IBUS 302: International Finance

1. IBUS 302: International Finance Topic 7–Interest Rate Parity II Lawrence Schrenk, Instructor

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

3. 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

4. Two Connections • A Connection: • And the reverse.

5. 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).

6. 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.

7. 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(£/$) = 0.6000 • F12(£/$) = 0.5800 (→ F12($/£) = 1.7241) • i£ = 9% • i$ = 10%

8. Example 1: An Arbitrage Opportunity Strategy 1 Strategy 2 ≠ $1.10 $1.13 £0.6540 F12($/£) = 1.7241 i$ = 10% i£ = 9% S(£/$) = 0.6000 $1.00 $1.00 £0.6000

9. Practice • Is arbitrage possible if... S($/€) = 1.4900, so S(€/$) = 0.6711 F($/€) = 1.4975 i$ = 6% i€ = 7% • Exercise: • Calculate the two strategies. • Does the IRP requirement hold?

10. Practice (cont’d) • We could tell that covered interest arbitrage is possible, since • The dollar is at a forward discount • FIRP ($/£) > S ($/£) • 1.4975 > 1.4900 • But the dollar interest is less • i$ < i€ • 6% < 7%

11. 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

12. Practice (same numbers) • We now know arbitrage is possible if... S($/€) = 1.4900, so S(€/$) = 0.6711 F($/€) = 1.4975 i$ = 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.

13. 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

14. 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(€/$) ≠ S(€/$)

15. Deviations form Interest Rate Parity

16. 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▪

17. 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.