Foreign Exchange Arithmetic: JAIIB/DBF Paper 2 (Module A) Unit 5

Foreign Exchange Arithmetic: Jaiib /DBF Paper 2 (Module A) Unit 5

Dear bankers,

As we all know that  is Foreign Exchange Arithmetic for JAIIB Exam. JAIIB exam conducted twice in a year. So, here we are providing the Foreign Exchange Arithmetic (Unit-5), Business Mathematics and Finance (Module A), Accounting Finance for Bankers-Paper 2.

♦Foreign Exchange

Foreign Exchange is the trading of one currency for another. For example, one can swap the U.S. dollar for the Indian Rupees. Foreign exchange transactions can take place on the foreign exchange market, also known as the Forex Market.

Fundamentals of Foreign Exchange

There are three fundamental aspects of this general mechanism of foreign exchange.

  • Almost every country has its own currency (legal tender, distinctive unit of account) and the useful possession of the currency, can normally be had only in that country, in which it passes.
  • The exchange from one currency for another is, mostly, put though by the banks by means of bookkeeping entries carried out in the two centres concerned.
  • Almost all exchanges of one currency for another are affected with the help of credit instruments.

Indian Forex Market

  • The exchange rate movements in the Indian forex market do not necessarily follow the international trend, particularly in the short run. The main reason for this is the restriction on the free flow of capital into or out of the country. Prior to the method ‘Liberalised Exchange Rate Management System’ (LERMS) the Reserve Bank fixed the buying and selling rates and the market would remain within the ceiling and the floor, thus fixed by the Reserve Bank. However, at present, the forces of demand and supply in the local Interbank market derive the Exchange rate.

Direct and Indirect Quote

  • The quote is direct when the price of one unit of foreign currency is expressed in terms of the domestic currency.
  • The quote is indirect when the price of one unit of domestic currency is expressed in terms of Foreign currency.
  • Since the US dollar (USD) is the most dominant currency, usually, the exchange rates are expressed against the US dollar. However, the exchange rates can also be quoted against other countries’ currencies, which is called as cross currency.
  • Now, a lower exchange rate in a direct quote implies that the domestic currency is appreciating in value. Whereas, a lower exchange rate in an indirect quote indicates that the domestic currency is depreciating in value as it is worth a smaller amount of foreign currency.

♦Some Basic Exchange Rate Arithmetic

Cross Rate

  • If a person wants to remit Euros from India, and as a banker, and for argument sake, rupees/ Euros are not normally quoted and therefore, what we have to do is first buy dollars against the rupees and the same dollars will be disposed off overseas to acquire the Euros.
  • If a rate in Mumbai market are US 1 Dollar- Rs 60.8450/545 and rates in London market are US 1 Dollar=Euros 0.7587 we will gets US 1 dollar for Rs 60.8545 and for one Us dollar we will get Euro 0.7587, thus we can form a sort of chain rule as under;

How many Rs.= 1 Euro

If 0.7587 Euro= US 1 dollar

Therefore, 1 Euro= Rs. 60.8545/0.7587

Or 1 Euro= Rs. 80.21

If an export customer has a bill for 100000 pound, the bank has purchase the Pound from him and give an equivalent amount in rupees to the customer. Presuming the inter-bank market quotations for spot delivery are as follows:

US 1 dollar= Rs 60.8450/545

The London market is quoting cable (STG/DLR) as

1 pound= US 1.9720/40 Dollar

The bank has to sell pound in the London market at US 1.9720, ie. The market’s buying rate for Pound 1. The US dollars so obtained have to be disposed off in the local inter-bank market at US 1 dollar= Rs 60.8450 (market’s buying rate) for US dollar.

By chain rule, we get:

Pound 1= 1.9720*60.8450

= Rs 119.9863

Chain Rule

Calculation of the cross rate is based on common sense approach. However, it can be reduced to a rule known as the chain rule with similar steps.

Value Date

The value date is a date on which the exchange of currencies actually takes place. Based on this concept, we have the following types of exchange rates.

  • Cash/ready: it is the rate when an exchange of currencies takes place on the date of the deal.
  • TOM: When the exchange of currencies takes place on the place on the next working day, i.e, tomorrow it is called the TOM rate.
  • Forward Rate: If the exchange of currencies takes place after period of spot date, it is called the forward rate. Forward rates generally are expressed by indicating a premium/ discount for the forward period.
  • Premium: When a currency is costlier in forward or say, for a future value date, it is said to be at a premium. In the case of the direct method of quotations, the premium is added to both the selling and buying rate.
  • Discount: If currency is cheaper in the forward of for a future value date, it is said to be at a discount. In the case of a direct quotation, the discount is (deducted) subtracted from both the rates, i.e buying and selling rates.

♦Forward Exchange Rates

  • The forward exchange rate (also referred to as forward rate or forward price) is the exchange rate at which a bank agrees to exchange one currency for another at a future date when it enters into a forward contract with an investor.

Forward Rate

The Exchange rate for settlement on a date beyond the spot is naturally different and the same is called the forward rate.

Forward rate has two components:

  • Spot Rate
  • Forward point reflecting the interest rate differentials adjustment for different settlement dates.

(i)Forward Point

Let us suppose that spot rate of US$/Euro is

Spot     Euro 1= US$ 1.3180

The exchange rate three months forward is

3 months       Euro 1= US $1.3330

The difference of 150 points referred to is the forward point

The following factors determine the forward point:

  • Supply and demand for the currency for the settlement date. If there are more buyers for a particular date then sellers, the forward point will be different from the situation if there were more sellers than buyers for that particular settlement date.
  • Market view, i.e. expectations, about the future and developments likely to take place in interest rates and foreign exchange.
  • The interest rate differential between the countries. For the period in question, whose currencies are being exchanged.

Calculating forward points

We can the approximate forward points for a given forward period with the help of the following information:

Spot exchange rate= 15000

Interest rate differential= 3% per annum

Forward period= 90 days

No. of days in a year (360 or 365)= 365 days

The formula is as

Spot rate ×Interest rate differential ×Forward period/100×No. of days in the year

1500×3×90/100×360= 0.01125

Forward differential, is also known as the “Swap Rate”. Three months forward rate for a US$/ Euro can be calculated by adjusting spot rate with the forward differential.

Interest differential from forward points:

The formula for calculating the interest rate differential from the forward point is as under:

Interest rate differential = Forward points ×No. of days in the year ×100/ Spot rate× Forward period

Continuing the above example,  we have

=0.01125×360×100/1.50×90=3% annum

Forward differential formula = Spot rate- Forward rate


  • Arbitrage is an operation by which one can make risk free profits by undertaking off setting transactions Arbitrage can be in interest rates, i.e. borrow in one centre and lend in another at a higher rate. Arbitrage can occur in exchange rates also. However, with the present day efficient communication system, arbitrage opportunities are very rare.

In the above example forward rate, i.e Euro 1= US dollar 1.5436, would perfectly offset the interest rate differential and can be calculated as follows:

Principal+ interest of US dollar investment = US $ 159

Principal + interest of Euro loan= Euro 103

Therefore, Euro 103

Or Euro 1= US$ 159/103=US$ 1.5436

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