Chapter 23
Forward and Futures Contracts
Innovative Financial Instruments
Dr. A. DeMaskey
An Overview of
Forward and Futures Trading

Forward contracts are negotiated directly
between two parties in the OTC markets.
–
–

Individually designed to meet specific needs
Subject to default risk
Futures contracts are bought through brokers on
an exchange.
–
–
–
No direct interaction between the two parties
Exchange clearinghouse oversees delivery and settles
daily gains and losses
Customers post initial margin account
Futures vs. Forward Contracts
Design
flexibility
Credit risk
Liquidity risk
Futures
Standardized
Forwards
Customized
Clearinghouse
Each party
Depends on
trading
Negotiated
exit
Hedging With Forwards and
Futures

Create a position that will offset the price
risk of another holding.
–
Short hedge
•
–
supplements a long commodity holding with a short
forward position
Long hedge
•
supplements a short commodity holding with a long
forward position
Relationship Between Spot
and Forward Prices

The basis is the spread between the spot
and futures price for the same asset at the
same point in time T:
–
–
–
–
Bt,T = St - Ft,T
Initial basis
Maturity basis
At maturity, the forward price converges to the
spot price (FT,T = ST)
Basis Risk

Profit from short hedge:
–
–


Bt,T - B0,T = (St - Ft,T) - (S0 - F0,T)
Terminal value of hedge equals cover basis minus
initial basis.
Real exposure is correlation between future
changes in the spot and forward contract prices
Basis risk is small if price movements are highly
correlated
–
–
Basis risk = 0 for forwards
Basis risk > 0 for futures
Optimal Hedge Ratio
Net profit of short hedge position:
 t  S t  S 0   Ft ,T  F0,T  N   S   F  N 
Variance of this value:

2
t ,T

2
S
 
 N 
2
2
F
 2N COVS,F
Minimizing and solving for N:

N 
COVS, F

2
F
  S
 
  F

 p

Valuing Forwards and Futures
The value of unwinding a forward position early:
Vt ,T  Q Ft ,T  F0,T   1  i 
T t 
The value of a futures, which are marked-to-market is:
V

t ,T

 Q  F

t ,T
F

0,T

* = the possibility that forward and futures prices for the same
commodity at the same point in time might be different.
The Cost of Carry Model

If you buy a commodity now for cash and store it
until you deliver it, the price you want under a
forward contract would have to cover:
–
–
–

the cost of buying it now
the cost of storing it until the contract matures
the cost of financing the initial purchase
These are the cost of carry necessary to move the
asset to the future delivery date.
F0,T  S 0  SC 0,T  S 0  PC0,T  i0,T  D0,T 
The Relationship Between
Spot and Forward Prices

Contango
–

Premium for owning the commodity
–
–

high storage costs and no dividends
convenience yield
results from small supply at time 0 relative to
what is expected at time T (after the crop
harvest)
Backwarded market
–
future is less than spot
Relationship Between Futures
Price and Expected Future
Spot Price

Pure Expectations Hypothesis
–

Normal Backwardation
–

F0,T = E(ST)
F0,T < E(ST)
Normal Contango
–
F0,T > E(ST)
Applications and Strategies

Interest Rate Forward and Futures
–
–
Short-term
Long-term
Equity Index Futures
 Currency Forward and Futures

Long-Term Interest Rate
Futures

Treasury bond and note contract mechanics
–
–
–
–
–
–
–
–
–
–
CBT $100,000 face value
T-bond >15 year maturity
T-note 10 year - bond with 6.5 to 10 year maturity
T-note 5 year - bond with 4.25 - 5.25 years
Delivery any day during month of delivery
Last trading day 7 days prior to the end of the month
Quoted in 32nds
Yield quoted is for reference
Treasury bonds pay semiannual interest
Conversion factors for differences in deliverable bonds
A Duration Based Approach to
Hedging
 Dmod S
S
N 
 i 
 Dmod F
F

 i  the " yield beta"
Treasury Futures Application

A T-Bond/T-Note (NOB) Futures Spread
–
–
–
expecting a change in the shape of the yield
curve
unsure which way rates will change
long one point on curve and short another point
Short-Term Interest Rate
Futures

Eurodollar and Treasury bill contract mechanics
–
–



Chicago Mercantile Exchange (CME or “Merc”),
International Monetary Market (IMM), LIFFE
LIBOR
Altering bond duration with futures contracts
Creating a synthetic fixed-rate funding with a
Eurodollar strip
Creating a TED spread
Stock Index Futures
Intended to provide a hedge against
movements in an underlying financial asset
 Hedging an individual stock with an index
isolates the unsystematic portion of that
security’s risk
 Stock index arbitrage

–
prominent in program trading
Currency Forwards and
Futures

Currency quotations
–
–
–

Direct (American) quote in U.S. dollars
Indirect (European) quote in non U.S. currency
Reciprocals of each other
Interest rate parity and covered interest
arbitrage

 T  
 1  RFR FC 
 
 365  

S0 
 T 

 1  RFR USD 
365



F0,T
The Internet
Investments Online
www.fiafli.org
www.e-analytics.com/fudir.htm
www.futuresmag.com
www.mfea.com/planidx.html