Commodities, futures, and
forward contracts
Purpose: Discuss the use of futures
contracts in investment
strategies
The futures game has a long
history
n
In Europe
u Futures
n
trading since the 1600s
In North America
u Commodity
trading mechanisms originated in
colonial times
u Today’s organized futures exchanges trace their
roots back to the early 1800s
Large variety of futures contracts
now being traded
fungible agricultural commodities
n petroleum products
n metals (precious and otherwise)
n T-bills, T-bonds, and other financial
contracts
n currencies
n indices
n
Other possibilities in the next
twenty years:
bulk freight rates
n more stock market indices
n inflation indices
n GNP series, real estate indices, and other
economic indicators
n perhaps even electronic components
n
The basics of futures trading
n
n
n
n
n
n
warehouse receipts
spot price
futures contract terms
futures price
basis
basis risk
Basis & Basis Risk
Basis
Futures
Spot
n
n
n
The “basis” is the difference between the futures
price and the spot price
“Basis risk” refers to the risk that the basis may
fluctuate
Hedging gets rid of price risk, replacing it with
basis risk
The basics of futures trading
n
n
n
n
n
n
warehouse receipts
spot price
futures contract terms
futures price
basis
basis risk
n margins and limits
n marking to market
n the clearinghouse
Marking to Market
n
10:00 AM
u
u
Smith buys @ $1
Jones sells @ $1
Closing price = $1.05
Settlement:
n
u
u
Smith makes 5¢
Jones loses 5¢
Margins and Limits
n
n
n
Margin equals the maximum that can be lost in one day’s
trading
Upper and lower limits define margin
Margins normally established by vote among the traders on
the exchange
u
u
n
What are incentives for keeping margins small?
What are incentives for increasing margins?
Exchanges and regulators can change margin in emergency
Clearinghouse
Clearinghouse holds all margin deposits
n This amount equals twice the amount that is
exposed to risk
n Ancestors of modern clearinghouses are
also the ancestors of central banks
n
The cast of characters in the
futures game
Hedgers
n Speculators
n Arbitrageurs
n
Hedgers:
They want to reduce their business risks
n They trade risks with one another
n There is a long history
n
Speculators:
People with valuable information are
naturally attracted to futures trading
n What good do they do?
n
u Informed
speculators enhance pricing
efficiency
u Uninformed speculators contribute liquidity
Arbitrageurs:
People with access to several marketplaces
n Look for imbalances
n
u profit
n
from them as they arise
What good do they do?
u quickly
eliminate imbalances
Some trading examples to
illustrate arbitrage
n
“crush” spread
u live
hogs and pork bellies
F any
pair of commodities for which the first is
directly convertible into the second
u soy
beans into soy bean meal and soy bean oil
F any
set of commodities for which the raw material is
directly convertible into a standard package of
refined commodities
Some trading examples to illustrate
arbitraging the basis
Basis too big
n Basis too small
n Basis just right
n Inverted market
n
Warm-up Example: Problem 1
£ 600,000
$1,000,000
$1=£0.60
NY
$1,200,000
LON
£1 = €1.40
$1 = € 0.70
FRA
€ 840,000
Profit = $200,000
Basis too big
The following prices are observed:
n
n
Coffee costs $55.50 per hundredweight spot, and
$60 for 180-days forward
Storage costs $1 per hundredweight in a bonded,
insured warehouse (paid in advance)
u
n
You have a million pounds in storage already
U.S. Treasury Bills yield 3.00% compounded
daily, for the 180-day maturity
Basis too big
Do the following:
n
n
Buy coffee in the spot market and store it (total
cost: $56.50 per hundredweight, reflecting price
plus storage cost).
Sell this coffee in the forward market for $60 per
hundredweight.
Basis too big
n
Present value is –56.50 future value is 60,
and n is 180 days
u riskless
yield of 12.19% compounded daily
u better than T-bills.
n
So let’s reflect: What was out of balance in
this situation? What adjustments will
occur?
Basis too big
1,000,000 lbs.
$565,000
Money $55.50 = 100 lbs.
today
3%
$573,420.69
Coffee
today
Storage $1
Money
later $60 = 100 lbs.
Coffee
later
$600,000
Profit = $26,579.31
1,000,000 lbs.
What is not balanced?
Basis too small
The following prices are observed:
n
n
n
Coffee costs $59.25 per hundredweight in the spot
market, and $60 for 180-days forward
Storage costs $1 per hundredweight in a bonded,
insured warehouse
u You have 1,000,000 pounds in storage already
U.S. Treasury Bills yield 3.00% compounded
daily, for the 180-day maturity
Basis too small
Do the following:
n Sell coffee in the spot market for $59.25
n Buy coffee in the forward market for $60
per hundredweight, to replace what you sold
Basis too small
n
Present value is 59.25, future value is –60,
and n is 180 days
u riskless
yield of 2.55% compounded daily
u you can borrow from your coffee stores for less
interest than the U.S government pays
n
So let’s reflect: What was out of balance in
this situation?
Basis too small
1,000,000 lbs.
$592,500
Money $59.25 = 100 lbs.
today
Storage $1
3%
$601,330.55
Coffee
today
Money
later $60 = 100 lbs.
Coffee
later
$600,000
Profit = $1,330.55
1,000,000 lbs.
What is not balanced?
Basis OK
The following prices are observed:
n
n
n
Coffee costs $61.05 per hundredweight in the spot
market, and $ 62.975 for 180-days forward
Storage costs $1 per hundredweight in a bonded,
insured warehouse, paid in advance
u You have 1,000,000 pounds in storage already
U.S. Treasury Bills yield 3.00% compounded
daily, for the 180-day maturity
Basis OK
n
If you buy more coffee, the present value is –62.05, future
value is 62.975 and n is 180 days.
u
u
u
n
riskless yield of 3% compounded daily, same as the T-bill rate
There is no advantage in buying more coffee
Keeping the coffee you already have is a breakeven move
If you sell coffee that you will later need to replace, you
would receive $61.05 now and would have to pay $62.975
later to replace it
u
u
u
cost of capital for this “loan” would be 6.30%
There is no advantage relative to the current rate of 3%
There is no incentive to sell coffee already in storage
Contango
Basis
Futures
Spot
n
A condition in which distant delivery prices for
futures exceed spot prices, often due to the
costs of storing and insuring the underlying
commodity
Forwardation
Price
Futures Price
Time until Delivery
n
In general, futures contracts for later months are
quoted at higher prices than those for nearby months
(‘forwardation’), reflecting carrying charges such as
storage and interest costs
u
These costs increase as time to delivery grows longer
Inverted Market
The following prices are observed:
n
n
n
Coffee costs $80 per hundredweight in the spot
market, and $60 for 180-days forward.
Storage costs $1 per hundredweight in a bonded,
insured warehouse. You have a million pounds in
storage already.
U.S. Treasury Bills yield 3.00% compounded
daily, for the 180-day maturity.
Inverted Market
n
The spot price is higher than the forward price,
and the basis is negative
u
u
n
There is clearly no incentive to continue storing coffee
You would sell all your supply that is not needed for
use during the next six months, in anticipation of a
declining price.
So let’s reflect: What factors could explain this
situation? What adjustments will result from the
inversion?
Price
Backwardation
Futures Price
Time until Delivery
n
n
A market condition in which a futures price is
lower in the distant delivery months than in the
near delivery months
Why does this happen?
Further Practice
n
For further practice in arbitraging the basis,
see problems 6 & 7
Forward Discount
Condition in which a currency's forward
price is lower than its spot price
n Example:
n
u Spot
u Forward
n
$1.16 = € 1
$1.15 = € 1
Why does this happen?
u Market
participants expect higher inflation
in Europe than in the U.S.
Forward Discount
Condition in which a currency's forward
price is lower than its spot price
n Another example:
n
u Spot
u Forward
n
€ 0.86 = $1
€ 0.84 = $1
Why does this happen?
u Market
participants expect higher inflation
in the U.S. than in Europe
Arbitraging breakdowns in
interest rate parity (Problem 3)
The following prices are observed:
n Dollar per Euro exchange rate is 1.15 spot
and 1.16 for 180-day forward
n German interest rate is 5.00% compounded
daily (365-day year)
n U.S. interest rate is 3.00% compounded
daily
Arbitraging interest parity (Problem 3)
€ 869,565.22
$1,000,000
NY
today
$1.15 = € 1
3%
$1,014,903.88
NY
later
FRA
today
5%
$1.16 = € 1
FRA
later
$1,033,875.03
Profit = $18,971.15
€ 891,271.58
What is not balanced?
Arbitraging breakdowns in
purchasing power parity
The following prices are observed:
n
n
n
n
Swiss Franc per Dollar exchange rate is 1.30 spot
and 1.30 for 180-day forward
Spot gold is CHF 481 per ounce in Zurich and
$370 in New York
Gold futures (180-day) are CHF 493 per ounce in
Zurich and $375.51 in New York
U.S. interest rate is 3.00% compounded daily;
Swiss rate is 5.00%
Are the spots and forwards aligned with interest rates?
Arbitraging purchase parity
CHF 481,000
$370,000
NY
today
$375,510
$1.00 = CHF 1.30
ZUR
today
Spot 370
Future 375.51
Spot 481
Future 493
NY
later
ZUR
later
$1.00 = CHF 1.30
$379,230.77
Profit = $3,720.77
CHF 493,000
What is not balanced?
Arbitraging purchase parity
n
See Problem 4 for more practice with
precious metals
Arbitraging purchase parity (Problem 4)
£ 500,000
3,333.33 oz.
$1,000,000
NY
today
$1.00 = £ 0.50
Spot 150
Future 154.50
R = 3%
$1,014,903.88
NY
later
LON
today
$1.00 = £ 0.48
LON
later
$1,072,916.67
Profit = $58,012.78
£ 515,000
What is not balanced?
Arbitraging purchase parity
n
See Problem 5 for practice with equities
Equities as commodities (Problem 5)
$ 1,000,000
€ 869,565.22
FRA
today
$1.15 = € 1
Spot 1000
Future 1040
Dividend 1.5%
R = 5%
€ 891,271.58
FRA
later
NY
today
$1.16 = € 1
NY
later
€ 909,482.76
$ 1,055,000
Profit = € 18,211.18
What is not balanced?
Fed Funds Rate Declines
1,000 • Index
$1,000,000
Money Index = 1000
today
4% APR
2%
Equities
today
Dividends 1.5%
$1,010,022.22 Money Index = 1005.14 Equities
Later
Later
(182 days)
$1,020,140
Profit = $10,117.78
(182 days)
1,000 • Index
What is not balanced?
Let’s Pause for a Question
n
n
n
n
Question: What happens when dividend yield on
the index exceeds the safe rate?
Hint: “Storage costs” (that is, dividends) are
benefits when the equities are the underlying
commodities
Hint: In the case under discussion, the combined
impact of interest and storage cost is positive
Answer: Index futures show forwardation during
the period of low interest rates
S&P 500 Index Futures 10/31/03
1056
1054
1052
1050
1048
1046
1044
Spot
3-Dec
4-Mar
4-Jun
4-Sep
4-Dec
5-Mar
5-Jun
5-Sep
Bonds as commodities (Problem 8)
$1,007,424.38
3.00%
$1,000,000
NY
today
NY
90 days
$1,008,045.53
3.15%
3.20%
Profit = $621.15
NY
180 days
$1,015,905.29
Additional Lessons
n
n
Futures markets are a way to rely on the
marketplace for forecasts of future supply and
demand (price discovery).
Questions:
u Is the futures price an unbiased predictor of
what the spot price will be on the maturity
date?
u Is the risk of holding the underlying asset a
relevant concern for a diversified investor?
Futures contracts and APT
factors
n
Question: What becomes of risk if there are
futures contracts available for all the factors
relevant to investors?
u GNP
u Inflation
u Other
factors
Should a financial institution or
institutional investor hedge?
Theoretically, the answer is no
But, the “real world” answer may be yes:
n
n
n
it may be costly for clients to hedge on their own
clients may not have access to knowledge about the institution’s
natural position
hedging is like buying insurance
u
u
n
it allows managers to turn their attention from risks beyond their control
concentrate on value-drivers they can influence
the marketplace has an advantage in forecasting, so managers don’t
need to try predicting the future
Practical problems with hedging
Marking to market
Suppose you are naturally long in wheat, and hedge by
shorting futures
n
Futures
Spot
Uncertain Future
Place Hedge
Practical problems with hedging
Marking to market
n
Then prices rise, bringing a series of margin calls that
leave you scrambling to hold the hedge
Scramble to Hold Hedge
Futures
Spot
Place Hedge
Uncertain Future
Practical problems with hedging
Marking to market
n
Then prices fall, bringing profits from the futures side of
the hedge to offset the losses in your “natural” position
Scramble to Hold Hedge
Futures
Spot
Uncertain Future
Place Hedge
Practical problems with hedging
Marking to market
n
But prices turn up again, and finally you can’t meet the
margin calls
Scramble to Hold Hedge
Futures
Spot
Place Hedge
Forced Out of Hedge
Uncertain Future
Practical problems with hedging
Marking to market
n
Then, prices fall again, and without the hedge you sell the
inventory at a loss
Scramble to Hold Hedge
Forced Out of Hedge
Futures
Spot
Uncertain Future
Place Hedge
Sell Inventory
Practical problems with hedging
n
n
Futures
But prices continue rising to a level that would have given
you a profit, before falling again.
You are unhappy, and blame your misfortune on poor
timing.
Scramble to Hold Hedge
Forced Out of Hedge
Spot
Place Hedge
Sell Inventory
Practical problems with hedging
Marking to market
n
With insufficient liquidity
u
u
you may be forced out of the hedge early
and may even lose twice: once on the futures, again on
the spot
Practical problems with hedging
Taxes
n
Problem: outcomes from futures trading may be
taxed differently than outcomes from “natural”
position
u Can’t predict which side of hedge will gain and
which side will lose
u So, hedge doesn’t balance after tax