Question

CIRP. Jason Smith is a foreign exchange trader with Citibank. He notices the following quotes. Spot exchange rate SFr1.6627/$ Six-month forward exchange rate SFr1.6558/$ Six-month $ interest rate 3.5% per year Six-month SFr interest rate 3.0% per year a. Ignoring transaction costs, is the interest rate parity holding? b. Now assume that the forward exchange rate is not given, but that the spot forward exchange rate and two interest rates are given as above. Determine the forward exchange rate. c. Going back to the four numbers given above, what steps would be needed to make an arbitrage profit? Assuming that Jason Smith is authorized to work with $1,000,000 for this purpose, how much would the arbitrage profit be in dollars?

Answer 1

Answer:

Answer explained below

Explanation:

A.

For six months, rSFr => 1.50% and r$ => 1.75%.

Since the exchange rate is in SFr/$ terms, the appropriate expression for the interest rate parity relation is

F/S => [ (1 +  rSFr ) / ( 1 + r$) ]

then we can also say

F/S *( 1 + r$) => (1 +  rSFr )

Now Left side => F/S *( 1 + r$) => [ ( 1 + 6.558) / ( + 1.6627) ] * (1 +0.0175)

Left side => 1.0133

and Right side =>  (1 +  rSFr ) => 1.0150

Since the left and right sides are not equal, IRP is not holding.

B and C.

Since IRP is not holding, there is an arbitrage possibility.

As 1.0133 < 1.0150,

we can say that the EuroSFr quote is more than what it should be as per the quotes for the other three variables. And, we can also say that the Euro$ quote is less than what it should be as per the quotes for the other three variables. Therefore, the arbitrage strategy should be based on borrowing in the Euro$ market and lending in the SFr market. The steps are as as follows. -

Borrow $1000000 for six-months at 3.5% per year and then we will pay back

=> $1000000 * (1 + 0.0175) => $1,017,500 six months later.

Convert $1000000 to SFr at the spot rate to get SFr 1662700.

Lend SFr 1662700 for six-months at 3% per year. Will get back

=> SFr1662700 * (1 + 0.0150) => SFr 1,687,641 six months later.

Sell SFr 1687641 six months forward. The transaction will be contracted as of the current date but delivery and settlement will only take place six months later. So, sixmonths later exchange

SFr 1,687,641 for => SFr 1687641 ⁄ SFr 1.6558/$ => $1,019,230.

The arbitrage profit six months later is 1019230 - 1017500 = $1,730