Exchange Market
• Physical or virtual location where buyers
and sellers meet in order to trade
securities or commodities
Exchange Market
• Anonymous trading
• Risks are assumed by the clearing
corporation
Exchange Market
• Types of available products
– Futures contracts
• Financial futures contracts
– Interest rates
– Currencies
– Indexes
• Commodities
– Agricultural products
– Metals
– Livestock, etc.
Exchange Market
CLIENT A
RISK
CLIENT B
Broker
Exchange Market
Broker
Margin
Clearing
Corporation
Margin
Futures Contract
• A futures contract is an agreement that
obliges the buyer to take delivery of a
specific quantity of an underlying asset, at a
specific date, and at a price established at
the time of the transaction.
• Conversely, the seller is obliged to deliver a
specific quantity of an underlying asset, at a
specific date, and at a price established at
the time of the transaction.
Futures Contract
• The value of a futures contract is zero
when initiated
– Delivery price identical to the forward price
– The contract develops value as the forward
price change
– Zero-sum game
• What is lost by one is gained by the other
• No initial payment
– Performance bond required
The Payoff of a Forward Contract
• The payoff of a long position
Pt – D
• The payoff of a short position
D – Pt
where…
Pt = Price of the underlying asset at the maturity of
the contract
D = Delivery price
The Payoff of a Forward Contract
• Futures contracts have a linear profit and
loss profile
• Zero-sum game
– What is lost by one is gained by the other
The Payoff of a Forward Contract
+
+
Profit
Profit
Price
Price
Loss
Loss
-
Profit and loss for a long position
Profit and loss for a short position
Futures Contract
• Example
– Suppose we are in June and a coffee
producer wants to sell his September
harvest at the current market price of $2
per pound. At this price, the producer
would realize a return of 25%.
Futures Contract
• Example
– A futures contract expiring in September will be
sold at a price of $2.
– The producer is committing himself to deliver the
coffee at a price of $2 per pound in September.
He is obliged to do so even if the price of coffee
rises.
– However, he is protected against a drop in the
price since the buyer is obliged to purchase the
coffee at a price of $2.
Futures Contract
In September : $3/lb In September : $1/lb
• The producer is obliged • The producer sells
to sell coffee at $2/lb
coffee at $2/lb
• Opportunity cost of
• Profit of $1/lb
$1/lb
• The counterparty incurs
• The counterparty
a loss of $1/lb
realizes a profit of $1/lb
Contract Specifications
•
•
•
•
•
•
Contract size and value
Minimum price fluctuations
Daily price limits
Delivery month
Trading hours
Delivery location
Settlement
• Delivery by an offsetting transaction
– Taking an opposite position to the initial position
• Settlement by delivery
– The short position holder initiate the delivery
process at any time after the first notice day
• Cash settlement
– The long and the short must pay or receive a
payment in cash instead of having to accept or to
make delivery of the merchandise
Specifications
Specifications
Specifications
Margin Requirements and Marking
to Market
• Margin
– Good faith deposit or performance bond
– Determined by the exchange or clearinghouse as a
fixed amount per contract or as a percentage of the
total contract value (3% to 10% of the contract value)
• Initial margin
– The required deposit at the contract inception
– Adjustments are being made at the end of every
days (daily settlement, mark to market)
• Maintenance margin
– The amount that must be maintained in the account
at all time
Margin Requirements and Marking to
Market
• Margin call
– A margin call is issued when the account falls under
the maintenance margin level. The account must then
be immediately brought back to the initial margin
level.
Margin Requirements and Marking to
Market
• Example
– Long position on 1 Coffee futures
– Size : 37,500 pounds
– Initial margin : $2,500 per contract
– Maintenance margin : $2,000 per contract
Margin Requirements and Marking to
Market
Day
Futures Price
(Cents per
Pound)
Aug. 15
49.45
Aug. 16
48.95
($187.50)
($187.50)
$2,312.50
Aug. 17
49.25
$112.50
($75.00)
$2,425.00
Aug. 18
48.65
($225.00)
($300.00)
$2,200.00
Aug. 19
48.50
($56.25)
($356.25)
$2,143.75
Aug. 20
48.25
($93.75)
($450.00)
$2,050.00
Aug. 21
48.00
($93.75)
($543.75)
$1,956.25
Aug. 21
Daily $
Gain/Loss
Cumulative
$
Gain/Loss
Margin
Account
Balance
Required
Deposit
(Surplus)
$2,500.00
Deposit $543.75
$543.75
$2,500.00
Aug. 22
48.45
$168.75
($375.00)
$2,668.75
($168.75)
Aug. 23
48.75
$112.50
($262.50)
$2,781.25
($281.25)
Pricing of Futures/Forwards
Cost of Carry Model
• Price of a futures contract
– Priced so that the investor is indifferent about:
• buying the asset immediately and paying the
carrying costs associated with holding the asset
until the delivery date, or
• buying a futures contract
– Carrying costs
• Financing, storage, and insurance.
Cost of Carry Model
• Futures price
– The price of a futures is established by
determining the arbitrage free price (the
indifference price).
• Two possible choices
– Buy the asset immediately and keep it until needed
» Loss of interest rate income
» Storage fees
– Buy a futures contract in order to buy the asset
» Interest rate income
» No storage fees
• What do you do?
Basis
• Basis
– The spread between the
spot and the futures price
• Contango (Normal)
– The futures price is higher
than the spot price
• Backwardation
(Inversion)
– The futures price is lower
than the spot price
Basis
•
Contango (Normal)
– The basis is widening when
futures prices increase faster or
decline slower than the spot
price.
– The basis is narrowing when
futures prices decline faster or
rise slower than the spot price.
•
Backwardation
– The basis is widening when
futures prices decline faster or
rise slower than the spot price.
– The basis is narrowing when
futures prices rise faster or
decline slower than the spot
price.
Normal Market
• A normal market is characterized by
adequate supplies of the underlying asset
through all delivery months. Prices reflect
all or at least some of the carrying costs.
Cash and Carry Arbitrage
• Arbitrage
– According to the law of one price in finance,
two assets generating the same cash flows
should sell for the same price.
– Arbitrage consist of taking advantage of price
discrepancies between two or more assets
generating the same cash flows.
Cash and Carry Arbitrage
• Example
– Asset XYZ
– Spot (cash) price = $100
– Futures price expiring in one year = $110
– Storage costs per year = $8
– Fair or theoretical value of the futures = $108
Cash and Carry Arbitrage
• Example
– $108 is the indifference price. Since the
futures price is $110 than there is an arbitrage
opportunity.
– Purchase of the undervalued asset (in the
cash market) and sale of the overvalued asset
(the futures contract).
Cash and Carry Arbitrage
• Arbitrage
Cash
flow
Today:
1.
Borrow $100
+ $100
2.
Purchase the asset at the spot price
- $100
3.
Sell a futures at $110
$0
Total cash flow
$0
One year later:
1.
Deliver the asset and receive the payment
+ $110
2.
Repay loan and storage costs ($100 + $8)
- $108
Total cash flow
+ $2
Reverse Cash and Carry Arbitrage
• Example
– Asset XYZ
– Spot (cash) price = $100
– Futures price expiring in one year = $105
– Storage costs per year = $8
– Fair or theoretical value of the futures = $108
Reverse Cash and Carry Arbitrage
• Example
– $108 is the indifference price. Since the
futures price is $105 than there is an arbitrage
opportunity.
– Purchase of the undervalued asset (the
futures contract) and sale of the overvalued
asset (in the cash market).
Reverse Cash and Carry Arbitrage
• Arbitrage
Cash
flow
Today:
1.
Sell the asset at the spot price
- $100
2.
Invest $100
+ $100
3.
Buy a futures at $105
$0
Total cash flow
$0
One year later:
1.
Accept delivery of the asset and make the payment
- $105
2.
Collect proceeds (principal + storage costs) from
investment ($100 + $8)
+ $108
Total cash flow
+ $3
Conditions Which Facilitate
Arbitrage
•
•
•
•
Ease of short selling
A large supply of the underlying asset
High storability
Non-seasonal production and/or
consumption
Conditions Which Facilitate
Arbitrage
• Arbitrage can easily be performed with
financial futures
• Arbitrage is more difficult to execute on
commodities.
– When shortages occur, market participants
places a higher value on the benefits of
owning the physical commodity.
– The spot price will be values at a higher price
then the futures price (backwardation or
inverted market)
Inverted Markets
• An inverted market typically results from a
shortage of the underlying asset in the
cash market. The spot price increases
above the futures price. Futures prices for
the nearest delivery months are also
above the deferred month prices.
The Relationship Between Forward Prices
and Spot Prices
•
•
The futures price of an asset providing no income is always higher than the spot price
The futures price of an asset providing a known income could be lower than the spot
price
Types of operations
• Hedging with futures contracts
• Speculation with futures contracts
• Arbitrage with futures contracts
Hedging with futures contracts
• Hedging is an operation that aims to
reduce or eliminate risk
• Short hedge and long hedge
• Perfect and imperfect hedge
• Basis risk
• The optimal hedge ratio
Long Hedge
• A long hedge aims to protect against rising prices
between the present and the time when the asset is
needed.
• Example of a perfect hedge
– You want to buy 1000 troy ounces of gold in 3
months
– Actual price = $350 per ounce
• Storage fees = $10 per ounce per month, which implies that
the fair futures price should be equal to $380 per troy ounce
• Buy 10 gold futures contracts on the New York Mercantile
Exchange (COMEX division) at $380 per troy ounce
– Spot price at expiry = $400 per ounce
Long Hedge
• Example of a perfect hedge
Today:
Cashflow
1.
Initial cash in the account ($350 x 1000 ounces)
- $350,000
2.
Invest $350,000
+ $350,000
3.
Long 10 futures contracts at $380
$0
Total cash flow
$0
1.
Accept delivery of 1000 troy ounces of gold and make the
payment
- $380,000
2.
Collect proceeds (principal + storage costs) from
investment [$350 + (3 x $10)] x 1000 ounces
Three months later:
Perfect hedge
+ $380,000
$0
Perfect Hedge
•
Conditions for a perfect hedge
1. The holding period matches the expiration
date of the futures contract
2. The asset being hedged matches the asset
underlying the futures contract
•
When these conditions are not met, the
hedger is exposed to a basis risk
Imperfect Hedge
•
Basis
– The spread between the spot and the
futures price
– At expiry, the basis is worthless
– Prior to expiry, the basis can fluctuate
unexpectedly
Imperfect Hedge
•
Example of an imperfect hedge
–
–
You want to buy 1000 troy ounces of gold in 3
months
Actual price = $350 per ounce
•
•
–
–
Storage fees = $10 per ounce per month, which implies
that the fair futures price should be equal to $380 per troy
ounce
Buy 10 gold futures contracts on the New York Mercantile
Exchange (COMEX division) at $380 per troy ounce
You must close the position one month prior to
expiry
Spot price in two months = $400 per ounce
Imperfect Hedge
• Example of an imperfect hedge
Today:
Cash flow
1.
Initial cash in the account ($350 x 1000 ounces)
- $350,000
2.
Invest $350,000
+ $350,000
3.
Long 10 futures contracts at $380
$0
Total cash flow
$0
Two months later:
1.
2.
3.
Proceeds from the sale of 10 futures contracts at $400
[($400 - $380) x 10 ] x 1000 ounces
+ $20,000$
Purchase of 1000 troy ounces of gold in the cash market
at $400 per ounce
- $400,000
Collect proceeds (principal + storage costs) from
investment [$350 + (2 x $10)] x 1000 ounces
+ $370,000
Optimal Hedge Ratio
• The basis risk is usually linked to the interest rate
fluctuations (changes in the cost of financing)
• Commodities including agricultural and energy
based assets entail higher basis risk then other
products.
– In case of shortage, holding the physical
commodities is more valuable then holding the
futures contract.
– The spot or cash price will be worth much more than
the futures contract (inverted or backwardation
Optimal Hedge Ratio
• There is a high basis risk when one of the
following conditions is not met:
– A large supply of the underlying asset
– Storability of the underlying asset
– Non-seasonal production and/or consumption
– Ease of short selling
Optimal Hedge Ratio
• When the basis risk is not high, a hedge
ratio of 1 is appropriate
• If there is not maturity or asset match, the
hedge ratio needs to be adjusted to reflect
the historical or expected price correlation
between the futures contract and the
asset.
Optimal Hedge Ratio
• A hedge where the futures contract uses
an underlying asset similar but not the
same as the physical asset being hedged
is called a cross-hedge.
– The hedge ratio might be different than 1.
– The correlation between the assets and their
respective volatility have to be taken into
account.
Optimal Hedge Ratio
• The optimal hedge ratio (H)
H = Corr(PF) (SDP / SDF)
where:
SDP = standard deviation of changes in the spot price (P),
SDF = standard deviation of changes in the futures price (F),
Corr(PF) = coefficient of correlation between changes in CP and F.
Optimal Hedge Ratio
• Example
A portfolio manager wants to reduce, by
$10 M, for three months, the market risk of
her portfolio composed of shares of
American companies.
The three-month standard deviation of the
portfolio is 0.25, and the three-month
standard deviation of the S&P/TSX 60
index is 0.20. The correlation between the
portfolio and the index is 0.88.
Optimal Hedge Ratio
• Example:
SDP = 0.25
SDF = 0.20
Corr(PF) = 0.88
H = Corr(PF) (SDP / SDF)
H = 0.88 (0.25 / 0.20) = 1.10
The size of the futures on the S&P/TSX 60 index is
$200 times the index level. If the index is valued at 500
then each contract has a value of $100,000 ($200 x
500). In order to hedge the portfolio manager must
sell:
1.10 x ($10 M / $100,000) = 110 contracts
If she is not taking into account the volatility or the
Speculation with futures
contracts
• The futures market is particularly attractive
to speculators for the following reasons:
– Ease of entry and exit
– Variety of opportunities
– Leverage
– Excitement