Lecture Presentation Software
to accompany
Investment Analysis and
Portfolio Management
Eighth Edition
by
Frank K. Reilly & Keith C. Brown
Chapter 21
Chapter 21
Forward and Futures Contracts
Questions to be answered:
• What are the differences in the way forward and
futures contracts are structured and traded?
• How are the margin accounts on a futures
contract adjusted for daily changes in market
conditions?
• How can an investor use forward and futures
contracts to hedge an existing risk exposure?
Chapter 21
Forward and Futures Contracts
• What is a hedge ratio and how should it be
calculated?
• What economic functions do the forward and
futures markets serve?
• How are forward and futures contracts valued after
origination?
• What is the relationship between futures contract
prices and the current and expected spot price for
the underlying commodity or security?
Chapter 21
Forward and Futures Contracts
• How can an investor use forward and futures
contracts to speculate on a particular view about
changing market conditions?
• How do agricultural futures contracts differ from
those based on financial instruments, such as stock
indexes, bonds, and currencies?
• How can forward and futures contracts be
designed to hedge interest rate risk?
Chapter 21
Forward and Futures Contracts
• How are implied forward rates and actual forward
rates related?
• What is stock arbitrage and how is it related to
program trading?
• How can forward and futures contracts be
designed to hedge foreign exchange rate risk?
• What is interest rate parity and how would you
construct a covered hedge interest arbitrage
transaction?
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 Contract Mechanics
• With commodity futures, it usually is the case that
delivery can take place any time during the month at the
discretion of the short position
• Forward contracts may not require either counterparty to
post collateral
• Futures exchange requires each customer to post an initial
margin account in the form of cash or government
securities when the contract is originated
• The margin account is marked to market at the end of
each trading day according to that day’s price movements
• All outstanding contract positions are adjusted to the
settlement position set by the exchange after trading ends
Hedging With Forwards and Futures
• Create a position that will offset the price risk of
another holding
– holding a short forward position against the long
position in the commodity is a short hedge
– a long hedge supplements a short commodity holding
with a long forward position
Hedging With Forwards and Futures
• Relationship between spot and forward price
movements
– basis is spot price minus the forward price for a
contract maturing at date T:
BtT = St - Ft,T
– forward price converges to the spot price as the
contract expires
– hedging exposure is correlation between future
changes in the spot and forward contract prices and
can be perfectly correlated with customized contracts
Hedging With Forwards and Futures
• Calculating the Optimal Hedge Ratio
– net profit from the position
 t  S t  S 0   Ft ,T  F0,T  N   S   F  N 

2
t ,T


N 
2
S
 
 N 
2
COVS, F

2
F
2
F
 2N COVS,F
  S
 
  F

 p

Forward and Futures Contracts:
Basic Valuation Concepts
• Forward and futures contracts are not
securities but, rather, trade agreements that
enable both buyers and sellers of an
underlying commodity or security to lock in
the eventual price of their transaction
Valuing Forwards and Futures
• Valuing forwards
Vt ,T  Q Ft ,T  F0,T   1  i 
T t 
•Valuing futures
•contracts are marked to market daily
* = the possibility that forward and futures prices
for the same commodity at the same point in time
might be different

V  t ,T  Q  F  t ,T  F  0,T

The Relationship Between Spot and
Forward Prices
• 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 - high storage costs and no
dividends
• Premium for owning the commodity
– convenience yield
– results from small supply at date 0
relative to what is expected at date T
(after the crop harvest)
• Backwardated market - future is less
than spot
Financial Forwards and Futures:
Applications and Strategies
• Originally, forward and futures markets were
organized largely around trading agricultural
commodities
• Recent developments in this area have involved
the use of financial securities as the asset
underlying the contract
• Interest rate forwards and futures were among
the first derivatives to specify a financial
security as the underlying asset
– forward rate agreements
– interest rate swaps
Financial Forwards and Futures:
Applications and Strategies
• 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
Financial Forwards and Futures:
Applications and Strategies
• A duration-based approach to hedging
 S 


S  S  S  Dmod S  iS n  S

N 

 

S
 F  F  Dmod F  i F n  F


 F 
 Dmod S
S

N 
 i 
 Dmod F
F
 i  the " yield beta"
Financial Forwards and Futures:
Applications and Strategies
• 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  Foreign Interest Rate 

365  


Forward  Spot 

 T  
 
 1  U.S. Interest Rate 
 365  

Currency Forwards and Futures

 T  
 1  RFR FC 
 
F0,T 
365  


S0 
 T 

 1  RFR USD 
 365  

• Where:
• T = the number of days from the joint settlement of the
futures and cash positions until they mature
• RFRUSD = the annualized risk-free rate in the United States
• RFRFC = the annualized risk-free rate in the foreign
market
The Internet
Investments Online
http://www.futuresmag.com
http://www.nfa.futures.org
http://www.futuresbasics.com
http://www.tfc-charts.w2d.com
End of Chapter 22
–Forward and Futures Contracts
Future topics
Chapter 23
• Option Contracts