CH 7 International Arbitrage and Interest Rate Parity

Graphic Analysis of Interest Rate Parity -Points representing a discount: -Points representing a premium: -Points representing IRP: -Points below the IRP line: -Points above the IRP line:

-Points representing a discount: points A and B (foreign interest rate> home interest rate) -Points representing a premium: points C and D (foreign interest rate< home interest rate) -Points representing IRP: points A, B, C, D (any point on the diagonal line) -Points below the IRP line: points X and Y -Points above the IRP line: point Z

3 forms of arbitrage

1. locational arbitrage 2. Triangular arbitrage 3. Covered Interest Arbitrage

Considerations When Assessing Interest Rate Parity

1. transaction costs, 2. political risk, 3. differential tax laws

Political risk

A crisis in the foreign country could cause its government to restrict any exchange of the local currency for other currencies.

Does Interest Rate Parity Hold?

Compare the forward rate (or discount) with interest rate quotations occurring at the same time. -Due to limitations in access to data, it is difficult to obtain quotations that reflect the same point in time.

Differential Tax Laws

Covered interest arbitrage might be feasible when considering before-tax returns but not necessarily when considering after-tax returns. (occurs when tax rates in both countries differs)

Gains from triangular arbitrage

Currency transactions are conducted in the spot market to capitalize on the discrepancy in the cross exchange rate between two countries.

Derivation of Interest Rate Parity

F= S(1+p) F= forward rate n months from now

Realignment due to triangular arbitrage

Forces exchange rates back into equilibrium

Implications when determining the forward premium

If the forward premium is equal to the interest rate differential as just described, then covered interest arbitrage will not be feasible.

Interest Rate Parity

In equilibrium, the forward rate differs from the spot rate by a sufficient amount to offset the interest rate differential between two currencies.

Interpretation of Interest Rate Parity

Interest rate parity does not imply that investors from different countries will earn the same returns.

Points below the IRP line: points X and Y

Investors can engage in covered interest arbitrage and earn a higher return (beneficial) by investing in foreign currency after considering foreign interest rate and forward premium or discount. -upward pressure on spot rate of foreign currency -downward pressure on the forward rate of foreign currency

EX: as Japanese investors engage in covered interest arbitrage, the high demand to buy

Japanese yen forward will place upward pressure on the one year forward rate of the yen

How arbitrage reduces transaction costs

Locational arbitrage limits the differences in a spot exchange rate quotation across locations, while covered interest arbitrage ensures that the forward rate is properly priced. -Thus, an MNC's managers should be able to avoid excessive transaction costs.

Example of Covered Interest Arbitrage $800,000 to invest current spot rate of the pound= $1.60 90 day forward rate of pound= $1.60 90 day interest rate in US= 2% 90 day interest rate in UK= 4%

Step 1: $800,000/1.60= 500,000 pounds Step 2: Sell 520,000 (4%) pounds 90 days forward Step 3: In 90 days when deposit matures, you can fulfill the contract obligation by converting you 520,000 pounds into $832,000

Example of Triangular Arbitrage

Step 1: USD $10,000/1.6= 6,250 pounds Step 2: 6,250 pounds (x) MYR8.1= MYR50,625 Step 3: MYR50,625 (x) .20= USD$10,125 This leads to a $125 profit

Example of Triangular Arbitrage Accounting for Bid/Ask Spreads

Step 1: USD$10,000/1.61(the ask price of USD to pounds)= 6,211 pounds Step 2: 6,211 pounds (x) MYR8.1 (BANK'S bid)= MYR50,310 Step 3: MYR50,310 (X) $.20 (BANK's bid price)= $10,062 Profit of only $62 which is lower than previous example because the bid/ask is used

Transaction costs

The actual point reflecting the interest rate differential and forward rate premium must be farther from the IRP line to make covered interest arbitrage worthwhile

Forward Premiums across Maturities

The annualized interest rate differential between two countries can vary among debt maturities, and so will the annualized forward premiums.

Covered interest arbitrage by Non- U.S. Investors

The concept of covered interest arbitrage applies to any two countries for which there is a spot rate and a forward rate between their currencies as well as risk-free interest rates quoted for both currencies.

Explaining changes in the forward rate

The forward rate is indirectly affected by all the factors that can affect the spot rate (S) over time, including inflation differentials, interest rate differentials, etc. The change in the forward rate can also be due to a change in the premium.

Effect of the interest rate differential

The relationship between the forward premium (or discount) and the interest rate differential according to IRP is simplified in an approximated form:

Comparison of Arbitrage Effects

Thus, arbitrage tends to allow for a more orderly foreign exchange market.

Points above the IRP line: point Z

U.S. investors would achieve a lower return on a foreign investment than on a domestic one. -downward pressure on spot rate of foreign currency -upward pressure on the forward rate of foreign currency

Currency Quotes for Locational Arbitrage Example

You buy from the banks ask rate (their sell rate) at $1.61 an you sell the bid (their buy rate) to the ZYN bank for $1.61 which makes you only break even.

Example of Locational Arbitrage

You can buy NZ dollars from North bank at $.640 (the banks selling price) and sell to the south bank at their bid (buy price) of $.645. If you invest 10,000/.640= 15,625 * .645= 10,078 leaving you with a $78 profit.

Gains from locational arbitrage

are based on 1. the amount of money used and 2. the size of the discrepancy

International Arbitrage

capitalizing on a discrepancy in quoted prices by making a risk-less profit - arbitrage will cause prices to realign

Realignment due to covered interest arbitrage

causes market realignment -Step 2 in example (selling British pounds forward) causes a downward pressure on the 90 day forward rate. Once the rate is discounted to equal the US rate there is no longer an advantage

If the forward premium deviates substantially from the interest rate differential, then

covered interest arbitrage is possible. -In this type of arbitrage, a short-term investment in some foreign currency is covered by a forward sale of that foreign currency in the future. In this manner, the investor is not exposed to fluctuation in the foreign currency's value.

The threat of triangular arbitrage ensures that

cross exchange rates are properly set

Triangular Arbitrage

currency transactions in the spot market to capitalize on discrepancies in the cross exchange rates between two currencies

Locational arbitrage may occur if

foreign exchange quotations differ among banks. -The act of locational arbitrage should force the foreign exchange quotations of banks to become realigned, after which locational arbitrage will no longer be possible.

The threat of covered interest arbitrage ensures that

forward exchange rates are properly set. -Any discrepancy will trigger arbitrage, which should eliminate the discrepancy.

Realignment due to locational arbitrage

drives prices to adjust in different locations so as to eliminate discrepancies -EX: high demand for NZ dollars in previous example will cause a shortage and the north bank will have to raise their ask price. South Bank will be forced to lower its bid price

According to the theory of interest rate parity (IRP), the size of the forward premium (or discount) should be

equal to the interest rate differential between the two countries of concern. -If IRP holds then covered interest arbitrage is not feasible, because any interest rate advantage in the foreign country will be offset by the discount on the forward rate. -Thus, covered interest arbitrage would not generate higher returns than would be generated by a domestic investment.

How to Test Whether Interest Rate Parity Holds: The Location of the points.....

provides an indication of whether covered interest arbitrage is worthwhile

Because the forward premium of a currency (from a U.S. perspective) is influenced by the interest rate of that currency and the U.S. interest rate and because those interest rates change over time, it follows that the

forward premium changes over time. -Thus, a forward premium that is large and positive in one period, when the interest rate of that currency is relatively low, could become negative (reflecting a discount) if that interest rate rises above the U.S. level.

Covered interest arbitrage is based on the relationship between the

forward rate premium and the interest rate differential. -The size of the premium or discount exhibited by the forward rate of a currency should be about the same as the differential between the interest rates of the two countries of concern. -In general terms, the forward rate of the foreign currency will contain a discount (premium) if its interest rate is higher (lower) than the U.S. interest rate.

Part 2: Covered

hedging the position against interest rate risk

Changes in Forward Premiums over Time

illustrates the relationship between interest rate differentials and the forward premium over time, when interest rate parity holds. The forward premium must adjust to existing interest rate conditions if interest rate parity holds.

Accounting for spreads

investor must account for the effects of the spread between the bid and ask quotes and of the spread between deposit and loan rates -Example in book PG 235

How to Test Whether Interest Rate Parity Holds: For points to the right of the IRP line,

investors in the home country should consider using covered interest arbitrage, since a return higher than the home interest rate (ih) is achievable.

The threat of locational arbitrage ensures that

quoted exchange rates are similar across banks in different locations

Timing of Realignment in Covered Interest Arbitrage

may require several transactions before realignment is completed

Realignment is focused on the forward rate in covered interest arbitrage

the forward rate is likely to experience most if not all of the adjustment needed to achieve realignment -However, the spot rate could have upward pressure from step 1 of exchanging USD to pounds

How to Test Whether Interest Rate Parity Holds: Of course, as investors and firms take advantage of such opportunities,

the point will tend to move toward the IRP line -Covered interest arbitrage should continue until the interest rate parity relationship holds.

Locational arbitrage

the process of buying a currency at the location where it is priced cheap and immediately selling it at another location where it is priced higher

Part 1: interest arbitrage

the process of capitalizing on the difference between interest rates between two countries

Covered Interest Arbitrage

the process of capitalizing on the interest rate differential between two countries while covering your exchange rate risk with a forward contract

Accounting for the Bid/ Ask Spread of Triangular Arbitrage

transaction costs (bid/ask spread) can reduce or even eliminate the gains from triangular arbitrage

Triangular arbitrage is related to cross exchange rates. A cross exchange rate between two currencies is determined by the

values of these two currencies with respect to a third currency. -If the actual cross exchange rate of these two currencies differs from the rate that should exist, triangular arbitrage is possible. -The act of triangular arbitrage should force cross exchange rates to become realigned, at which time triangular arbitrage will no longer be possible.