Question

Interest rates in India are 5.25% p.a. and in Brazil they are currently at 2.5% p.a. The BRL/INR spot rate is 13.37.

(a) Calculate the theoretical three-year forward rate of the BRL implied by Interest Rate Parity.

(b) Now assume the actual two-year forward rate is BRL/INR 15.20. What, if any, is the percentage return from engaging in Covered Interest Arbitrage? Assume a transaction cost of 0.3% in the spot and the forward market. (Calculate the result as a percentage of your initial borrowing, accurate to 4 decimal places, making sure to include any opportunity cost in your calculations)

Answer 1

Solution:

Let assemble the information given by question

Spot Rate BRL/INR = 13.37

Interest rate in India 5.25%

Interest Rate in Brazil 2.50%

What does spot rate BRL/INR = 13.37 means it says that 1 BRL = 13.37 INR, it means we will get 13.37 INR in exchange of 1 BRL

Question has asked us to calculate the three year forward rate of the BRL by implied Interest rate parity (IRP)

Let first understand what does mean interest rate parity (IRP)

IRP is the fundamental equation that governs the relationship between interest rates and currency exchange rates. The basic premise of IRP is that hedged returns from investing in different currencies should be the same, regardless of their interest rates.

IRP is the concept of no-arbitrage in the foreign exchange markets (the simultaneous purchase and sale of an asset to profit from a difference in the price). Investors cannot lock in the current exchange rate in one currency for a lower price and then purchase another currency from a country offering a higher interest rate

Formula to calculate forward rate is

Fo = So*[(1+Ia)^t]/[(1+Ic)^t], where

Fo is the forward rate

So is the spot rate

Ia is the interest rate in country a

Ic is the interest rate in country c

t is the no of year

Let put the given information in the formula, we gets

Fo = 13.37*[(1+0.0525)^3/[(1+0.025)^3]

Fo = 13.37*1.1659/1.0769

Fo = 13.37*1.0826

Fo = 14.4750

Three year Forward rate of BRL to INR is 14.4750

Part (2)

Now question has given the two year forward rate of BRL/INR is 15.20, it means we will get 15.20 INR in exchange of 1 BRL

Transaction cost is 0.3% in spot/forward market

Interest rate in India is 5.25%

Interest rate in Brazil is 2.50%

Spot Rate is 13.37

As per the given information it is been very clear that rupee is weaken in future from today because we are getting more INR in exchange of 1 BRL i.e. 15.20 INR in future in comparison to today i.e. 13.37 INR or in other words we can say that BRL is appreciating in future rate, in such a case where we know which currency is appreciating and which currency is weakening in that case we have to borrow in that country whose currency is weakening in future and invest in that country whose currency is appreciating in future

Let borrow Rs.1,00,000.00 in India and convert that into BRL by using spot rate and then invest that amount in Brazil (we may borrow any amount to show the profitability through arbitrage process)

Borrowed Fund = Rs.1,00,000.00

Rate of Interest on Borrowed Fund 5.25%

Convert INR into BRL by using spot rate @13.37 with transaction cost of 0.3%

BRL = (INR/Spot Rate)*(1-Transaction cost)

= (100000/13.37)*(1-0.03)

= 7479.4316*0.997

=7456.9932 BRL

Now Invest these BRL in Brazil @2.5%

Amount of Investment grows in two Year as follows:

= Invested Fund(1+R)^t

=7456.9932(1+0.025)^2

=7456.9932*1.050625

=7834.5035 BRL

Now after two year of Investment, we will convert this fund again into INR and repay the borrowed money with accumulated Interest, which we have borrowed earlier

Let calculate the amount payable in India with accumulated Interest

Borrowed money (BM) = 100000

Interest Rate (R) = 5.25%

Time (t) = 2 Year

Amount Payable = BM*(1+R)^t

=100000*(1+0.0525)^2

=100000*1.1076

=110760 INR

Now convert the available Invested BRL into INR with the available actual forward rate with transaction cost @0.30%, by using this formula and get the value of Amount invested in INR

INR = (BRL*Forward rate)*(1-Transaction cost)

= 7834.5035*15.20*(1-0.03)

=119084.4532*0.997

=118727.1998

Now we have both the figure of amount payable and amount invested in INR, now let net off the both figure and get the profit earned from the arbitrage process

Profit = Amount Invested – Amount Payable

= 118727.1998 – 110760

= 7967.1998 or 7.9672% of the Borrowed fund

We have earned a profit of 7.9672 % by using arbitrage process, without putting own fund in the market, this is the beauty of this process, which help arbitrager to earn the money by using this simple technique method without investing any money from their pocket.