Corporate finance chapter 014 forward and futures prices

Chapter 14: Forward &
Futures Prices

Objective
1

•How to price forward and futures
•Storage of commodities
•Cost of carry
•Understanding financial

Copyright © Prentice Hall Inc. 2000. Author: Nick Bagley, bdellaSoft, Inc.

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
7 Financial Futures

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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


Terms
– Open, High, Low, Settle, Change, Lifetime
high, Lifetime low, Open interest
– Mark-to-market
– Margin requirement
– Margin call

3


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

4


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
S1 − F
− h = rAu = rAu ( syn ) =
+ rf ⇒ F = (1 + rf + h ) S 0
S0
S0

5


Spot-Futures Price Parity for
Gold

(

)

T

• A contract with life T: F = 1 + r f + h S 0
• 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
6


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
•Au==Gold
Gold

7


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

8


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

9


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  σ S2 

µ s = S0e

 rf +  t

2 


t

≠ 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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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
12

14.11 “Implied” Dividends
• From the last slide, we may obtain the
implied dividend

D = (1 + r ) S − F

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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
$ denominated Forward on Yen $ Denominated 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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