CHAPTER 14
FORWARD AND FUTURES PRICES
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Objectives
To explain the economic role of futures markets
To show what information can and cannot be inferred from forward and futures prices.
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14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10
14.11
14.12
14.13
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Outline
Distinctions Between Forward and Futures Contracts
The Economic Function of Futures Markets
The Role of Speculators
Relation Between Commodity Spot and Futures Prices
Extracting Information from Commodity Futures Prices
Spot-Futures Price Parity for Gold
Financial Futures
The Implied Risk-Free Rate
The Forward Price Is Not a Forecast of the Spot Price
Forward-Spot Parity with Cash Payouts
Implied Dividends
The Foreign-Exchange Parity Relation
The Role of Expectations in Determining Exchange Rates
Summary
Futures contracts make it possible to separate the decision of whether to physically store a commodity
from the decision to have financial exposure to its price changes.
Speculators in futures markets improve the informational content of futures prices and make futures
markets more liquid than they would otherwise be.
The futures price of wheat cannot exceed the spot price by more than the cost of carry:
The forward-spot price parity relation for gold is that the forward price equals the spot price times the
FS C
cost of carry:
F  S (1  r  s)
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This relation is maintained by the force of arbitrage.
One can infer the implied cost of carry and the implied storage costs from the observed spot and
forward prices and the risk-free interest rate.
The forward-spot parity relation for stocks is that the forward price equals the spot price times 1 plus
the risk-free rate less the expected cash dividend.
F  S (1  r )  D
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This relation can therefore be used to infer the implied dividend from the observed spot and forward
prices and the risk-free interest rate.
The forward-spot price parity relation for the dollar/yen exchange rate involves two interest rates:
where F is the forward price of the yen, S is the current spot price, rY is the yen interest rate, and r$ is
F
S
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1  r$ 1  rY
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the dollar interest rate.
If the forward dollar/yen exchange rate is an unbiased forecast of the future spot exchange rate, then
one can infer that forecast either from the forward rate or from the dollar-denominated and yendenominated risk-free interest rates.