Question

James Clark is a foreign exchange trader with Citibank. He notices the following quotes. __________________________________________________________________________________________________

Spot exchange rate USD1.2051/SFr

Six-month forward exchange rate USD1.1922/SFr

Six-month $ interest rate 8% per year

Six-month SFr interest rate 10% per year

___________________________________________________________________________________________________

Is there an arbitrage opportunity? If yes, determine the arbitrage profit in Swiss Francs. Assume that James Clark is authorized to work with $1,000,000. Input your answer without any currency information.

Answer 1

We know that as per Interest rate parity theory any change in the interest rate between two countries will be setoff by the change in foreign exchange rate

Accordingly,As per IRP

F = S*(1+ia)/(1+ib)

Where ia and ib are the interest rates in both the countries F and S are the spot and forward rates.

Accordingly, Given Quotations were USD / SFr = 1.2051

ia = 8/2 = 4% per 6 months

ib = 10/2 = 5% per 6 months

Now as per IRP the forward rate will be F = 1.2051 * (1.04/1.05) = 1.193623

But it is given the forward rate is 1.1922 which is lower than the rate calculated as per IRP theory . That means when we are converting the amount earned in SFr to USD we are getting lower than the amount that we should get as per IRP theory

This can be better understood from below

Given $1,000,000

We will borrow $1,000,000 at a rate of 4% per 6 months

After 6 months we will end up paying $1,000,000 + $1,000,000 * 0.04

$1040000

Amounnt of SFr required to repay = 1040000/1.1922 = 872336.9

We will invest the $1,000,000 amount in Sfr

Amount invested will be $1,000,000/1.2051 = 829806.655

After 6 months we will get 829806.655 + 829806.655 * 5%

= 871296.988 SFr

It Can be seen that we are unable to make arbitrage profit . This is because The rate calculated as per IRP theory is greater than the actual forward rate