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IBUS 302: International Finance

Topic 6–Interest Rate Parity I

Lawrence Schrenk, Instructor

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Learning Objectives

1. Define arbitrage.▪ 2. Explain interest rate parity.3. Describe and calculate covered interest

arbitrage.▪

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 Requirements1. Positive Profit2. No Risk3. 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

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

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Asset Cash Flow 1

Cash Flow 2

Cash Flow 3

Price

A $10 $25 $15 $45

B $15 -$10 $10 $10

C $25 $15 $25 $50

Arbitrage versus Equilibrium What happens when investors take

advantage of arbitrage? ▪ 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…

There is no arbitrage. This can either

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:

Real (empirical or market) data, and Values predicted by a theory

The simple no arbitrage example: 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)

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. Convert dollars into pounds.2. Make a risk free investment with the pounds.3. 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

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

£0.6000

$1.10

$1.00 ▪

£0.6540$1.13

Dollar Strategy 1 Non-Dollar Strategy

$1.00

i $ =

10%

i£ = 9%

S(£/$) = 0.6000

F12($/£) = 1.7241≠▪

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

£0.6000

$1.10

$1.00 ▪

£0.6540$1.10

Strategy 1 Strategy 2

$1.00

i $ =

10%

i£ = 9%

S(£/$) = 0.6000

F12 ($/£) = 1.6821=▪

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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:

This is the interest rate parity (IRP) requirement. FIRP is the forward rate predicted by IRP. ▪

Interest Rate Parity (IRP)

$

x

1$/x $/x

1IRP

iF S

i

Both in American Terms▪

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Example 2 (cont’d) So for our second example, the interest rate

parity condition

Holds because the actual value

Note: Small rounding error 1.6820 ≠ 1.6821

$ $

£ £

1 11$/£ $/£1 £/$ 1IRP

i iF S

i S i

1 1.10$/£ 1.68200.6000 1.09

F