3.4 Eurocurrency-eurobond arbitrage

Eurocurrency-Eurobond arbitrage depends on the level of short-term Eurocurrency interest rates and long-term Eurobond yields. As Eurobonds approach maturity, opportunities may arise to generate profit by borrowing short-term funds and using these funds to buy bonds. Suppose that there is a Eurobond denominated in currency y with a coupon rate iy, time to maturity of one year, a market price of P, and a face value of V. Let the spot and one-year forward rates be S and F respectively, and assume that the arbitrager can borrow x-denominated funds at i_x. The arbitrage operation consists of the following steps:

1. Borrowing PS units of x, which is equivalent to P units of y (the market price of the bond).

2. Buying the bond and holding it until maturity, when it pays V(1 + iy) units of y or V(1 + iy)F units of x at the current forward rate.

3. The value of the loan to be repaid (principal plus interest) is equal to PS(1 +

ix).

Arbitrage profit would therefore be

p = V(1 + i_y )F -PS(1 + i_x ) (3.19)

which means that the no-arbitrage condition is

V (1 + iy )F = PS(1 + ix ) (3.20)

¹ + ⁱx 0

V

or

Equation (3.20) can be written as P œ¹ + ⁱy Y F

_S , (3-21)

P (1 + iy )(1 + f )

¹ - ^y - (3.22)

V 1 +i

x

where f is the forward spread. If the bond is selling at par such that P = V, then equation (3.22) reduces to the CIP no-arbitrage condition, i_x - iy = f.

3.5 Arbitrage between currency futures and forward contracts

Currency futures and forward contracts represent transactions whereby the counterparties to the transaction are committed to the selling and purchase of a given amount of a particular currency some time in the future at an exchange rate determined at the present time. The difference between them is that futures contracts are standardised with respect to size and maturity date, whereas forward contracts are tailor-made, designed for specific needs.

Arbitrage between the forward and futures markets ensures that the exchange rates implicit in these contracts are equal or approximately so. Suppose that the exchange rate implicit in a futures contract for delivery in September was Fi(x/y), and the corresponding forward rate was F2(x/y). Obviously, the no-arbitrage condition is Fi(x/y) = F2(x/y). If Fi(x/y) < F2(x/y), the arbitrager would buy the futures contract on y and sell an equivalent amount of y forward to earn the difference. Again, the no-arbitrage condition would be different from the strict equality of the two rates because futures contracts involve marking to market, whereas forward contracts do not.

3.6 Real interest arbitrage

The term "real interest arbitrage" is not normally used in the literature. However, if covered interest arbitrage maintains covered interest parity and uncovered interest arbitrage maintains uncovered interest parity, then it is reasonable to put forward the idea that "real interest arbitrage" maintains real interest parity (RIP). This is so because RIP is derived either by combining other international parity conditions (UIP and ex ante PPP) or by the move­ment of funds from financial centres with low real rates of return to those with high real rates of return.

Let us see how this works. The no-arbitrage real interest parity condition is

^rx,t = ^ry,t ⁽³.²³⁾

where the real interest rates are defined as

^rx,t = ¹x,t ^{- P} x,t+1 ⁽³²⁴⁾

^ry,t= ⁱy,t ^{- P}y,t+1 ⁽³.²⁵⁾

where P is the inflation rate measured as the percentage change in the general price level. Hence the no-arbitrage condition can be written as

ⁱx,t ^-iy,t = ^Px,t+1 ^-P y,t+1 ⁽³.²⁶⁾

which says that the nominal interest rate differential is equal to the expected or subsequent inflation differential. Obviously, changes in supply and demand as a result of arbitrage will only affect the nominal interest rates, changing them to an extent that will be sufficient to equate the real interest rates. This is at least the conventional wisdom.

However, one may ask the following legitimate question: why would inves­tors whose base currency is x, investing in y and wanting to repatriate the receipts, be concerned about inflation in country y? Surely they should be concerned about inflation in country x, because it determines the purchasing power (in country x) of their return on investment in y. Moreover, they should also be more concerned about the return in terms of currency x than in terms of currency y, which means that the exchange rate factor, which is not incorpo­rated in the no-arbitrage relationship (3.26), is important and should be taken into account. This means that the no-arbitrage condition should be modified accordingly. Notice that the exact expression for the equality of real returns on both currencies is

1 + i_xt 1 + iyt

¹ + ⁱx, -⁽¹ + V⁾⁽¹ + W (3.28)

¹ + ^Px,t+1 ¹ + ^P x ,t + 1

where S_t+ ! is the percentage change in the exchange rate between t and t + 1. The left-hand side of equation (3.28) is the real return on currency x, whereas the right-hand side is the real return on y expressed in terms of currency x. Equation (3.28) can be simplified to produce

ⁱx,t ^-iy,t= ^St+1 ⁽³.²⁹⁾

which is uncovered interest parity. Now, notice that (ex ante) purchasing power parity tells us that

^Px,t+1 ^{- P} y ,t+ 1 = ^St+ 1 ⁽³.³⁰⁾

and so if we combine (3.29) and (3.30) we go back to the original condition. Thus it seems that what maintains RIP is not real interest arbitrage, in the sense that it is not a single operation that maintains the condition. Rather, the condition is maintained by two kinds of arbitrage: uncovered interest arbi­trage and intertemporal commodity arbitrage. The first kind of arbitrage maintains uncovered interest parity, whereas the second kind maintains purchasing power parity.