1 (of 20) IBUS 302: International Finance Topic 6–Interest Rate Parity I Lawrence Schrenk, Instructor.

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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 Profit

2. No Risk

3. 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$/£ 1.6820

0.6000 1.09F