• PAGE ONE
• INDEX
• HOME

Interest rate parity

L. Muralidharan

THERE are many theories on what influences the forward rate (premium/discount). It is believed that the interest rates of two countries influences the forward rate and swap points. Interest rate parity illustrates why a particular currency might be at a forward discount/premium. The currency of one country with a lower interest rate should be at a forward premium in terms of the currency of a country with higher interest rates and vice versa.

A firm should be indifferent about investing at home or investing abroad if the home interest rate equals the foreign interest rate plus the annualised forward exchange premium/discount on the foreign currency.

Similarly the firm should invest at home when the domestic interest rate exceeds the sum of the foreign interest rate plus the foreign exchange premium/discount, and it should invest abroad when the domestic rate is less than this sum. It is understood t hat the mere comparison of interest is not sufficient. Hence one should compare the interest rates differentials with the forward premium/discount rates to find out where the investments should be made for gain. The chances are many for speculators cashi ng in on interest rate differentials. This is technically referred to as covered interest arbitrage.

This discussion brings out a rule for arbitrage as follows:

If the interest rate differential (IRD) is greater than the premium/discount (annualised) rates, then invest in the currency bearing a higher rate of interest and the converse is also true.

If the interest rate differential (IRD) is lower than the premium/discount (annualised) rates, then invest in the currency bearing a lower rate of interest.

This brings out a second rule for arbitrage as follows:

Domestic rate Foreign rate +or Forward Premium/Discount rates invest in foreign shores.

Domestic rate > Foreign rate +ors Forward Premium/Discount rates invest in domestic shores.

*Consider the following exchange rates:

Canadian $1.5140 per US$ (Spot)

Canadian $1.5552 per US$ (6 months forward)

6 months interest rate: C$ 10 per cent pa

US$ 6 per cent pa

Work out the possibilities of arbitrage gain. Assume 1,000 units of currency.

*Based on the First Rule:

Since IRD 4 per cent (10 per cent-6 per cent) l the forward premium rate annualised 5.44 per cent, investment shall be made in the US (having lower rate of interest 610).

Based on the Second Rule:

Domestic center is Canada where the rate is 10 per cent US interest rate of 6 per cent + 5.44 per cent towards Forward Premium rate. Investment should be made in the US.

An illustration

Step 1: Borrow C$ 1,000 @ 10 per cent pa for six months term and convert at spot rate into US$660.50.

Step 2: Invest in US$660.50 @ 6 per cent pa for six months getting a maturity value of US$680.32 and revert to C$ at the forward rate. This would realise Canadian $1,058.03.

Step 3: Pay the loan borrowed in C$1,050 and gain C$8.03.

*Consider the following exchange rates:

FFr / $7.4675 (Spot)

FFr / $7.3706 (6 months forward)

Six months interest rate: FFr 8 per cent pa

$11 per cent pa

Work out the possibilities of arbitrage gain. Assume 1,000 units of currency.

*Based on the First Rule:

Since IRD 3 per cent (11-8 per cent) L the forward discount rate annualised 2.6 per cent, investment shall be made in the US (having higher interest rate 11>8)

Based on the Second Rule:

Domestic Center is France where the rate of interest is 8 per cent the US interest rate of 11 per cent - 2.6 per cent Forward Discount rate. The investment should be made in the US.

An illustration

Step 1: Borrow FFr 1,000 @ 8 per cent pa for six months term and convert at spot rate into US$ 133.91.

Step 2: Invest in US$133.91 @ 11 pa for six months, getting a maturity value of US$141.28 and revert to FFr at the forward rate. This would realise FFr 1,041.32.

Step 3: Pay the loan borrowed in FFr 1,040 and gain FFr 1.32.

Purchasing power parity

Forward rates are also believed to be influenced by the law of one price. This law says that a commodity will be priced the same regardless of the country in which it is purchased/sold. Based on the purchasing power of the consumers in the countries, the exchange rates are influenced. The purchasing power is once again dependent on the inflation rate plaguing the countries.

*Suppose over a period of two years, the US price index moves from 110 to 135 and the Japanese price index moves from 105 to 112. The spot exchange rate is $1=124.1545. What would be spot rate after two years from now? The answer is in Table 5.

*A customer in Germany buys an item for 335 DM. He makes enquiry in France for that item by the same time. The quotation is FFr 100. What is the spot rate of FFr in Germany?

Expectation theory

Forward rate and expected future spot rate are two different things to be understood. Forward rate is the rate negotiated for the delivery to be made/taken on a future date for a present transaction. Future spot rate is the actual rate prevailing on the agreed future date. An equilibrium is achieved only when the forward (premium/discount) points equal to the expected change in the future spot rate. However, it generally overshoots one way or the other.

Fisher's Inflation and Real Interest Rate Theory

Relative inflation rates also affect interest rates. The interest rate of one country is largely dependent on the inflation rates. Hence countries suffering higher inflation would experience higher interest rates and vice-versa is also true. High inflati on and high interest rate would add fuel to the fire, which in turn depreciates its currency against stronger foreign currency over time. If two countries experience the same, inflation rates would experience the same interest rates. This, in union with the Fisher effect, would mean that the difference in the money rate of interest would be equal to the expected difference in inflation rates.

AThe expected annual inflation in India is 5 per cent. The expected inflation for the US is 3.5 per cent. Estimate the expected one-year future spot rate, when the spot rate is Rs 46.62=$1. *Expected spot rate = (1 + inflation rate in India) / (1 + infla tion rate in the US) * Spot rate

=(1+0.05) / (1+0.035) * 46.62 = Rs 47.30

(Concluded)