Corporate finance chapter 014 forward and futures prices

Chapter 14: Forward & Futures Prices Objective •How to price forward and futures •Storage of commodities •Cost of carry... Chapter 14: Contents1 Distinction Between Forward & Futures Co

Chapter 14: Forward &

Futures Prices

Objective

•How to price forward and futures

•Storage of commodities

•Cost of carry

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

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

– Open, High, Low, Settle, Change, Lifetime

high, Lifetime low, Open interest

– Mark-to-market

– Margin requirement

– Margin call

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

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 $h/$S 0 , and sell it for S 1

• invest S0 in a 1-year T-bill with return r f , and purchase a 1-ounce of gold forward, F, for delivery in 1-year

0

1 )

( 0

0

S

F

S r

r

h S

S

S

f f

syn Au

Au = = − + ⇒ = + +

=

−

−

Spot-Futures Price Parity for Gold

• A contract with life 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

(1 r h) S0

Rule of One Price: No

Arbitrage Profits

Purchase Actual

Au

Sell T-Bill

Sell

Au Forward

Sell

Actual Au

Settle T-Bill

Settle

Au Forward

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 - rf

Financial Futures

• With no storage cost, the relationship

between the forward and the spot is

• Any deviation from this will result in an

arbitrage opportunity

f

r

F S

+

=

1

14.8 The “Implied” Risk-Free Rate

• Rearranging the formula, the implied

interest rate on a forward given the spot is

• This is reminiscent of the formula for the

0 0 1

0

1, T

if

;

1

S

S

F r

S

F









=

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

• If this is indeed correct, then the forward

price is not an indicator of the expected spot price at the maturity of the forward

F e

S e

S r t r t

S f





 +

0

2 0

2

σ

µ

Forward-Spot Parity with

Cash Payouts

• The S0 - F relationship becomes

• Note: (forward price > the spot price) if

(D < r S)

• Because D is not known with certainty,

this is a quasi-arbitrage situation

D rS

S

F r

F

D

+

+

=

1

0

14.11 “Implied” Dividends

• From the last slide, we may obtain the

implied dividend

Exchange Rate Example

15000 ¥ (Borrowed)

15450 ¥

15450 ¥

(Repaid)

£100 (Invested)

£109 (Matures)

Time

3% ¥/¥ (direct)

3% ¥/£/£/¥

•150 ¥/£

9%£/£

Forward ¥/£

The Foreign Exchange Parity

Relation

• We used the diagram to show that

• Recall there is a time structure of

interest, and the appropriate risk free

rate should be used

Y

Yen for

Spot d

Denominate

$ r

1

Yen

on Forward

d denominate

$

+

= +