Arrangements

Initial Margin - funds deposited to provide capital to absorb

losses

Marking to Market - each day the profits or losses from the new

futures price are reflected in the account

Maintenance or variation margin - an established value below

which a traders margin may not fall

Margin call - when the maintenance margin is reached, broker

will ask for additional margin funds


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Basis and Basis Risk

Basis - the difference between the futures price and thespot price: b(t)=F(t)-S(t)

Basis Risk - the variability in the basis that will affectprofits and/or hedging performance

t=0 t t=T

K

F(t)

S(t)

F(T)=S(T)

S(0)

b(t)


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Trr foreigndomeSF)(

00

=

where

F0is the forward price

S0 is the current exchange rate

Foreign Exchange Futures

or

T

foreign

domestic

r

rSF

++=

1

100

Direct exchange rate quote: The exchange rate is expressed as dollars per the foreign currency

Indirect exchange rate quote:

The exchange rate is expressed as the foreign currency per the dollar


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FX hedging example: Boeing

Boeing is a US-based manufacturer.

It has sold a turbine engine to a British firm for 1,000,000. The sale is in March and the payment will be done 3

months later, in June.

FX exposure (currency risk): a depreciation of the pound inthree months will negatively affect the amount received.

Alternatives:

Remain unhedged;

hedge in the forward market;

hedge in the money market, or

hedge in the options market (we will see this later).


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Spot exchange rate: $1.7640 /

UK 90-day borrowing rate: 10% (2.5% per quarter)

UK 90-day investment rate: 8% (2% per quarter)

US 90-day borrowing rate: 8% (2% per quarter) US 90-day investment rate: 6% (1.5% per quarter)

Boeings forecast for spot rate in 3 months: $1.76 /

FX futures contracts on March, June, Sep and Dec.

90-day futures rate: $1.7540 / (2.2674% p.a. discount) Each futures contract is for buying/selling 10,000

Data


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Unhedged position

$/1.76

Value in $ of

Boeings 1m

1,760,000

pro

fit

s

losses

depreciates appreciates


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Money market hedge

borrow

1,000,000

(1 + 0.025)

Receives

1,000,000

= 975,610 = $1,720,976 ($1.764 / )

pay

invest

$ $

and buy $

in T-Bill, debt cost or cost of capital?


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Futures hedge

$/

1.76

Value in $ of Boeings 1m AR

1,760,000

pro

fit

s

losses

1.754

1,754,000

Need 1,000,000/10,000 = 100 futures contracts


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Interest Rate Hedging

Owners of fixed-income portfolios protecting against a rise

in rates Corporations planning to issue debt securities protecting

against a rise in rates

Investor hedging against a decline in rates for a planned

future investment Exposure for a fixed-income portfolio is proportional to

modified duration

Can synthesize an interest swap using forwards

10. Futures and Forwards(1) (1)

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