### PowerPoint Slides 6

```IBUS 302:
International Finance
Topic 6–Interest Rate Parity I
Lawrence Schrenk, Instructor
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Learning Objectives
1.
2.
3.
Define arbitrage.▪
Explain interest rate parity.
Describe and calculate covered interest
arbitrage.▪
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Arbitrage
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Arbitrage Definition


The practice of taking advantage of the price
differential between two markets by buying
and selling assets.
Three Requirements
1.
2.
3.
Positive Profit
No Risk
No Investment
Note: (3) implies (2).
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Arbitrage Characteristics


The Law of One Price
Other Considerations


Simultaneous Positions
Long and Short Positions
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Self-Financing Strategies


No Investment Strategy
Short Positions



Short Selling
Borrowing
How to Capture Arbitrage


Long in Higher Priced Portfolio (lend)
Short in Lower Priced Portfolio (borrow)
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A Simple Example
Asset
Cash Cash Cash
Flow 1 Flow 2 Flow 3
Price
A
\$10
\$25
\$15
\$45
B
\$15
-\$10
\$10
\$10
C
\$25
\$15
\$25
\$50
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Arbitrage versus Equilibrium


What happens when investors take
What should happen to the prices in the
example?



Of Asset A and B?
Of Asset C?
Arbitrage is ‘Self-Eliminating’–Equilibrium is
restored. ▪
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Non Arbitrage Pricing

If markets are efficient and in equilibrium…


This can either



There is no arbitrage.
Set a limit on prices, or
Determine prices exactly.
Applications


Determining FX Rates
Pricing Derivative Securities
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Notation

We need to distinguish:



The simple no arbitrage example:



Real (empirical or market) data, and
Values predicted by a theory
The actual price of asset C is \$50.00
The predicted, no arbitrage value is \$55.00
Subscripts will distinguish theoretical values:


P = \$50.00
PNA = \$55.00 (NA for no arbitrage)
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Interest Rate Parity
(IRP)
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Spot and Forward Rates


What is the relationship between spot and
forward rates?
Could…




S(\$/£) = 1.7700, and
F6(\$/£) = 1.7720 ▪
Would this allow arbitrage?
Depends! ▪
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FX Rates and Interest Rates


Any spot rate can exist with any forward rate,
but…
There will be arbitrage if the risk free rates of
interest are not correct.
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Interest Rate Parity


A ‘parity’ relationship holds if arbitrage is not
possible.
Interest rate parity (IRP) is a relationship
between




The domestic risk free rate
The foreign risk free rate
The spot rate
The forward rate
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Two Strategies/Same Investment
Dollar Strategy...

1.
Make a risk free investment with dollars.
Non-Dollar Strategy simultaneously...

1.
2.
3.
Convert dollars into pounds.
Make a risk free investment with the pounds.
Sell the proceeds from (2) forward for dollars
Same investment In both strategies, you...




Begin with dollars
Make only risk free investments
End with dollars
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Example 1: An Arbitrage
Opportunity

Data




S(£/\$) = 0.6000
F12(£/\$) = 0.5800 (→ F12(\$/£) = 1.7241)
i£ = 9%
i\$ = 10%

i = annual, risk free rate of interest
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Example 1: An Arbitrage
Opportunity
Dollar Strategy 1
\$1.10
Non-Dollar Strategy
≠
\$1.13
▪
£0.6540
F12(\$/£) = 1.7241
i\$ = 10%
i£ = 9%
\$1.00 ▪
S(£/\$) = 0.6000
\$1.00
£0.6000
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Example 2: No Arbitrage

Data




S(£/\$) = 0.6000
F12(£/\$) = 0.5945 (→ F12(\$/£) = 1.6821)
i£ = 9%
i\$ = 10%

i = annual, risk free rate of interest
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Example 2: No Arbitrage
Strategy 1
\$1.10
Strategy 2
=
\$1.10
▪
£0.6540
F12 (\$/£) = 1.6821
i\$ = 10%
i£ = 9%
\$1.00 ▪
S(£/\$) = 0.6000
\$1.00
£0.6000
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Interest Rate Parity (IRP)


If both strategies yield the same amount, then there is
no arbitrage.
 Note: buying/selling forward required to eliminate
FX risk!
For this to occur, the following relationship must hold:
1  i\$ 
FIRP  \$/x   S  \$/x  

1  i x 
Both in American Terms▪

This is the interest rate parity (IRP) requirement.
 FIRP is the forward rate predicted by IRP. ▪
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Example 2 (cont’d)


So for our second example, the interest rate
parity condition
1  i\$ 
1 1  i\$ 
FIRP  \$/£   S  \$/£  



1  i £  S  £/\$  1  i £ 
Holds because the actual value
1 1.10 
F  \$/£  
 1.6820


0.6000 1.09 
Note: Small rounding error 1.6820 ≠ 1.6821
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