Chapter 7 - International Arbitrage and Interest Rate Parity

Forward rate can be expressed as

(1 + p) * S

Excessive transaction costs should theoretically be avoidable due to

1. Locational arbitrage limiting differences in spot exchange rate quotations across locations 2. Covered interest arbitrage ensuring that forward rate is properly priced

Steps to covered interest arbitrage

1. Make short-term investment in some foreign currency 2. Make forward sale of that foreign currency in the future --> not exposed to fluctuation in the foreign currency's value

Arbitrage

At the same time

The size of the premium (or discount) in forward exchange rate should, under IRP, be

about the same as the differential between the interest rates of the countries of concern

Realignment occurs as a result of

arbitrage (capitalizing on a discrepancy in quoted prices by making a riskless profit)

Covered interest arbitrage is the process of

capitalizing on the difference in interest rates between two countries while covering your exchange rate risk with a forward contract (for exchange rates) *Based on the relationship between the forward rate premium and the interest rate differential

Triangular arbitrage is related to

cross-exchange rates

The threat of covered interest arbitrage ensures that

forward exchange rates are properly set

The forward rate of a country will contain a discount if its interest rate is

higher than the counter country's interest rate (under IRP)

IRP does NOT imply that

investors in different countries will earn the same returns *It rather reflects a comparison between foreign versus domestic investment in risk-free interest-bearing securities by a particular investor; if IRP holds, investors cannot use covered interest arbitrage to earn higher returns on a foreign investment than they could earn on a domestic investment

For all points to the left of the IRP line,

investors in the FOREIGN country could use covered interest arbitrage

For all points to the right of the IRP line,

investors in the HOME country could use covered interest arbitrage to earn a return higher than the home interest rate

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

its interest rate rises above the interest rate of the other currency

Arbitrage in covered interest arbitrage suggests that

one can guarantee a return on funds that exceeds the returns that could be achieved domestically

Generalized formula for IRP

p = F - S / S = ih - if p = forward premium F = forward rate S = spot rate ih = domestic interest if = foreign interest

Transaction costs/large bid-ask spreads lessen or remove

profits earned in triangular arbitrage

The yield curve describes the relationship for a given moment in time between

the annualized yield of risk-free debt and the time to maturity *Upward slope = annualized interest rate is higher for longer terms to maturity

When the quoted cross-exchange rate is more than the real cross exchange rate (real being obtained from the formula),

the bank is exchanging too many units of a currency for another and asking for too many units of that currency in exchange for the other currency

The IRP line is

the diagonal line on which points in line with IRP lie *Covered interest arbitrage is not possible under conditions represented by points along the IRP line

The forward premium changes over time given that

the forward premium of a currency is influenced by both the interest rate of that currency and the interest rate of the other currency

The forward rate of a currency for a specified future date is determined by

the interaction of demand for the contract (forward purchases) versus the supply (forward sales)

The cross-exchange rate between two currencies is determined by

the values of these two currencies with respect to a third currency *Simply divide their rates in the third currency by one another to get their rate in each other's currency

If discrepancies occur in the FX market, with quoted prices of currencies varying from what their market prices should be,

then certain market forces will realign the rates

Unlike locational and triangular arbitrage, covered interest arbitrage

ties up funds *Therefore the strategy is not advantageous if the return is equal to or less than the return that could be earned on a domestic deposit

When the forward rate is less than the spot rate

we say that the forward rate exhibits a discount

When the forward rate is more than the spot rate

we say that the forward rate exhibits a premium

For all situations in which the foreign interest rate is higher than the home interest rate, the forward rate should exhibit a

DISCOUNT approximately equal to that difference

Explain in general terms how various forms of arbitrage can remove any discrepancies in the pricing of currencies

If there is a discrepancy in the pricing of a currency, one may capitalize on it by using the various forms of arbitrage described in the chapter. As arbitrage occurs, the exchange rates will be pushed toward their appropriate levels because arbitrageurs will buy an underpriced currency in the FX market (and increase in demand for currency places upward pressure on its value) and will sell an overpriced currency (an increase in the supply of currency for sale places downward pressure on its value).

The threat of triangular arbitrage ensures that

cross exchange rates are properly set

Locational arbitrage is relevant because it explains why

exchange rate quotations amongst banks around the world will seldom differ from one another (aided by technology)

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 (therefore covered interest arbitrage would not generate higher returns than would be generated by a domestic investment)

The forward exchange rate is usually the source of rebalancing in cases of covered interest arbitrage because

it is less liquid than the spot exchange rate and therefore more sensitive to shifts in supply and demand conditions

The threat of locational arbitrage ensures that

quoted exchange rates are similar across banks at different locations

The larger the degree by which a foreign interest rate exceeds the home interest rate,

the larger will be the forward discount of the foreign currency specified by the IRP formula *If the foreign interest rate is less than the home interest rate, there would be a forward premium

The Theory of Interest Rate Parity states that

the size of the forward premium/discount should be equal to the interest rate differential between the two countries of concern p = [ (1+i(h)) / (1+i(f)) ] - 1

Assume that the British pound's one-year forward rate exhibits a discount. Assume that IRP continually exists. Explain how the discount on the British pound's one-year forward discount would change if British one-year interest rates rose by 3 percentage points while U.S. one-year interest rates rose by 2 percentage points.

The one-year forward rate discount on pounds would become more pronounced (by about 1 percentage point more than before) because the spread between the British interest rates and U.S. interest rates would increase (with British increasing more than U.S.)

The following should be considered when assessing interest rate parity

1. Transaction costs *When present, the point that indicates that actual interest rate differential and forward rate premium must be farther from the IRP line to make covered interest arbitrage worthwhile 2. Political risk *Risky because a government could institute a ban on exchanging currencies, thereby making forward contract inaccessible 3. Differential tax laws

Locational arbitrage may occur if

FX quotations differ among banks

Triangular arbitrage strategy

1. Buy overpriced currency with counter currency 2. Use overpriced currency to buy base currency in cross-exchange rate (i.e. comparison to $ for GBP and MYR with MYR overpriced; (1) buy GPB with $, (2) buy MYR with GBP, (3) buy $ with MYR)

Covered interest arbitrage is composed of two parts

1. "interest arbitrage" (referring to the process of capitalizing on the difference between interest rates between two countries) 2. "covered" (referring to hedging position against exchange rate risk)

The gains from locational arbitrage are based on two factors

1. Amount of money that is used to capitalize on exchange rate discrepancy 2. Size of exchange rate discrepancy

Steps to locational arbitrage

1. Buy currency at location where it is priced cheap 2. Immediately sell the currency at location where it is priced high *Break even unless bid price of one bank is higher than ask price of another bank

Speculation

Over time

For all situations in which the foreign interest rate is less than the home interest rate, the forward rate should exhibit a

PREMIUM approximately equal to that difference