Question

You see the following quotes: St = $1.2050/£, Ft+6 = $1.2100/£, i£ = 4%, and i$ = 3%.

(a) Do these rates offer covered interest arbitrage opportunity?

(b) If yes, which way the arbitrage capital move? Calculate the arbitrage profit.

Answer 1

Before we proceed let us discuss about interest rate arbitrage theory -

Every country will not have the same level of interest rate one country will have a lower rate and other will have a higher rate . Hence there exits an arbitrage opportunity by investing in high interest giving countries and borrowing from the low interest countries . This is offset wth the help of change in exchange fluctuation between both the currencies.

A) According to IRP theory.

The Formula for IRP is where A is the price currency and B is the base currency

F = S*(1+ia)/(1+ib)

F = Forward rate

S = Spot Rate

ia = Interest in price currency country

ib = Interest in base currency country

Given the interest rate per year let us calculate the 6 months interest since we were given the forward rate for 6 months.

i£ = 4% and i$ = 3%

hence 6 months rate will be i£ = 2% and i$ = 1.5%

Hence he forward rate as per the IRP theory will be F = (1.2050 * 1.015)/1.02 = 1.99093

But in the market the spot rate turns to be 1.21

Hence there exists an covered arbitrage opportunity

B) For making arbitrage we have to borrow in the country in which we have low interest rate and invest in the country in which we have high interest rate

Accordingly capital will be borrowed in $ and invest in £

Let us make arbitrage will 100$

we will borrow 100$

After 6 months we have to pay 100 + 1.5 = 101.5$

We will Invest this 100$ in pounds

we will get 100/1.2050 = 82.98755 pounds

Now we will invest this amount we get 82.98755 + 82.98755 * 0.02 = 84.6473

Let us convert this into dollar with given spot rate after 6 months

84.6473 * 1.21 = 102.4232

We have to pay 101.5 and we got 102.4232

That means we can make profit of 0.92323$ using $100 as the arbitrage amount.