Question

Consider the following information:

r _US = 5 5%

r _UK = 5 7%

E₀ = \(2 per pound

F₀ = \)1.97/£ (one-year delivery)

where the interest rates are annual yields on U.S. or U.K. bills. Given this information:

a. Where would you lend?

b. Where would you borrow?

c. How could you arbitrage?

Short answer

a. UK

b. US

c. Total cash flow 0.079

Step-by-step solution

Given information

r _US = 5 5%

r _UK = 5 7%

E₀ = $2 per pound

F₀ = $1.97/£ (one-year delivery)

Calculation of the place where to lend ‘a’

Lending in UK as the rate of return is greater.

Calculation of the place where to buy ‘b’

Borrowing in US as the lending rate is smaller.

Calculation of how to arbitrage ‘c’

As per interest rate parity relationship: F₀ = E₀ x 1 + r_f(US) / 1 + r_f(UK)

= 2.00 x 1.05 / 1.07

= 1.9626

Hence to create an arbitrage profit, let’s use the following strategy:

Action	Initial Cash flow	Cash flow at Time T
Enter a contract to sell￡1.07 at a future price F0 =$1.97	0	1.07 x (1.97 - E1)
Borrow $2.00 in the US	2.0	- 2.00 x 1.05
Convert the borrowed dollars to pound and lend it to the UK at 7% interest rate	-2.0	1.07 x E1
Total	0	0.079