IRP and Arbitrage

1. IRP and Arbitrage

2. The Foreign Exchange Market (FOREX) • Purpose – assist clients in the conduct of international commerce • Not a marketplace, but a worldwide “linkage” • Two main participants • Interbank market – “wholesale” (core of the whole process) (most trades are “speculative”) • Client market – “retail”

3. Overview of the Spot Market • The immediate purchase or sale of foreign exchange • Quotes of these exchange rates are in “direct” or “indirect” terms • Direct – price is in U.S. $$ • Indirect – price in terms of the amount of foreign currency per U.S dollar NOTE: terms are reciprocals

4. Foreign Exchange (FX) Traders • Buy currency at their “bid” price • Sell currency at their “ask” price • Obviously, BID<ASK • Standard trade = $10,000,000 (or equivalent foreign currency)

5. Terms of the Trade Say that we are trading $ for £ at the price of 0.6752 £/$ • “big figure” “small figure” • Big figure – everyone knows; is the same for all traders • Small figure – differs among traders • (ASK – BID) ≈ 5 small figures or “points”

6. Overview of the Forward Market • Involves contracting today for the future purchase or sale of currency • Rates COULD be the same as the spot rate, but are usually • Higher (at a premium) OR • Lower (at a discount) • Buying FX forward – taking a “long position” • Selling FX forward – taking a “short position”

7. Overview of the Forward Market (Con’t) • Four Main aspects of the forward market • Its decentralized. Its idiosyncratic. It depends on the buyers and sellers. • Agreements can be written for any maturity. • There is no specific settlement date. • Agreements can be written for any currency the parties agree to.

8. Forward Trades • Can be classified as 1 of 2 transactions • Outright – speculative (11% of interbank FX trading) • Swaps – mitigate currency exposure inherent in trade (56% of interbank trading) • Forward premium – its common to express the premium or discount of a forward rate in annualized terms of the % deviation from the spot rate

9. Forward Premium Example • Given: Info on the Canadian $ • 3 month forward premium = $0.7939 • Spot rate = $0.7950 • Calculate the annualized forward premium and whether its trading at a forward premium or discount F3M – S *4*100 = $0.7939-$0.7950 *400 = -0.55% S $0.7950 • Definitely trading at a forward discount

10. More on Swaps • They’re a combination of a forward contract and spot contract • A trader in need of a foreign currency will be matched with a trader in need of domestic currency (for the same time period) • An intermediary will bring the two together • Each borrows in their own currency, exchanges with the other party through a spot contract, and reverses the transaction in the future through a forward contract.

11. International Parity Relationships • Arbitrage plays a critical role • Simultaneously buying and selling the same or equivalent assets for the purpose of making guaranteed profits • Interest Rate Parity • Is an arbitrage condition that must hold when international financial markets are in equilibrium

12. Interest Rate Parity • Based on the fact that when you invest, you have two options • Invest domestically at the U.S. interest rate • Maturity Value = $invested * (1+i$) OR • Invest in a foreign country at the foreign interest rate and protect against any negative changes in the exchange rate by selling the maturity value of the foreign investment forward To Do This…

13. Investing in a Foreign Country • Exchange your dollars for the foreign currency at the spot rate. • Maturity Value = Foreign (1/S) • Invest the foreign currency at the foreign exchange rate • Maturity Value = Foreign (1/S) * (1+iForeign) • Sell the maturity value forward in exchange for a predetermined dollar amount, which is…

14. Investing in a Foreign Country (Con’t) • Sell the maturity value forward in exchange for a predetermined dollar amount, which is $[(1/S)(1+iForeign)]Forward • This makes the foreign investment a perfect substitute for the domestic investment - you have “hedged” the exchange rate risk

15. Arbitrage Equilibrium • Dictates that the future dollar proceeds from investing in the two equivalent investments must be the same (1+i$) = (F/S)(1+iForeign) Return on U.S. investment Return on Foreign Investment • This is a formal statement of IRP

16. Arbitrage Equilibrium (Con’t) • If IRP holds, then you’ll be indifferent between the two investments • If not, this gives rise to “covered interest arbitrage” opportunities • Why would IRP not hold? • Transaction costs • Capital controls (we’ll get back to these)

17. Example 1 • Annual interest rates • United States = 5% • United Kingdom = 8% • Spot Rate = $1.50/£ • 1-year forward rate = $1.48/£ • You can borrow $1,000,000 or £666,667 • Is there an arbitrage opportunity??? (AKA is there an opportunity to make a profit?)

18. Example 1 (Con’t) • First, check if IRP is holding • (F/S)(1+i£) = (1.48/1.50)(1.08) = 1.0656 • Since 1.05 < 1.0656 Return on U.S. investment Return on U.K. investment IRP is not holding, there is an arbitrage opportunity • Since the rate is lower in the U.S., borrow in the U.S., lend in the U.K.

19. Example 1 (Con’t) • Borrow $1,000,000 in the U.S. • In one year, you’ll need to pay back $1,000,000*(1+.05) = $1,050,000 • Buy £666,667 on the spot market using the $1,000,000 • Invest the £666,667 in the U.K. The maturity value will be £720,000 • Sell the £720,000 forward for $1,065,600 = (£720,000)*($1.48/£)

20. Example 1 (Con’t) • In one year • Receive the maturity value of the U.K. investment (£720,000) • Deliver this to the other party in the forward contract to get $1,065,600 • Pay back the $1,050,000 loan in the U.S. • You have $16,500 left over = PROFIT • Never invested any of own money, never bore any risk • “covered interest arbitrage”

21. Example 2 • Quarterly interest rates • United States = 2% • Germany = 1.25% • Spot Rate = €1.0114/$ • Forward Rate = €1.0101/$ • To decide if IRP holds, convert these first to direct terms • Spot rate = $0.9887/€ • Forward rate = $0.9900/€

22. Example 2 (Con’t) • Compute the return in Germany (F/S)(1+i€) = (.9900/.9887)*(1.0125) = 1.0138 • Since 1.02 > 1.0138 Return on U.S. investment Return on U.K. investment IRP is not holding, there is an arbitrage opportunity • Since the rate is higher in the U.S., borrow in Germany, lend in the U.S.

23. Example 2 (Con’t) • Borrow €1,011,400 in Germany. Need to pay back €1,024,042 in 3 months. • Buy $1,000,000 on the spot market. • Invest it in the U.S. for a maturity value of $1,020,000. • Buy €1,024,042 forward in exchange for $1,013,803 via the forward rate

24. Example 2 (Con’t) • In three months • Receive the maturity value of the U.S. investment = $1,020,000. • Deliver $1,013,803 to the other party in the forward contract and receive €1,024,042. • Pay off the German loan with that. • Have $6,197 left. Profit

25. Example 3 • Given annual interest rates • United States = 0.05 • United Kingdom = 0.10 • We want to look at a three month investment, so we need to convert these rates to quarterly rates • United States = (0.05/4) = 0.0125 • United Kingdom = (0.10/4) = 0.0250

26. Example 3 (Con’t) • Rather than comparing just the rates themselves, another way to determine if there is an arbitrage opportunity is to compare the forward premium with a “standardized interest rate differential” • If the two are different, an arbitrage opportunity exists

27. Example 3 (Con’t) • Calculate the forward premium F – S = 1.52 – 1.50 = 0.0133 S 1.50 • Next, to see if IRP holds (returns are the same), calculate the “standardized interest rate differential” iUS – iUK = 0.0125 – 0.0250 = -0.0122 (1+ iUK)1.0250 • Since the two differ, there is an arbitrage opportunity

28. Example 3 (Con’t) • Since the difference in the interest rates is negative, it tells us that the interest rates in the U.S. are “too low” • Borrow in the U.S., lend in the U.K.

29. Example 3 (Con’t) • Borrow $100,000 in the U.S. Need to pay back $101,250 in 3 months. • Convert the $100,000 to £ on the spot market for £66,666. • Invest in the U.K. The maturity value will be £68,333. • Lock in this amount at the forward rate to receive $103,866. • Pay back the U.S. loan • Have $2,616 profit.

30. Example 4 • Quarterly interest rates • United States = 0.0091 • United Kingdom = 0.0300 • Forward Rate = $1.45 • Spot Rate = $1.48 • Does an arbitrage opportunity exist?

31. Example 4 (con’t) • Calculate the forward premium • It is -0.203 • Calculate the interest rate differential • It is also -0.203 • There is no arbitrage opportunity

32. What happens when arbitrage takes place? • Arbitrage opportunities last only a short while, as IRP is restored quickly. HOW? • For example, if the interest rate is lower in the U.S. than the U.K., every trader: • Borrows in the U.S. • Buys the £ on the spot market • Invests the £ • Sells the £ forward • What happens?

33. What happens when arbitrage takes place? (Con’t) • The interest rate in the U.S. goes up (because of lots of borrowing) • The interest rate in the U.K. goes down (because of the increase in loanable funds) • The pound appreciates in the spot market (because of increased demand) • The pound depreciates in the forward market (because of increased supply) restoring IRP

34. Why IRP may not hold • If IRP held, or was always quickly restored, deviations from IRP would be • Randomly distributed • Have an expected value of zero • However, deviations from IRP hardly hover around zero. WHY? • Transaction Costs - Because of bid-ask spreads, arbitrage profit may become non-positive • Capital Controls - Sometimes governments restrict inflows/outflows for macro reasons.

35. Why IRP may not hold (Con’t) • So, deviations from IRP don’t represent unexploited profitable arbitrage opportunities • But rather, • Non-profitable exchanges • Barriers to cross-border exchange