Question

The spot exchange rate for the British pound is $1.2576. The U.S. interest rate is 0.25 percent, and the British interest rate is 0.50 percent. A futures contract on the exchange rate for the British pound expires in 110 days. (a) Find the appropriate futures price. [3M] (b) Find the futures price under the assumption of continuous compounding. [3M] (c) Suppose the actual futures price is $1.3250. Is the future contract mispriced? If yes, how could an arbitrageur take advantage of the mispricing? Use the price obtained from (a).

Answer 1

Answer to the question:

Given: Spot rates for British pound = $ 1.2576 per pound

Interest rate in US = 0.25 % p.a. i.e. .0025

British Interest rate is = 0.50 % p.a. i.e. .005

futures contract on the exchange rate for the British pound expires in 110 days, therefore we have to calculate 110 days forward rate

a) For calculating the forward rate (future price) we have use Interest rate parity theory (IRPT)

As per IPRP, Forward rate = 1 + Interest rate in $ * period

                      Spot Rate         1 + Interest rate in £ * period  

Therefore 110 days Forward rate i.e. X is

                                X            = 1 + (0.0025*110/360 days)

                             $1.2576        1 + (0.005*110/365 days)

After solving the above equation we get that the value of X = $ 1.2566 per £

b) Calculation of forward rate (future price), if interest rate is continuously compounding

Forward rate = 1 + Interest rate in $ * period

           Spot Rate        1+Interest rate in £ * period

Therefore 110 days Forward rate if interest is continuously compounded i.e. X is =                      X            = 1 + (e.25)*110/360 days

                             $1.2576        1 + (e.50)*110/365 days

=                              X            = 1 + 0.00250344*110/360 days

                             $1.2576        1 + 0.00501315*110/365 days

After solving the above equation we get that the value of X = $ 1.256637 per £

c) Now if actual future price is $1.3250 per £,

Then we can say that future contract price is mispriced.

Since in the given case, future price is mispriced the investor can get the advantage by investing in that currency whose interest rate is lower. i.e.

An investor can get the advantage by investing in US $.