Chapter 14: Future Prices
Objective
Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley
•How to price forward and futures
•Storage of commodities
•Cost of carry
•Understanding financial
1
futures
Chapter 14: Contents
1 Distinction Between Forward &
Futures Contracts
2 The Economic Function of Futures
Markets
3 The Role of Speculators
4 Relationship Between Commodity
Spot & Futures Prices
5 Extracting Information from
Commodity Futures Prices
6 Spot-Futures Price Parity for Gold
8 The “Implied” Risk-Free Rate
9 The Forward Price is not a Forecast
of the Spot Price
10 Forward-Spot Parity with Cash
Payouts
11 “Implied” Dividends
12 The Foreign Exchange Parity
Relation
13 The Role of Expectations in
Determining Exchange Rates
7 Financial Futures
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14.1 Distinction Between
Forward & Futures Contracts
• parties agree to exchange some item in the future at a
delivery price specified now
• the forward price is defined as the delivery price which makes
the current market value of the contract zero
• no money is paid in the present by either party to the other
– the face value of the contract is the quantity of the item specified
in the contract multiplied by the forward price
– the party who agrees to buy the specified takes the long
position, and the party who agrees to sell the item takes the
short position
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Terms
– Open, High, Low, Settle, Change, Lifetime
high, Lifetime low, Open interest
– Mark-to-market
– Margin requirement
– Margin call
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Characteristics of Futures
• Futures are:
– standard contracts
– immune from the credit worthiness of buyer
and seller because
• exchange stands between traders
• contracts marked to market daily
• margin requirements
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14.2 The Economic Function
of Futures Markets
• The futures markets facilitate the reallocation of exposure to commodity
price risk among market participants
• But:
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– by providing a means to hedge the price risk
associated with storing a commodity, futures
contracts make it possible to separate the
decision of whether to physically store a
commodity from the decision to have
financial exposure to price changes
7
The Economic Function of
Futures Markets (Continued)
• A distributor, j, may hedge by
– selling the commodity on the spot market
now at a price S
– selling short a futures contract at a price F
and deliver the commodity at a specified
time in the future
• there will be a carrying cost Cj for distributor
j, and she will store only if Cj < F - S
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The Economic Function of
Futures Markets (Continued)
• The difference between the futures price
and the spot price, F - S, is called the
spread, and governs how much wheat
will be stored, and by whom
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The Economic Function of
Futures Markets (Continued)
• Suppose the commodity is wheat, and
next year’s crop is expected to be much
higher than average, then futures prices
may be lower than the spot, (the spread
may be negative,) nobody will store
wheat
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The Economic Function of
Futures Markets (Continued)
• The existence of the futures market for
wheat conveys information to all
producers, distributors, and consumers;
and this eliminates the necessity for
market participants to gather and
process information in order to forecast
the future spot price
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14.3 The Role of Speculators
– Hedger
• anyone using a futures market to reduce risk
– Speculator
• anyone who takes a position in the market
(increasing his risk) in order to profit from his
forecasts of future spot prices
– (A producer, distributor or consumer who chooses
not to hedge her risk may be considered to be a
speculator)
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The Role of Speculators:
Example
– Suppose that the current 1-month futures in
wheat is $1.5/bushel, and a farming family
with stored wheat believes that the price will
rise to $2.00
– Not hedging the stored wheat results in the
family being exposed to the vagrancies of
the wheat market, and it becomes, in effect,
a wheat speculator (just like their cobbler
cousins who are long wheat futures)
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The Role of Speculators:
Gamblers and Wasters
• Critic: “Speculators have no social value”
• Answer:
– Successful speculators make the market
• more efficient as an information resource
• provide liquidity when it is needed, which is when
producers, distributors, and consumers can’t or won’t
hedge
• more efficient by contributing towards recovering the
fixed costs of providing a futures exchange
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14.4 Relationship Between
Commodity Spot and Futures
Prices
• Arbitrageurs place an upper bound on
futures prices by locking in a sure profit
on futures prices if the spread between
the futures price and spot price becomes
greater than the cost of carry, F - S  C
– the cost of carry varies as a function of time
and warehousing organization
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14.5 Extracting Information
from Commodity Futures
Prices
• Case 1 If (Futures Price < Current Spot)
– Then the futures price is an indicator of the
expected future spot price
• The futures price is a biased estimate
because there are risk premiums and
discounts associated with holding the
commodity
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Extracting Information from
Commodity Futures Prices
• Case 2 If (Futures Price > Current Spot)
– Then the futures price is not an indicator of
the expected future spot price
• The spread cannot exceed the cost of carry
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14.6 Spot-Futures Price Parity
for Gold
• In the case of gold futures, arbitrage
establishes an upper- and lower-bound
on the spread between the futures and
spot prices, resulting in the spotfutures price-parity relationship
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Spot-Futures Price Parity for
Gold
• There are two ways to invest in gold
• buy an ounce of gold at S0, store it for a year
at a storage cost of $h/$S0, and sell it for S1
• invest S0 in a 1-year T-bill with return rf, and
purchase a 1-ounce of gold forward, F, for
delivery in 1-year
S1  S 0
S F
 h  rAu  rAu ( syn)  1
 r f  F  1  r f  h S 0
S0
S0
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Spot-Futures Price Parity for
Gold


• A contract with life T: F  1  r f  h S 0
T
• This is not a causal relationship, but the
forward and current spot jointly
determine the market
• If we know one, then the rule of one
market determines that we know the
other
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Spot-Futures Price Parity for
Gold
• The following diagram shows how to
create synthetic gold, T-bills, or gold
forward contract from the other two
• All prices are predetermined,
– except the price of the one year of the
forward and the price in one year of the
gold, but the difference between them is
equal to the known financing and storage
costs
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Rule of One Price: No
Arbitrage Profits
Purchase Actual
Au
Sell
T-Bill
Sell
Actual Au
Settle
T-Bill
Sell
Au Forward
Settle
Au Forward
•Au = Gold
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Implied Cost of Carry
• As a consequence of the forward-spot
price parity relationship, you can’t extract
information about the expected future
spot price of gold (unlike one wheat
case) from futures prices
• The implied cost of carry (per $spot) is
h = (F - S0)/S0 - r
f
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14.7 Financial Futures
• We now focus on financial futures
– standardized contracts for future delivery of
stocks, bonds, indices, and foreign currency
– they have no intrinsic value, but represent
claims on future cash flows
– they have very low storage costs
– settlement is usually in cash
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Financial Futures
• With no storage cost, the relationship
between the forward and the spot is
F
S
T
1  rf 
• Any deviation from this will result in an
arbitrage opportunity
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Financial Futures: Example
• Consider shares in Bablonics, Inc, trading
at $50 each, ($5,000 for a round lot);
assume 6-month T-bills yield 6%
(compounded semiannually)
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Bablonics, Inc (Continued)
• 1 Purchase one round lot of stock at spot
– This results in a negative cash flow today of
$5,000 (out), and will generate a cash flow
of 100*Spot6m (in) in six months
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Bablonics, Inc (Continued)
• 2 Cover today’s negative cash flow by
selling short $5,000 worth of 6-month Tbills with a face value of 5000 (1+
0.06/2)^0.5 = $5,150
• The cash flow today is $5,000 (in), and
the cash flow in six months time will be
$5,150 (out)
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Bablonics, Inc (Continued)
• 3 Cover the risk exposure by selling 100
shares forward at the equilibrium price of
5000*(1+0.06/2)^0.5 = $5,150
– There is no cash flow today, but the value of
this forward contract in six months time will
be $(Spot6m - 5,150)
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Bablonics, Inc (Continued)
• -$5,000 (long stock) + $5,000 (short
bond) + $0 (short forward) = $0
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Bablonics, Inc (Continued)
• Cash Flow in 6-Months
+ $Spot6m (settle long stock) - $5,150 (settle
short bond) +($5,150 - $Spot6m) (settle
forward) = $0
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Bablonics, Inc (Conclusion)
• If your net risk-free investment was zero,
– and you receive nothing
• that is what you should expect
– and you expect to:
• received positive value with no risk, then the
rule of one price has been violated
• lose value with no risk, then reverse the
direction of all transactions, and again you
profit with no risk
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14.8 The “Implied” Risk-Free
Rate
• Rearranging the formula, the implied
interest rate on a forward given the spot
is
1
T
F
F  S0
r     1; if T  1, r 
S0
 S0 
• This is reminiscent of the formula for the
interest rate on a discount bond
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14.9 The Forward Price is not
a Forecast of the Spot Price
• Following the diagrams in Chapter 12 we
might suppose that the expected price of
a stock is   S2 
 s  S0e
t
 rf   t
2 

 S0e
rf t
F
• If this is indeed correct, then the forward
price is not an indicator of the expected
spot price at the maturity of the forward
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The Forward Price is not a
Forecast of the Spot Price
• The forward price is obtained without risk
from the current spot and riskless bond
• The spot value at a future date is
obtained by investing in the security and
accepting (market) risk, and this risk
must be rewarded
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14.10 Forward-Spot Parity
with Cash Payouts
• So far we have assumed that there is no
dividend
– Now suppose that everybody expects an
uncertain dividend in 1 year of D
– It is not possible to replicate D because of
this uncertainty
– We will treat D as if it were known with
certainty, and only deal with 1-year forwards
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Forward-Spot Parity with Cash
Payouts
• The S0 - F relationship becomes
DF
S0 
 F  S  rS  D
1 r
• Note: (forward price > the spot price) if
(D < r S)
• Because D is not known with certainty,
this is a quasi-arbitrage situation
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14.11 “Implied” Dividends
• From the last slide, we may obtain the
implied dividend
D  1  r S  F
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14.12 The Foreign Exchange
Parity Relation
• Recall from Chapter 2 the following
diagram:
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Exchange Rate Example
Time
Japan
15000 ¥
(Borrowed)
U.K.
•150 ¥/£
3% ¥/¥ (direct)
3% ¥/£/£/¥
15450 ¥
15450 ¥
(Repaid)
£100
(Invested)
9%£/£
Forward ¥/£
£109
(Matures)
The Foreign Exchange Parity
Relation
• We used the diagram to show that
$ denominate d Forward on Yen $ Denominate d Spot for Yen

t
1  r$ 
1  rY t
• Recall there is a time structure of
interest, and the appropriate risk free
rate should be used
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14.13 The Role of
Expectations in Determining
Exchange Rates
– Consider a world in which there are two
countries, Domestic & Foreign, and
conditions are such in each country that the
the yield curves are flat, with yields of 5%
and 10% respectively
– Further assume that the exchange rate is 1
today
– The 1-year forward is 1*1.05/1.10=0.9545
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The Role of Expectations in
Determining Exchange Rates
– If the interest rate in Foreign is higher than
in Domestic, one explanation may be that
the rate of inflation is higher.
– Assume no taxes, and the interest rate
difference is the result inflation being 5%
and 10% respectively
– Then the price dynamics of both countries
will result in an exchange rate of 0.9545 next
year, which is also the forward rate
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The Role of Expectations in
Determining Exchange Rates
– In real life, things are not so simple, but
several mechanisms may be postulated that
support the expectations hypothesis
– International investor confidence, and their
forecasts of inflation, place price pressure on
both spot and forward exchange rates
through the international bond market
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