Futures
 Futures Markets
 Futures and Forward
 Trading Mechanism
 Speculation versus Hedging
 Futures Pricing
 Foreign Exchange, stock index, and Interest Rate
Futures
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Using Futures to manage foreign exchange rate risk
Index futures
Interest rate futures
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Futures and Forwards
 Forward - an agreement calling for a future delivery of an
asset at an agreed-upon price
 Futures - similar to forward but feature formalized and
standardized characteristics
 Key difference in futures
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Secondary trading - liquidity
Marked to market
Standardized contract units
Clearinghouse warrants performance
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Key Terms for Futures Contracts
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Futures price - agreed-upon price at maturity
Long position - agree to purchase
Short position - agree to sell
Profits on positions at maturity
Long = spot minus original futures price
Short = original futures price minus spot
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Futures Listings
 Page 758 (with explanations on page 757).
 Example:
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
Pick up agricultural contract; let’s look at the
March 2010 maturity corn contract
Each contract calls for delivery of 5,000 bushels
Profit for long
Profit for short
Chapter 1: Overview
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Futures vs Option
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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
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Trading without and without a Clearinghouse
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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 trader’s margin may not fall.
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Margin and Trading Arrangements
Margin call - when the maintenance margin is
reached, broker will ask for additional margin
funds
Convergence of Price - as maturity approaches the
spot and futures price converge
Delivery - Actual commodity of a certain grade with
a delivery location or for some contracts cash
settlement
Cash Settlement – some contracts are settled in cash
rather than delivery of the underlying assets
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Example: Maintenance margin
 Suppose the maintenance margin is 5% while the
initial margin was 10%. Still consider the March
maturity Corn contract. The initial purchase price
is $3.92 per bushel. How low the price of Corn
future price can go before the investor receives a
margin call?
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Example: Marking to Market
 Page 764
Chapter 1: Overview
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Trading Strategies
 Speculation 

short - believe price will fall
long - believe price will rise
 Hedging 

long hedge - protecting against a rise in price
short hedge - protecting against a fall in price
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Hedging Revenues (Futures Price = $67.15)
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Basis and Basis Risk
 Basis - the difference between the futures price
and the spot price

over time the basis will likely change and will
eventually converge
 Basis Risk - the variability in the basis that will
affect profits and/or hedging performance
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Futures Pricing
Spot-futures parity theorem - two ways to acquire an
asset for some date in the future


Purchase it now and store it
Take a long position in futures
With a perfect hedge the futures payoff is certain -there is no risk. A perfect hedge should return the
riskless rate of return
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Hedge Example
 Investor owns an S&P 500 fund that has a current
value equal to the index of $1,300
 Assume dividends of $20 will be paid on the index
at the end of the year
 Assume futures contract that calls for delivery in
one year is available for $1,345
 Assume the investor hedges by selling or shorting
one contract
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Hedge Example Outcomes
Value of ST
1,305
1,345
1,405
1,365
1,365
1,365
Payoff on Short
(1,345 - ST)
Dividend Income
Total
( F0  D)  S 0

S0
(1,345  20)  1,300
 5%
1,300
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General Spot-Futures Parity
( F0  D)  S 0
 Rf
S0
Rearranging terms
F0  S0 ( s  rf )  D  S0 (1  rf  d )
dD
S0
Multiple period formula: page 802 (22.2).
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Arbitrage Possibilities
 If spot-futures parity is not observed, then
arbitrage is possible
 If the futures price is too high, short the futures
and acquire the stock by borrowing the money at
the riskfree rate
 If the futures price is too low, go long futures,
short the stock and invest the proceeds at the
riskfree rate
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Theories of Futures Prices
 Expectations
 Normal Backwardation
 Contango
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Foreign Exchange Futures
 Futures markets
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Chicago Mercantile (International Monetary Market)
London International Financial Futures Exchange
MidAmerica Commodity Exchange
Active forward market
Differences between futures and forward markets
Spot and forward prices in foreign exchange – page 815
Foreign exchange futures
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Pricing on Foreign Exchange
Futures
Interest rate parity theorem
Developed using the US Dollar and
British Pound
 1  rUS
F0  E0 
 1  rUK



T
where
F0 is the forward price
E0 is the current exchange rate
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Text Pricing Example
rus = 5%
T = 1 yr
ruk = 6%
E0 = $1.60 per pound
1
 1.05 
F0  $1.60
  $1.585
 1.06 
If the futures price varies from $1.58 per
pound arbitrage opportunities will be present.
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Hedging Foreign Exchange Risk
A US firm wants to protect against a decline in profit
that would result from a decline in the pound
 Estimated profit loss of $200,000 if the pound
declines by $.10
 Short or sell pounds for future delivery to avoid
the exposure
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Hedge Ratio
Hedge Ratio in pounds
$200,000 per $.10 change in the pound/dollar exchange rate
$.10 profit per pound delivered per $.10 in exchange rate
= 2,000,000 pounds to be delivered
Hedge Ratio in contacts
Each contract is for 62,500 pounds or $6,250 per a $.10 change
$200,000 / $6,250 = 32 contracts
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Stock Index Contracts
 Available on both domestic and international
stocks
 Advantages over direct stock purchase
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lower transaction costs
better for timing or allocation strategies
takes less time to acquire the portfolio
 Major stock index futures – page 821
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Index Arbitrage
Exploiting mispricing between underlying stocks and
the futures index contract
 Futures Price too high - short the future and buy
the underlying stocks
 Futures price too low - long the future and short
sell the underlying stocks
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Market Neutral Strategy
To protect against a decline in level stock prices,
short the appropriate number of futures index
contracts
 Less costly and quicker to use the index contracts
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Example
Portfolio Beta = .8
Decrease
= 2.5%
S&P 500 = 1,000
S&P falls to 975
Portfolio Value = $30 million
Project loss if market declines by 2.5% = (.8) (2.5) = 2%
2% of $30 million = $600,000
Each S&P500 index contract will change $6,250 for a 2.5% change in the
index
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Example -- continued
H=
Change in the portfolio value
Profit on one futures contract
=
$600,000
= 96 contracts short
$6,250
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Uses of Interest Rate Hedges
 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
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Example
Portfolio value
= $10 million
Modified duration
= 9 years
If rates rise by 10 basis points (.1%)
Change in value = ( 9 ) ( .1%) = .9% or $90,000
Present value of a basis point (PVBP) = $90,000 / 10 = $9,000
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Example -- continued
H=
PVBP for the portfolio
PVBP for the hedge vehicle
=
$9,000
$90
= 100 contracts
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SWAP
 A portfolio manager owns a $100 million of long-
term bonds paying a coupon of 7%
 He switches it to a floating rate issue based on the
6-month LIBOR rate
 Page 832 shows the payoff from SWAP
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Swap Dealer
Page 831
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