Commodities, futures, and
forward contracts
Purpose: Discuss the use of futures
contracts in investment
strategies
How to build a forward
contract
■  Combine
two primary assets into a new
product
◆  Buy
the underlying
◆  Store it for later delivery
◆  Pay for the underlying and the storage with
100% debt financing
S&P Case-Shiller Composite
Home Price Index
Oct 2015
Living Yield Curve
■  http://stockcharts.com/freecharts/
yieldcurve.php
The cast of characters in the
futures game
■  Hedgers
■  Speculators
■  Arbitrageurs
Hedgers:
■  They
want to reduce their business risks
■  They trade risks with one another
■  There is a long history
Speculators:
■  People
with valuable information are
naturally attracted to futures trading
■  What good do they do?
◆  Informed
speculators enhance pricing
efficiency
◆  Uninformed speculators contribute liquidity
Arbitrageurs:
■  People
with access to several
marketplaces
■  Look for imbalances
◆  profit
■  What
from them as they arise
good do they do?
◆  quickly
eliminate imbalances
Some trading examples to
illustrate arbitrage
■  “crush”
◆  live
spread
hogs and pork bellies
✦  any
pair of commodities for which the first is
directly convertible into the second
◆  soy
beans into soy bean meal and soy bean
oil
✦  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
■  Basis too small
■  Basis just right
■  Inverted market
Warm-up Example: Problem 1
£ 700,000
$1,000,000
$1=£0.70
NY
$1,050,000
LON
£1 = €1.35
$1 = € 0.90
FRA
€ 945,000
Profit = $0,000
Basis too big
The following prices are observed:
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)
■
◆
■
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:
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
value is –56.50 future value is 60,
and n is 180 days
■  Present
◆  riskless
yield of 12.19% compounded daily
◆  better than T-bills.
■  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
Storage $1
Money
later $60 = 100 lbs.
$600,000
Profit = $26,579.31
Coffee
today
Coffee
later
1,000,000 lbs.
What is not balanced?
Basis too small
The following prices are observed:
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
◆  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:
■  Sell coffee in the spot market for $59.25
■  Buy coffee in the forward market for $60
per hundredweight, to replace what you
sold
Basis too small
value is 59.25, future value is –60,
and n is 180 days
■  Present
◆  riskless
yield of 2.55% compounded daily
◆  you can borrow from your coffee stores for
less interest than the U.S government pays
■  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
Money
later $60 = 100 lbs.
$600,000
Profit = $1,330.55
Coffee
today
Coffee
later
1,000,000 lbs.
What is not balanced?
Basis OK
The following prices are observed:
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
◆  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
■
If you buy more coffee, the present value is –62.05,
future value is 62.975 and n is 180 days.
◆
◆
◆
■
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
◆
◆
◆
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
Futures
Basis
Spot
■
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
■
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
◆
These costs increase as time to delivery grows longer
Inverted Market
The following prices are observed:
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
■
The spot price is higher than the forward price,
and the basis is negative
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
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
■  For
further practice in arbitraging the
basis, see problems 3 & 4
Forward Discount
■  Condition
in which a currency's forward
price is lower than its spot price
■  Example:
◆  Spot
◆  Forward
■  Why
$1.46 = € 1
$1.45 = € 1
does this happen?
◆  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
■  Another example:
◆  Spot
◆  Forward
■  Why
€ 0.66 = $1
€ 0.64 = $1
does this happen?
◆  Market
participants expect higher inflation
in the U.S. than in Europe
Arbitraging breakdowns in
interest rate parity
The following prices are observed:
■  Dollar per Euro exchange rate is 1.0846
spot and 1.0928 for 180-day forward
■  German interest rate is 3.00%
compounded daily (365-day year)
■  U.S. interest rate is 1.00% compounded
daily
Arbitraging interest parity
€ 921,998.89
$1,000,000
NY
today
$1.0846 = € 1
1%
$1,004,943.62
NY
later
$1,022,576.95
Profit = $17,633.34
FRA
today
3%
$1.0928 = € 1
FRA
later
€ 935,740.26
What is not balanced?
Arbitraging breakdowns in
purchasing power parity
The following prices are observed:
Swiss Franc per Dollar exchange rate is 1.10
spot and 1.11 for 180-day forward
■  Spot gold is CHF 1221 per ounce in Zurich and
$1110 in New York
■  Gold futures (180-day) are CHF 1280 per
ounce in Zurich and $1142.65 in New York
■
Are these prices in balance?
Arbitraging purchase parity
CHF 1,221,000
$1,110,000
NY
today
$1.00 = CHF 1.10
Spot 1110
Future 1142.65
$1,142,650
NY
later
Spot 1221
Future 1280
$1.00 = CHF 1.11
$1,153,153.15
Profit = $10,503.15
ZUR
today
ZUR
later
CHF 1,280,000
What is not balanced?
Arbitraging purchase parity
■  See
Problem 14 for more practice with
precious metals
Arbitraging purchase parity (Problem 14)
£ 1,020,000
1,000 oz.
$1,700,000
NY
today
$1.00 = £ 0.60
Spot 1,020
Future 1050.60
R = 1%
$1,708,404.15
NY
later
$1,811,379.31
Profit = $102,975.16
LON
today
$1.00 = £ 0.58
LON
later
£ 1,050,600
What is not balanced?
Arbitraging purchase parity
■  See
Problem 15 for practice with equities
Equities as commodities (Problem 15)
$ 1,000,000
€ 770,000.00
FRA
today
$1 = € 0.77
Spot 1324
Future 1363.72
Dividend 1.5%
R = 5%
€ 789,220.98
FRA
later
€ 836,000.00
Profit = € 46,779.02
NY
today
$1 = € 0.80
NY
later
$ 1,045,000
What is not balanced?
Fed Funds Rate Declines from 4% to 2%
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
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
$1,007,424.38
3.00%
$1,000,000
NY
today
$1,008,045.53
3.15%
3.20%
Profit = $621.15
NY
90 days
NY
180 days
$1,015,905.29
Bonds as Commodities
■  For
additional practice, see problems
20-23
Additional Lessons
Futures markets are a way to rely on the
marketplace for forecasts of future supply and
demand (price discovery).
■  Questions:
◆  Is the futures price an unbiased predictor of
what the spot price will be on the maturity
date?
◆  Is the risk of holding the underlying asset a
relevant concern for a diversified investor?
■
Futures contracts and APT
factors
■  Question:
What becomes of risk if there
are futures contracts available for all the
factors relevant to investors?
◆  GNP
◆  Inflation
◆  Other
factors
Should a financial institution or
institutional investor hedge?
Theoretically, the answer is no
But, the “real world” answer may be yes:
■
■
■
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
◆
◆
■
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
Futures
Spot
Uncertain Future
Place Hedge
Practical problems with
hedging
Marking to market
■
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
■
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
■
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
■
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
■
■
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
■
With insufficient liquidity
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
■
Problem: outcomes from futures trading may
be taxed differently than outcomes from
“natural” position
◆  Can’t predict which side of hedge will gain
and which side will lose
◆  So, hedge doesn’t balance after tax