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**IBUS 302: International Finance**

Topic 7–Interest Rate Parity II Lawrence Schrenk, Instructor

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Learning Objectives Describe and calculate covered interest arbitrage. ▪ Discuss reasons for a deviation from interest rate parity.▪

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**Interest Rate Parity (IRP)**

Recall, for no arbitrage, the following relationship must hold: This is the interest rate parity (IRP) requirement. FIRP is the forward rate predicted by IRP. Both in American Terms

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Two Connections A Connection: And the reverse.

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**Two Connections (cont’d)**

The Two Connection: In words If the dollar is depreciating (FIRP($/x) > S($/x)), the dollar interest return must be higher (i$ > ix). If the dollar is appreciating (FIRP ($/x) < S($/x)), the dollar interest return must be lower (i$ < ix).

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**FX/Interest Rate Relationships**

If dollar is at a forward discount, i.e., FIRP ($/£) > S ($/£) There will be less demand for the dollar, It will cost more dollars to buy one pound The dollar will depreciate against the pound Then i$ > i£ The interest rate on dollars must be higher to offset the depreciation. Otherwise the two strategies would not yield the same dollar value.

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Example 1 Revisited To capture the arbitrage opportunity, do you borrow or lend dollars? If the FX market is efficient, what should happen to the rates in example 1? S(£/$) = F12(£/$) = (→ F12($/£) = ) i£ = 9% i$ = 10%

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**Example 1: An Arbitrage Opportunity**

Strategy Strategy 2 ≠ $1.10 $1.13 £0.6540 F12($/£) = i$ = 10% i£ = 9% S(£/$) = $1.00 $1.00 £0.6000

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**Practice Is arbitrage possible if... Exercise:**

S($/€) = , so S(€/$) = F($/€) = i$ = 6% i€ = 7% Exercise: Calculate the two strategies. Does the IRP requirement hold?

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Practice (cont’d) We could tell that covered interest arbitrage is possible, since The dollar is at a forward discount FIRP ($/£) > S ($/£) > But the dollar interest is less i$ < i€ 6% < 7%

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**Capturing the Arbitrage Profit**

If arbitrage is possible, To capture the profit Go short in the less valuable strategy Here, borrow at the lower return Go long in the more valuable strategy Here, lend (invest) at the higher return Net the difference

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**Practice (same numbers)**

We now know arbitrage is possible if... S($/€) = , so S(€/$) = F($/€) = i$ = 6% i€ = 7% How do you exploit covered interest arbitrage? Borrow at the lower return (i$ = 6%) Lend (Invest) at the higher return (i€ = 7%) Do it.

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**Implications Recall the IRP requirement:**

So, if there is no arbitrage, the forward rate is strictly a function of... The spot rate The two risk free rates of interest

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**Key Idea: Differentials**

Forward rates are determined by differentials in the risk free return (i). If the risk free rates are equal, i$ = i€, FIRP($/€) = S($/€) FIRP(€/$) = S(€/$) If the risk free rates are not equal, i$ ≠ i€, FIRP($/€) ≠ S($/€) FIRP(€/$) ≠ S(€/$)

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**Deviations form Interest Rate Parity**

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Transaction Costs Transaction costs are central in we can, in practice, get an arbitrage profit. Arbitrage is only practical if the arbitrage profit exceeds the transaction costs required to get it. You cannot exploit small deviations from IRP.▪ Arbitrage Practical▪

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Capital Controls If governments limit the flow of capital across political borders, There are capital controls. If the demand for a currency increases The currency appreciates But capital controls may limit the supply of the currency.

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