IBUS 302: International Finance

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

2. Learning Objectives • Define arbitrage.▪ • Explain interest rate parity. • Describe and calculate covered interest arbitrage.▪

3. Arbitrage

4. Arbitrage Definition • The practice of taking advantage of the price differential between two markets by buying and selling assets. • Three Requirements • Positive Profit • No Risk • No Investment Note: (3) implies (2).

5. Arbitrage Characteristics • The Law of One Price • Other Considerations • Simultaneous Positions • Long and Short Positions

6. 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)

7. A Simple Example

8. 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. ▪

9. 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

10. 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)

11. Interest Rate Parity (IRP)

12. 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! ▪

13. 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.

14. 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

15. Two Strategies/Same Investment • Dollar Strategy... • Make a risk free investment with dollars. • Non-Dollar Strategy simultaneously... • 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

16. 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

17. Example 1: An Arbitrage Opportunity Dollar Strategy 1 Non-Dollar Strategy ≠▪ $1.10 $1.13 £0.6540 F12($/£) = 1.7241 i$ = 10% i£ = 9% S(£/$) = 0.6000 $1.00 ▪ $1.00 £0.6000

18. 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

19. Example 2: No Arbitrage Strategy 1 Strategy 2 =▪ $1.10 $1.10 £0.6540 F12 ($/£) = 1.6821 i$ = 10% i£ = 9% S(£/$) = 0.6000 $1.00 ▪ $1.00 £0.6000

20. 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: • This is the interest rate parity (IRP) requirement. • FIRP is the forward rate predicted by IRP. ▪ Both in American Terms▪

21. 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