International Arbitrage Chapter 6 International Arbitrage

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

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.

Types of Arbitrage Locational arbitrage Triangular arbitrage Covered interest arbitrage

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.

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

Example 2 USD/PKR 86.75 /95 * If you trade $100,000 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 1 Calculations Profit : Rs 0.50 / $ Bank A USD / PKR 86.75 /95 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 Bank A Bank B

Problem Beal Bank Yardley 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

Triangular Arbitrage

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

Cross Exchange Rate Currency A into currency B 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

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

Triangular Arbitrage USD GBP PKR Value of Rs in $ Value of £ in $

Suppose Example 4 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

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

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

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

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

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.

Covered interest arbitrage tends to force a relationship between forward rate premiums and interest rate differentials.

Suppose Example 4 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

Investment in UK Investment in US 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

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

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

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

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.

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).

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.

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)

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

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.

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

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

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.

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.

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.

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

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.

Explaining Changes in Forward Premiums 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 t0 t2 t1 Interest Rates iA iU.S. time Forward Rates Spot and SA FA

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.

Impact of Arbitrage on an MNC’s Value 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 Forces of Arbitrage

Chapter Review International Arbitrage Locational Arbitrage Triangular Arbitrage Covered Interest Arbitrage Comparison of Arbitrage Effects

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

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