Chapter 10
Foreign Exchange
Futures
1
© 2004 South-Western Publishing
Outline
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Forward rates
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Interest rate parity
Purchasing power parity
Foreign currency futures
Dealing with the exposure
Interest Rate Term Structure
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http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve
The Real Rate of Interest

The nominal interest rate (the stated rate)
can be expressed as the sum of:
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The real rate
An inflation premium and
A risk premium
The Real Rate of Interest
(cont’d)

The real rate reflects the rate of return
investors demand for giving up the current
use of funds
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–
–
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Indicates people’s willingness to postpone
spending their money
Is not directly observable
Hovers in the 3% to 4% range
The Inflation Premium

The inflation premium reflects how the
general price level is changing
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Measures how rapidly the money standard is
losing its purchasing power
In the past 75 years, U.S. inflation has averaged
about 3.2% annually
The Risk Premium

The risk premium is the component of
interest rates that is most difficult to
measure
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Risk-averse investors expect to be compensated
for risks they take
The price of a risky security must reflect a risk
premium to entice someone to buy it
The magnitude of the risk premium depends on
how much risk the security carries
The higher the risk premium, the lower the price
FX Risk From A Business
Perspective
A Business Example of Economic Exposure
An American importer agrees to purchase 400
Swiss overcoats at a price of CHF1,200 each, for a
total of CHF480,000. The coats will take 3 months
to produce, and the importer is to pay for them
upon delivery.
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FX Risk From A Business
Perspective (cont’d)
A Business Example of Economic Exposure
(cont’d)
If the importer paid for the coats today, each coat
would cost the importer:
CHF1,200 x $0.8073/CHF = $968.76
The importer is concerned that the U.S. dollar
might weaken between now and coat delivery time.
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FX Risk From A Business
Perspective (cont’d)
A Business Example of Economic Exposure
(cont’d)
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If the dollar strengthens and the value of the Swiss
franc falls to $0.7500, the cost of each coat will be:
CHF1,200 x $0.7500/CHF = $900.00
If the dollar weakens to an exchange rate of
$0.9000, the cost of each coat will be:
CHF1,200 x $0.9000/CHF = $1,080.00
FX Risk From An Investment
Perspective
An Investment Example of Economic Exposure
You just placed an order with your broker to purchase 10,000
shares of Kangaroo Lager, trading on the Sydney Stock
Exchange. You can currently purchase the shares for
AUD1.45 apiece.
The current exchange rate is $0.5755/AUD. Thus, the shares
cost you:
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10,000 x AUD1.45 x $0.5755/AUD = $8,344.75
FX Risk From An Investment
Perspective (cont’d)
An Investment Example of Economic
Exposure (cont’d)
You hold the Kangaroo shares for six months, at
which time the shares sell for AUD1.95. This is a
return of
(1.95 – 1.45)/1.45 = 34.5%
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FX Risk From An Investment
Perspective (cont’d)
An Investment Example of Economic Exposure
(cont’d)
In six months, the exchange rate is $0.5500. If you were to sell
the shares, you would receive:
10,000 x AUD1.95 x $0.5500/AUD = $10,725.00
This is a return on investment of
($10,725.00 - $8,344.75)/$8,344.75 = 28.52%
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Managing Exchange rate risk
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
The spot exchange rate is the current
exchange rate for two currencies

The forward exchange rate is a contractual
rate between a commercial bank and a
client for the future delivery of a specified
quantity of foreign currency
Expectation Hypothesis
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The forward rate is an unbiased estimate of
the future spot rate for foreign exchange
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E.g., if forward rates show that the dollar is
expected to strengthen against the Swiss franc,
it would make sense to delay paying Swiss
francs as long as possible
Forward Rates derivation
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Purchasing power parity
Interest rate parity
Purchasing Power Parity
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Purchasing power parity is an arbitragebased idea that in a world of perfect
markets, the same good should sell for the
same price in different countries
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Assumes there are no trade barriers, no taxes,
etc.
Purchasing Power Parity
(cont’d)
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
Unexpected inflation causes the value of
the home currency to fall

Differentials in international inflation rates
can be a source of foreign exchange risk
Interest Rate Parity

Interest rate parity states that differences in
national interest rates will be reflected in
the currency forward market
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Two securities of similar risk and maturity will
show a difference in their interest rates equal to
the forward premium or discount, but with the
opposite sign
Interest Rate Parity (cont’d)
Computing Implied Foreign Interest Rates
It is now January 2, 2004. The six-months forward rate for the
British pound is £0.5658/$; the spot rate is £0.5576/$. Also,
the six-month T-bill rate is 1.01%.
What is the implied British 6-month interest rate based on the
interest rate parity relationship?
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Avoiding foreign, domestic or
direct, indirect quote confusion
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–
£.5576
X%
£.5576 *(1+x/2)
↔
If the forward is quoted per $1
£.5576 *(1+x/2) = .5658
1*(1+.0101/2)
–
(we should divide by the $ amount)
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$1
1.01%
1*(1+.0101/2)
or
per 1 £ (1.7674)
1*(1+.0101/2) = 1
£.5576 *(1+x/2) .5658
(we should divide by the £ amount)
Interest Rate Parity (cont’d)
Computing Implied Foreign Interest Rates (cont’d)
The implied British 6-month interest rate is 3.96%:
0.5658 1  RUK

0.5576 1  .0101
2
RUK  .0198  2  3.96%
The actual UK rate in early 2004 was 3.90%.
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Pricing of Foreign Exchange
Futures Contracts
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Futures prices are a function of
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–
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The spot price
The cost of carrying the particular asset or
financial instrument
For foreign currency futures, the cost of
holding one currency rather than another is
an opportunity cost measured by
differences in interest rates
Pricing of Foreign Exchange
Futures Contracts

A basic pricing model:
days to delivery 

Pf  spot rate  1  Red  Rlc 

365


where
Pf  futures price
Red  Eurodollar rate
Rlc  Local currency rate
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Pricing of Foreign Exchange
Futures Contracts (cont’d)
Pricing A Foreign Currency Futures Contract
Example
In the Land of Leptonia interest rates are 10.00%,
and the current dollar price of a Lepton is $0.4817.
The current Eurodollar deposit rate is 7.50%.
For how much should a 90-day futures contract on
Lepton’s sell?
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Pricing of Foreign Exchange
Futures Contracts (cont’d)
Pricing A Foreign Currency Futures Contract Example
(cont’d)
Using the equation:
90 

Pf  0.4817  1  0.075  0.100

365


 0.4787
The futures price for Leptons should be less than their cost in
the spot market. This is because Leptonia’s interest rates are
2.5% higher than the U.S. rate.
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Dealing With the Exposure
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Introduction
Ignore the exposure
Reduce or eliminate the exposure
Hedge the exposure
Introduction
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The portfolio manager needs to decide
whether to:
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Ignore the exposure,
Eliminate the exposure, or
Hedge the exposure
Ignore the Exposure
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Investors may be aware of economic
exposure but accept it as a fact of life
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Ignoring the exposure may be appropriate if
the dollar amount of the exposure is
relatively small
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Ignoring the exposure may be appropriate if
the dollar is expected to depreciate
Reduce or Eliminate the
Exposure
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Amounts to selling the foreign security or
reducing the size of the position

May be appropriate if the dollar is expected
to appreciate dramatically
Summary
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Reconcile expectation and Cost of Carry
hypothesis of pricing future contracts on
foreign exchange
Find forward exchange rate based on IRP and
PPP
Learn term structure of interest rates and its
use in pricing financial assets