Covered arbitrage with bid-offer spreads

Covered arbitrage with bid-offer spreads

To describe covered arbitrage when there are bid-offer spreads in both exchange and interest rates we have to remember that a price taker in the foreign exchange market (like our arbitrager)buys at the (higher)offer exchange rate and sells at the (lower)bid exchange rate of the market maker (the banker).A price taker in the money market borrows at the (higher)offer interest rate and lends at the (lower)bid interest rate of the market maker.

Arbitrage from the domestic currency to a foreign currency

Arbitrage in this case consists of the following steps:

1.The arbitrager borrows domestic currency funds (one unit)at the domestic offer interest rate, ia.

2.The borrowed funds are converted into the foreign currency at the spot offer rate, Sa, obtaining 1/Sa foreign currency units.This amount is invested at the foreign bid interest rate, img.

3.The foreign currency value of the invested amount at the end of the investment period is (1/Sa)(1+img).

4.This amount is reconverted into the domestic currency at the forward bid rate, Fb, to obtain (Fb/Sa)(1+img)domestic currency units.

5.The value of the loan plus interest is (1+ia)domestic currency units.

The covered margin in this case is

img

Since Fb/Sa=(1+f )/(1+m), where f is the forward spread and m is the bid-offer spread, it follows that

img

Because of the introduction of the bid-offer spreads, which are transactions costs, the no-arbitrage condition is no longer that, implying a deviation from CIP.It can be seen from Equation (5.19)and (5.20)that the covered margin is lower if we allow for the bid-offer spreads.

Arbitrage from a foreign currency to the domestic currency

Arbitrage in this case consists of the following steps:

1.The arbitrage borrows foreign currency funds (one unit)at the foreign offer interest rate, img.

2.The borrowed funds are converted into the domestic currency at the spot bid rate, Sb, obtaining Sb domestic currency units.This amount is invested at the domestic bid interest rate, ib.

3.The domestic currency value of the invested amount at the end of the investment period is Sb(1+ib).

4.This amount is reconverted into the foreign currency at the forward offer rate, Fa, to obtain (Sb/Fa)(1+ib)foreign currency units.

5.The value of the loan plus interest is (1+img)foreign currency units.

The covered margin in this case is

img

Since Sb/Fa=1/[(1+m)(1+f )], it follows that

img

Which again shows that the covered margin is lower if the bid-offer spreads are allowed for.