# Foreign Exchange Problem Set

PPP, IRP, Foreign Exchange Problem Set

Question 1:

The formula for interest parity is:

i_\$ – i_fc = (F-E)/E

Or that the interest rate differential between two countries is equal to the foreign exchange premium or discount.   We want to explore how this relationship can be used to exploit arbitrage opportunities? Before we explore this question in more detail, please tackle the following problem:

Say i_US = 15%

i_UK = 10%

The current spot rate is \$2/L

What is the implied forward rate? What if the value is different than this?

Question 2:

The formula for absolute purchasing power parity sets the domestic price of a good (in \$) equal to the spot exchange rate (\$/FC) multiplied by the foreign price of a good (in FC).  For example, if the exchange rate is \$2/L and the foreign price of a t-shirt is L5, then what should the domestic price sell for?  What if the value is different than this?

Question 3:

Now, ignore the bid ask spread and assume that we can either buy or sell at one price.  Also, suppose we are quoted to following exchange rates:

Frankfurt £/SF = 0.2

New York \$/SF = 0.40

London \$/£ = 1.90

How can astute trades profit from the distorted exchange rates?  How much money would you make if you started with \$1,900,000?

Solution

i_US – i_UK = (F-E)/E

(15%-10%) = (F-2)/2

5% x 2 +2 = F

F =\$ 2.10/L

Domestic price of a good (in \$) = Spot exchange rate (\$/FC) x Foreign price of a good (in FC)

Domestic price of a good (in \$) = (\$2 /L) x (L5)= \$ 10

Given London \$/£ = 1.90

However derived \$/£ = (0.40/0.20) = 2

Since there is a difference, arbitrage opportunity exists

Transactions:

£ purchased from \$1,900,000 = \$1,900,000/1.9 = £1000,000.

SF which could be bought from £1000,000 = (1/0.2 ) x 1000,000 = 5,000,000

Dollars which can be bought from SF 5,000,000 = 0.40 x 5,000,000 = \$2,000,000

Total profit which could be made is \$2,000,000 – \$1,900,000 = \$100,000