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# Chapter 6

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1. Chapter 6 International Arbitrage

2. Chapter Objectives • Arbitrage • Types of Arbitrage • Realignments due to different types of arbitrage • Interest Rate Parity

3. Arbitrage Def: Capitalizing on a discrepancy in quoted prices. Often, the funds invested are not tied up for any length of time and no risk is involved. • In response to the imbalance in demand and supply resulting from arbitrage activity, prices will realign very quickly, such that no further risk-free profits can be made.

4. Types of Arbitrage • Locational arbitrage • Triangular arbitrage • Covered interest arbitrage

5. Locational arbitrage “Action to capitalize on discrepancy in quoted exchange rates between banks” It becomes possible when a bank’s buying price is higher than another bank’s selling price for the same currency.

6. Bank A \$ 1 = Rs 85 Buy USD from Bank A Bank B \$ 1 = Rs 86 Sell it to Bank B Profit = Rs 1 / \$ Example 1 Bank A Bank B

7. Bank A USD/PKR 85.15 /86.25 Bank B USD/PKR 86.75 /95 * If you trade \$100,000 * Is locational arbitrage possible ? * Calculate the profit Example 2

8. Bank A USD / PKR 85.15 /86.25 Buy from Bank A @ Ask Price of 86.25 Bank B________ USD / PKR 86.75 /95 Sell to Bank B @ bid Price of 86.75 Profit :Rs 0.50 / \$ 0.50 * 100,000 = Rs 50,000 Example 1 Calculations Bank A Bank B

9. Problem Beal BankYardley Bank Bid price of NZ \$ \$ 0.401 \$ 0.398 Ask price of NZ \$ \$ 0.404 \$ 0.400 • Is locational arbitrage possible? • Assume you have USD 1 M • Calculate the profit

10. Triangular Arbitrage

11. Triangular arbitrage “Action to capitalize on a discrepancy where the quoted cross exchange rate is not equal to the rate that should exist at equilibrium” It is possible when a cross exchange rate quote differs from the rate calculated from spot rates

12. Cross Exchange Rate • It is an exchange rate @ which currencies other than US dollar can be exchanged Here we are concerned with exchanging Currency A into currency B by using • Rate of Currency A in terms of US- dollar & • Rate of Currency B in terms of US- dollar

13. Example 3 A Canadian firm needs Mexican Peso to buy Mexican goods • It has to find the peso value relative to Canadian \$ • This type of rate is termed as Cross Exchange rate Formula Value of peso in C\$= value of peso in USD value of C\$ in USD = \$0.07 \$0.70 Therefore 1 Peso =C\$ 0.10

14. USD Value of Rs in \$ Value of £ in \$ PKR GBP Value of Rs in £ Triangular Arbitrage

15. Example 4 Suppose GBP/USD spot rate: \$ 2.00 GBP/PKR Cross Exchange rate: Rs 112 PKR/USD Spot rate: \$ 0.02 • Is triangular arbitrage possible • Calculate the profit from triangular arbitrage

16. Calculation Step 1 Convert USD into GBP @ \$ 2 \$ 10000 / 2 = £ 5000 Step 2 Convert GBP into PKR @ Rs 112 (Cross Exchange Rate) £ 5000 * 110 = Rs 550000 Step 3 Covert PKR into USD @ \$ 0.02 Rs 550000 * 0.02 = \$ 11000 You Ended with : \$ 11000 You Started with: \$ 10000 Profit : \$ 1000

17. Actual Calculation Step 1 Convert USD into GBP \$ 2 \$ 10000 / 2 = £ 5000 Step 2 Convert GBP into PKR @ Rs 100 (Cross Exchange Rate) £ 5000 * 100 = Rs 500000 Step 3 Covert PKR into USD \$ 0.02 Rs 500000 / 50 = \$ 10000 You Ended with : \$ 10000 You Started with: \$ 10000 Profit : \$ 0

18. Cross Exchange Rate • We have to find the GBP value relative to PKR • This type of rate is termed as Cross Exchange rate Formula Value of GBP in PKR= value of GBP in USD value of PKR in USD = \$ 2 \$ 0.02 Therefore 1 GBP =100 PKR

19. Realignment due to triangle arbitrage • When the exchange rates of the currencies are not in equilibrium, triangular arbitrage will force them back into equilibrium.

20. Covered interest arbitrage Investment in a foreign money market security with a simultaneous forward sale of the currency denominating that security • It is the process of capitalizing on the interest rate differential between two countries and covering the exchange rate risk through forward contract.

21. Covered interest arbitragetends to force a relationship between forward rate premiums and interest rate differentials.

22. Example 4 Suppose GBP/USD spot rate: \$ 2.00 Interest rate on U.S. 90-day Deposit = 2% Interest rate on U.K. 90-day Deposit = 4% 3-month forward : \$ 2.00

23. Investment in UK • Convert USD into GBP @ \$ 2.00 Spot • Deposit in UK bank @ 4% Rate • After 3-months Convert principle plus interest @ forward rate of \$ 2.00 Investment in US • Deposit in US bank @ 2% Rate

24. UK Calculation • Convert USD into GBP @ \$ 2.00 Spot \$1000000 / 2 =£ 500000 • Deposit in UK bank @ 4% Rate £ 500000 * 4 % = £ 20000 • After 3-months Convert principle plus interest @ \$ 2.00 forward rate (£ 500000 + £ 20000 = £ 520000) £ 520000 * 2.00 = \$ 1040000

25. US Calculation • Deposit in US bank @ 2% Rate \$ 1000000 * 2 % = \$ 20000 \$ 1000000 + \$20000 Total = \$1020000

26. Comparing Profits • From UK \$ 1040000 • From US \$ 1020000 • Therefore it is better to take the benefit of interest rate differential and deposit in UK • You can achieve profit of \$ 20000 more

27. Benefits of understanding the concept of International Arbitrage • Locational arbitrage It ensures that quoted exchange rates are similar across banks in different locations. • Triangular arbitrage It ensures that cross exchange rates are set properly. • Covered interest arbitrage It ensures that forward exchange rates are set properly.

28. Interest Rate Parity (IRP) • Market forces cause the forward rate to differ from the spot rate by an amount that is sufficient to offset the interest rate differential between the two currencies. • Then, covered interest arbitrage is no longer feasible, and the equilibrium state achieved is referred to as interest rate parity (IRP).

29. Testing IRP • When IRP exists, the rate of return achieved from covered interest arbitrage should equal the rate of return available in the home country. • End-value of a \$1 investment in covered interest arbitrage = (1/S)(1+iF)F = (1/S)(1+iF)[S(1+p)] = (1+iF)(1+p) where p is the forward premium.

30. Derivation of IRP • End-value of a \$1 investment in the home country = 1 + iH • Equating the two and rearranging terms: p =(1+iH)– 1 (1+iF) i.e. forward =(1 + home interest rate) – 1 premium (1 + foreign interest rate)

31. Determining the Forward Premium Example: • Suppose 6-month ipeso = 6%, i\$ = 5%. • From the U.S. investor’s perspective, forward premium = 1.05/1.06 – 1  -.0094 • If S = \$.10/peso, then 6-month forward rate = S  (1 + p)  .10  (1 _ .0094)  \$.09906/peso

32. Determining the Forward Premium • Note that the IRP relationship can be rewritten as follows: F – S=S(1+p) – S= p =(1+iH)– 1 = (iH–iF) S S (1+iF) (1+iF) • The approximated form, p iH–iF, provides a reasonable estimate when the interest rate differential is small.

33. Interest Rate Differential (%) home interest rate – foreign interest rate 4 IRP line 2 -3 -1 1 3 Forward Discount (%) Forward Premium (%) -2 -4 Graphic Analysis of Interest Rate Parity

34. Interest Rate Differential (%) home interest rate – foreign interest rate 4 IRP line 2 -3 -1 1 3 Forward Discount (%) Forward Premium (%) -2 -4 Graphic Analysis of Interest Rate Parity Zone of potential covered interest arbitrage by foreign investors Zone of potential covered interest arbitrage by local investors

35. Test for the Existence of IRP • To test whether IRP exists, collect the actual interest rate differentials and forward premiums for various currencies. Pair up data that occur at the same point in time and that involve the same currencies, and plot the points on a graph. • IRP holds when covered interest arbitrage is not worthwhile.

36. Interpretation of IRP • When IRP exists, it does not mean that both local and foreign investors will earn the same returns. • What it means is that investors cannot use covered interest arbitrage to achieve higher returns than those achievable in their respective home countries.

37. Does IRP Hold? • Various empirical studies indicate that IRP generally holds. • While there are deviations from IRP, they are often not large enough to make covered interest arbitrage worthwhile. • This is due to the characteristics of foreign investments, including transaction costs, political risk, and differential tax laws.

38. iH – iF IRP line Zone of potential covered interest arbitrage by foreign investors Zone of potential covered interest arbitrage by local investors p Zone where covered interest arbitrage is not feasible due to transaction costs Considerations When Assessing IRP Transaction Costs

39. Considerations When Assessing IRP Political Risk • A crisis in the foreign country could cause its government to restrict any exchange of the local currency for other currencies. • Investors may also perceive a higher default risk on foreign investments. Differential Tax Laws • If tax laws vary, after-tax returns should be considered instead of before-tax returns.

40. iA Because of IRP, a forward rate will normally move in tandem with the spot rate. This correlation depends on interest rate movements, i.e. p iH–iF iU.S. Interest Rates t0 t1 t2 time SA Spot and Forward Rates FA t0 t1 t2 time Explaining Changes in Forward Premiums

41. Explaining Changes in Forward Premiums • During the 1997-98 Asian crisis, the forward rates offered to U.S. firms on some Asian currencies were substantially reduced for two reasons. • The spot rates of these currencies declined substantially during the crisis. • Their interest rates had increased as their governments attempted to discourage investors from pulling out their funds.

42. Forces of Arbitrage E (CFj,t ) = expected cash flows in currency j to be received by the U.S. parent at the end of period t E (ERj,t ) = expected exchange rate at which currency j can be converted to dollars at the end of period t k = weighted average cost of capital of the parent Impact of Arbitrage on an MNC’s Value

43. Chapter Review • International Arbitrage • Locational Arbitrage • Triangular Arbitrage • Covered Interest Arbitrage • Comparison of Arbitrage Effects

44. Chapter Review • Interest Rate Parity (IRP) • Derivation of IRP • Determining the Forward Premium • Graphic Analysis of IRP • Test for the Existence of IRP • Interpretation of IRP • Does IRP Hold? • Considerations When Assessing IRP

45. Chapter Review • Explaining Changes in Forward Premiums • Impact of Arbitrage on an MNC’s Value