Question

The current spot price of the British Pound in USD is USD 1.25. The USD risk-free rate is 2% while the British Pound risk-free rate is 3% for all maturities. Both rates are annual and continuously compounded.

1. a) Calculate the futures price of the British Pound in USD for delivery in six months.

2. b) Given the same spot rate and the same British Pound risk-free rate, calculate the

   implied annual risk-free rate in USD if the price of the equity futures contract in a)

   is 1.245.

3. c) How would an investor construct a portfolio to earn this rate of return?

Answer 1

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A. Interest rate parity:

As per Interest rate parity the difference in spot fate and forward rate exits due to differences in interest rate between two countries.

F/S = (e^ra)/(e^rb)
F= forward rate
S = spot rate. 1.25
ra = interest rate of price currency. 1% (1% for six months)
rb= interest rate of base currency. 1.5% (1.5% for six months)

F/1.25 = (1.01005)/(1.015113)

F= 1.24376

Future price is 1.244

B.

F/S = (e^ra)/(e^rb)
F= forward rate 1.245
S = spot rate. 1.25
ra = interest rate of price currency.
rb= interest rate of base currency. 1.5% (1.5% for six months)

1.245/1.25 = (e^ra)/(1.015113)

Ra= 1.099%

Implied Annual rate in US:
=1.099% *2
=2.198%
= 2.2% (approx)

C. As actual rate(2%) is less than derived rate(2.2%).

He can earn it by
Step 1.borrowing in the USA
2. Convert spot into the pound.
3. Invest in the pound.
4. Sell forward the invested amount.