Question

Suppose the Mexican peso British pound exchange rate is currently at 22, and short run interest rates in the UK is 2%. Explain (and compute) what will happen to the spot peso-pound exchange rate if the future pound-peso rate remains 0.04 and the Mexican interest rates is cut by 5%.

Answer 1

Here we need to apply Interest rate parity or IRP concept as per this concept the rate of borrowing shall be same in all the countries of the world Be it you borrow from USA or UK or Mexico or India or France or Japan your interest cost should be the same. This concept also states that if the interest rate of a country is higher than its currency would fall in future as people would like to borrow from countries offering cheaper rates of interests.

Therefore suppose if 1 pound = $ 1.5 today and interest rates in usa and uk are going to be 4 % and 6 % respectively it means interest rate in uk is more so pound will fall and dollar will increase in future.

Formula to determine Forward rate under IRP is following

FR(h/f)/SR(h/f)= 1+h int. rate/1+f int.rate

Here h = home currency and f = foreign currency

So here USD is our home currency and pound is foreign so put in formula we have

FR/1.5= 1.04/1.06 = FR = 1.5*0.9811= 1.4716 USD per 1 pound as we can see since interest rates in uk were higher pound declined after 1 year.

Coming to our question here Mexican peso is home currency and pound is foreign currency.

Putting in formula we will get Interest rates in mexico for one year as UK rate is 2% per annum already given also SR of 22 and FR of 1/0.04= 25 is also given.

25/22= 1+Mexician rate/1+0.002 = Mexician rate is 1.1386-1= 13.86% per annum.

Suppose in future Mexican rate is cut by 5% means it will be 13.86-5= 8.86%

We can see it is still way more than UK rate of 2 % so Peso will continue to fall and pound will continue to rise against peso but at a lower rate now naturally as interest rate difference is not 11.86% as earlier so pound will increase but at a slower rate.

Future peso/pound rate based on IRP is

FR/22= 1+0.0886/1+0.002= FR = 22*1.0886/1.002= 23.90.

?As we can see with mexico interest falling 5% it leads to its currency appreciation or pound depreciation by over 4% from 25 to 23.90.