Question

BL lives in the US and has $800,000 surplus funds that he wants to invest for one year in any currency. He receives the following quotes from a commercial bank:

Spot rate= 1 British Pound: $50-55

One-year forward rate= 1 British Pound: $58-64

One-year US interest rate= 6%

One year UK interest rate= 1%

(i) With supporting calculations, advise BL whether covered interest arbitrage is worthwhile.

(ii) Would your advice differ, if transaction costs in respect of the covered interest arbitrage amount to $5,000?

(iii) Using the interest rate parity model, calculate the interest differential between the two countries.

Answer 1

Surplus funds: $ 800000
Spot rate= 1 British Pound: $50-55
One-year forward rate= 1 British Pound: $58-64
One-year US interest rate= 6%
One year UK interest rate= 1%

(i)
If BL invest money in US itself and doesnt carry out arbitrage then inflow after 1 year will be :

Invest $ in US market at 6% for 1 year:

800000*(1.06) = $848000

However if covered interest arbitrage is carried out then following will be the inflow:

Sell $800000 spot to get pound @ 55

800000/55 = Pounds 14545.4545454

Invest this amount in UK market at 1% for 1 year

Pounds 14545.4545454 * (1.01) = Pounds 14690.90909090

Convert pounds into $ at forward rate of 58

Pounds 14690.90909090* 58 = $852072.72727272

Since $852072.72727272 > $848000 , it is clear that covered interest arbitrage is worthwhile

(ii)
If transaction costs in respect of the covered interest arbitrage amounts to $5,000 then our advice will differ as
$852072.72727272 - $5000 is not > $848000
and hence investing in US market will only be beneficial to BL.

(iii)
Covered interest rate parity is the relationship between spot rate, forward rate, and interest rates. According to this parity whichever currency has a lower ineterest rate will be at a forward premium wil be equal to the

interest rate difference/ interest rate factor of that currency

F/S = (1+rA)/ (1+rB) ie qoatation is in A/B

((58+64)/2 - (50+55)/2 ) * 1.01 = 8.585

Hence interest rate differential between 2 countries shall be 8.585% as per interest rate parrity model.