FUTURES
MARKETS
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.1
The Nature of Derivatives
A derivative is an instrument whose value
depends (is derived from) on the values
of other more basic underlying variables
• Futures Contracts
• Forward Contracts
• Swaps
• Options
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.2
Ways Derivatives are Used
• To hedge risks
• To speculate (take a view on the
future direction of the market)
• To lock in an arbitrage profit
• To change the nature of a liability
• To change the nature of an investment
without incurring the costs of selling
one portfolio and buying another
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.3
Positions
• Every transaction involves two positions
• Long position (agreement to buy in the future)
• Short position (agreement to sell in the future)
• Zero – sum game
1.4
What is the benefit of derivative markets ?
•
•
•
•
•
•
•
Efficiency
Liquidity
Ability to forecast trends
Transparency
Risk management
Portfolio diversification
Investment opportunities
Forward contracts
• A Forward contract is a contract where an investor A
(buyer) agrees with another investor B (seller)
•
•
•
•
That A will buy from B
An underlying asset (underlying instrument)
At a pre-specified price (forward price/rate)
At a pre-specified future date (delivery date)
• E.g. agree to sell 10 million barrels of oil (underlying
asset) at $100 per barrel (forward price) in 9 months
(delivery date)
Over The Counter (OTC)
• Forward contracts are between two parties (usually
between financial institutions and/or their clients) and
NOT via organized exchanges
• Over The Counter (OTC)
→ Investors determine the terms of the contract
→ Confidentiality
Disadvantages OTC
•
•
•
•
Limited transparency
Limited regulations
No official body for approving new products
Limited clearance procedures
Neutralize Position
• There is no secondary market
• As a result, the contract cannot be liquidated
• However, an investor can neutralize it by taking an exact
opposite position (same duration, same size)
• Short in 10 million barrels of oil at $100 per in 9 months
• Long in 10 million barrels of oil at $100 per in 9 months
Profit and Losses (P&L)
• Long position on a forward contract
– Profit (loss) when the price of the underling asset at
delivery is higher (lower) than the delivery price
• Short position on a forward contract
– Profit (loss) when the price of the underling asset at
delivery is lower (higher) than the delivery price
Example
• On the 8th of March we agree with our bank to buy
1,000,000 Pound Sterling at the exchange rate $1.55 in
90 days
• On the 6th of August the rate is rate $/BP is at $1.60
• Profit or loss?
• On the 6th of August we pay $1,550,000 to the bank
• We take 1,000,000 BP
• We sell them in the market for $1,600,000
• Profit : $50,000
• The bank losses the same amount (zero-sum game)
• We ignore transaction costs
Returns
• Sτ =
the spot price of the underlying at
delivery date
• Κ
The delivery (forward) price
=
• Profit from a long position on a FC:
(Sτ – Κ)
• Profit from a short position on a FC:
(Κ – Στ)
In the example:
• Sτ = 1.60
• Κ = 1.55
• Long Position
• Profit (Sτ – Κ) = $1.60 – $1.55 = $0.05
• For 1,000,000 BP = 1.000.000 x $0,05 = $50,000
Graphical representation
Introduction to hedging
A simple example
• Consider a company that has 1000 units of a product
that has a current price of 500 E/unit
• If the price goes up in 1 month
e.g. at 540 E/unit
Profit 40 Ε
• If the price goes down in 1 month
e.g. at 460 E/unit
Loss 40 Ε
Graph
Uncertainty
• What can the Company do ?
• Assume a forward contract on the product
exists
• short forward
for 1000 units at 500 E
Graph
Forward contracts
• Forward contracts are similar to futures except
that they trade in the over-the-counter market
• Forward contracts are popular on currencies and
interest rates
• A US company will pay £10 million for imports
from Britain in 3 months and decides to hedge
using a long position in a forward contract
Futures Contracts
• A futures contract is an agreement to
buy or sell an asset at a certain time in
the future for a certain price
• By contrast in a spot contract there is
an agreement to buy or sell the asset
immediately (or within a very short
period of time)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.23
Organized markets
• In contrast to forward contracts, futures contracts are traded
in organized exchanges
• The contracts are between the member and the exchange
and have the “guarantee” of the exchange
• Every contract has the same characteristics and this
standardization allows easy trading, liquidity, and easy
clearing
Most important Derivative
Exchanges in the US
Most important Derivative
Exchanges except US
Futures Price
• The futures prices for a particular contract
is the price at which you agree to buy or
sell
• It is determined by supply and demand in
the same way as a spot price
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.30
Electronic Trading
• Traditionally futures contracts have been
traded using the open outcry system
where traders physically meet on the floor
of the exchange
• Increasingly this is being replaced by
electronic trading where a computer
matches buyers and sellers
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.31
Examples of Futures Contracts
Agreement to:
– buy 100 oz. of gold @ US$600/oz. in
December (NYMEX)
– sell £62,500 @ 1.9800 US$/£ in
March (CME)
– sell 1,000 bbl. of oil @ US$65/bbl. in
April (NYMEX)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.32
Terminology
• The party that has agreed to buy has
a long position
• The party that has agreed to sell has a
short position
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.33
Example
• January: an investor enters into a long
futures contract on COMEX to
buy 100 oz of gold @ $600 in April
• April: the price of gold $615 per oz
What is the investor’s profit?
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
1.34
Futures markets
5 parties involved
(1)
(2)
(3)
(4)
(5)
Derivatives Exchange
Clearing House
Regulator
Members
Investors (speculators, hedgers,arbitrageurs)
Derivatives Exchange
→
Usually belongs to company that not only offers the
physical place where transactions take place but also
provides security and sets the rules
→ In many countries it works with electronic order
matching while in other it works with a pit
Pit: the traders and brokers transact in the form of an
auction-style open-outcry
The clearing house
→
→
→
clears all transactions
guarantees all trades
stands between the two parties
• Once a transaction takes place the clearer:
•
•
•
•
(α) records the transaction
(β) clears the transaction
(γ) estimate the margins
(δ) clear the obligations of the parties
Regulator
→
→
Securities and Exchange Commission (US)
Capital Market Committee (Greece)
For example in Greece the CMC may take regulatory
decisions that are equal to state laws
It regulates, the Athens Exchange, the clearing
organization, brokers, dealers, mutual funds, investment
trusts, etc
Futures Contracts
• Available on a wide range of underlying
• Exchange traded
• Specifications need to be defined:
– What can be delivered,
– Where it can be delivered, &
– When it can be delivered
• Settled daily
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
2.40
Delivery
• If a futures contract is not closed out before maturity, it is
usually settled by delivering the assets underlying the
contract.
• When there are alternatives about what is delivered,
where it is delivered, and when it is delivered, the party
with the short position chooses.
•
• A few contracts (for example, those on stock indices and
Eurodollars) are settled in cash
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
2.41
Some Terminology
• Open interest: the total number of contracts
outstanding
– equal to number of long positions or number of
short positions
• Settlement price: the price just before the final bell
each day
– used for the daily settlement process
• Volume of trading: the number of trades in 1 day
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
2.42
Differences Futures - Forwards
• Futures are standardized (when, where, what)
• Standardization is necessary for the efficient running of
the market
(α) since everybody transacts in the same contract the
market is liquid and the trade is easy
(β) there is a possibility for large trades since the
mechanics of buying/selling are easy to manage
(γ) transaction costs are lower since the traders do not
need to negotiate the terms in every trade
Other differences
• Futures are available for a large number of
underlying assets:
•
•
•
•
Weather derivatives
Pork bellies
Orange juice
Coffee
Weather derivatives
• Farmers, theme parks, airliners, gas and power
companies
• Heating degree days (HDD) or cooling degree days
(CDD) contracts
• Heating degree days are one of the most common types
of weather derivative.
daily settlement, mark to market
• Futures are settled daily
• i.e. at the end of the day the investors with
losses pay the loss to the investors with
gains
Margins
•
Futures: when a contract is initiated no money change hands
•
However, every party has to pay a “good faith” deposit or “Margin” to the
clearing organization
•
They are used as insurance
•
A margin is cash or marketable securities deposited by an investor with his
or her broker
•
The balance in the margin account is adjusted to reflect daily settlement
•
Margins minimize the possibility of a loss through a default on a contract
•
Initial margin requirement and maintenance margin
Example of a Futures Trade
• An investor takes a long position in 4
December gold futures contracts on
June 5
– contract size is 100 oz.
– futures price is US$380
– margin requirement is US$2,000/contract
(US$8,000 in total)
– maintenance margin is US$1,500/contract
(US$6,000 in total)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
2.53
Example of a Futures Trade
•
•
•
•
Position: 4 December Gold Futures
Every Futures is for 100 oz.
Price: $380 / oz
Thus: 4 x 100 x $380 = $152,000
• What dowe deposit: $2,000 x 4 = $8,000
• Leverage
Example of a Futures Trade
• Assume that at the end of the day the price
drops at $377
• We loose $3 x 400 oz ($1,200)
• Our margin account will reduce by $1,200
(down to $6,800)
Example of a Futures Trade
• Assume that at the end of next day the
price drops a further $3 at $374
• We loose another $1,200 and the margin
account now stands at $5,600
• Margin Call
Margins for stock futures in Greece
Example Trading with Margin
Example Leverage
Convergence of Futures to Spot
Futures
Price
Spot Price
Futures
Price
Spot Price
Time
(a)
Time
(b)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
2.62
Forward Contracts
• A forward contract is an OTC agreement to buy or sell
an asset at a certain time in the future for a certain price
• There is no daily settlement (unless a collateralization
agreement requires it).
• At the end of the life of the contract one party buys the
asset for the agreed price from the other party
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
2.63
Long & Short Hedges
• A long futures hedge is appropriate when
you know you will purchase an asset in
the future and want to lock in the price
• A short futures hedge is appropriate
when you know you will sell an asset in
the future & want to lock in the price
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.66
Arguments in Favor of Hedging
Companies should focus on the main
business they are in and take steps to
minimize risks arising from interest
rates, exchange rates, and other market
variables
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.67
Arguments against Hedging
• Shareholders are usually well diversified and
can make their own hedging decisions
• It may increase risk to hedge when competitors
do not
• Explaining a situation where there is a loss on
the hedge and a gain on the underlying can be
difficult
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.68
Basis Risk
• Basis is the difference between
spot & futures
• Basis risk arises because of the
uncertainty about the basis
when the hedge is closed out
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.69
Long Hedge
• Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
• You hedge the future purchase of an asset by
entering into a long futures contract
• Cost of Asset=S2 – (F2 – F1) = F1 + Basis
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.70
Short Hedge
• Suppose that
F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
• You hedge the future sale of an asset by
entering into a short futures contract
• Price Realized=S2+ (F1 – F2) = F1 + Basis
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.71
Choice of Contract
• Choose a delivery month that is as close as
possible to, but later than, the end of the life of
the hedge
• When there is no futures contract on the asset
being hedged, choose the contract whose
futures price is most highly correlated with the
asset price.
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.72
Optimal Hedge Ratio
Proportion of the exposure that should optimally be
hedged is
sS
hr
sF
where
sS is the standard deviation of DS, the change in the
spot price during the hedging period,
sF is the standard deviation of DF, the change in the
futures price during the hedging period
r is the coefficient of correlation between DS and DF.
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.73
Rolling The Hedge Forward
• We can use a series of futures
contracts to increase the life of a
hedge
• Each time we switch from 1 futures
contract to another we incur a type of
basis risk
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.74
The Futures/Forward Price
• In order top find the right future/forward
price for an asset we employ the same
methodology as for every investment
• Present Value approach
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
3.75
Notation
S0: Spot price today
F0: Futures or forward price today
T: Time until delivery date
r: Risk-free interest rate for
maturity T
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.76
1. Gold: An Arbitrage
Opportunity?
• Suppose that:
– The spot price of gold is US$600
– The quoted 1-year futures price of gold
is US$650
– The 1-year US$ interest rate is 5% per
annum
– No income or storage costs for gold
• Is there an arbitrage opportunity?
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.77
2. Gold: Another Arbitrage
Opportunity?
• Suppose that:
– The spot price of gold is US$600
– The quoted 1-year futures price of
gold is US$590
– The 1-year US$ interest rate is 5%
per annum
– No income or storage costs for gold
• Is there an arbitrage opportunity?
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.78
The Futures Price of Gold
If the spot price of gold is S & the futures price
for a contract deliverable in T years is F, then
F = S (1+r )T
where r is the 1-year (domestic currency) riskfree rate of interest.
In our examples,
S=600, T=1, and r=0.05 so that
F = 600(1+0.05) = 630
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.79
When Interest Rates are
Measured with Continuous
Compounding
F0 = S0erT
This equation relates the forward price
and the spot price for any investment
asset that provides no income and has
no storage costs
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.80
Another example
• 7-month forward on a zero coupon bind that matures in a
year
• Spot price = $965, interest rate 5.5% βάση
• S0 = $965, e = 2.71828, r = 0.055, Τ = (7/12)
• F0 = S0 er Τ = 965 e 0.055 (7/12) = $996.46
When an Investment Asset
Provides a Known Dollar
Income
F0 = (S0 – I )erT
where I is the present value of the income
during life of forward contract
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.82
Example
• 10-month forward on a stock that has a current
price of $20 and will pay a dividend per share of
$0.25 in 3, 6, 9 months from today
• What is the forward price if the dicopunt
rate is 6%?
• Ι
=
+
+
=
• F0 =
=
=
0.25 e -0.06 (3/12)
0.25 e -0.06 (6/12)
0.25 e -0.06 (9/12)
0.72791
(S0 – Ι) er Τ
(20-0.72791) e 0.06 (10/12)
$20.2
When an Investment Asset
Provides a Known Yield
F0 = S0 e(r–q )T
where q is the average yield during the life of
the contract (expressed with continuous
compounding)
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.85
Valuing a Forward Contract
• Suppose that
K is delivery price in a forward contract &
F0 is forward price that would apply to the contract today
• The value of a long forward contract, ƒ, is
ƒ = (F0 – K )e–rT
• Similarly, the value of a short forward contract is
(K – F0 )e–rT
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.86
Forward vs Futures Prices
• Forward and futures prices are usually assumed
to be the same. When interest rates are
uncertain they are, in theory, slightly different:
• A strong positive correlation between interest
rates and the asset price implies the futures
price is slightly higher than the forward price
• A strong negative correlation implies the
reverse
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.87
Stock Index
• Can be viewed as an investment asset paying
a dividend yield
• The futures price and spot price relationship
is therefore
F0 = S0 e(r–q )T
where q is the dividend yield on the portfolio
represented by the index during life of
contract
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.88
Stock Index
• For the formula to be true it is important that
the index represent an investment asset
• In other words, changes in the index must
correspond to changes in the value of a
tradable portfolio
• The Nikkei index viewed as a dollar number
does not represent an investment asset
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.89
Index Arbitrage
• When F0 > S0e(r-q)T an arbitrageur buys the stocks
underlying the index and sells futures
• When F0 < S0e(r-q)T an arbitrageur buys futures
and shorts or sells the stocks underlying the
index
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.90
Index Arbitrage
• Index arbitrage involves simultaneous trades
in futures and many different stocks
• Very often a computer is used to generate the
trades
• Occasionally (e.g., on Black Monday)
simultaneous trades are not possible and the
theoretical no-arbitrage relationship between
F0 and S0 does not hold
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.91
Futures and Forwards on Currencies
• A foreign currency is analogous to a security
providing a dividend yield
• The continuous dividend yield is the foreign
risk-free interest rate
• It follows that if rf is the foreign risk-free interest
rate
F0  S0e
( r rf ) T
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.92
Futures on Consumption Assets
F0  S0 e(r+u )T
where u is the storage cost per unit time as a
percent of the asset value.
Alternatively,
F0  (S0+U )erT
where U is the present value of the storage costs.
Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007
5.93