JAIIB AFM Module-C Unit 5 : Financial Mathematics /Forex Arithmetic

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Sep 8

JAIIB Paper 3 AFM Module C Unit 5 : Financial Mathematics /Forex Arithmetic (New Syllabus)

IIBF has released the New Syllabus Exam Pattern for JAIIB Exam 2023. Following the format of the current exam, JAIIB 2023 will have now four papers. The JAIIB Paper 3 (Accounting and Financial Management for Bankers) includes an important topic called "Financial Mathematics /Forex Arithmetic". Every candidate who are appearing for the JAIIB Certification Examination 2023 must understand each unit included in the syllabus. In this article, we are going to cover all the necessary details of JAIIB Paper 3 (AFM) Module C (FINANCIAL MANAGEMENT ) Unit 5 : Financial Mathematics /Forex Arithmetic Aspirants must go through this article to better understand the topic, Financial Mathematics /Forex Arithmetic, and practice using our Online Mock Test Series to strengthen their knowledge of Financial Mathematics /Forex Arithmetic. Unit 5 : Financial Mathematics /Forex Arithmetic

Foreign Exchange'

'Foreign Exchange' refers to the general mechanism by which a bank converts the currency of one country into that of another.
Foreign trade gives rise to foreign exchange.
Foreign trade is transacted (i.e. expressed and paid for) either in the currency of the exporter's country or that of the importer's country or that of a third country (like Pound Sterling, US Dollars, etc.), acceptable to both the exporter and the importer.

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 through by the banks by means of bookkeeping entries carried out in the two centres concerned.
Almost all exchanges of one currency for another are effected 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 modified '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 drive the exchange rate.

Direct And Indirect Quote

A currency quotation is the price of a currency in terms of another currency.
For example, $1 = Rs 75.00, means that one dollar can be exchanged for Rs. 75.00.
Alternatively, we may pay Rs 75.00 to buy one dollar.
A foreign exchange quotation can be either a direct quotation and or an indirect quotation, depending upon the home currency of the person concerned.

A direct quote is the home currency price of one unit of the foreign currency.
Thus, in the aforesaid example, the quote $1 = Rs. 75.00 is a direct quote for an Indian national.
An indirect quote is the foreign currency price of one unit of the home 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 of overseas to acquire the Euros.

Chain Rule

Calculation of the cross rate is based on a 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 next working day, i.e. tomorrow it is called the TOM rate.
SPOT: When the exchange of currencies takes place on the second working day after the date of the deal, it is called the spot rate.
Forward rate: If the exchange of currencies takes place after a 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 or 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

As discussed earlier, an exchange rate is the price at which currency can be bought or sold for another currency.
The date on which the values are exchanged can be any date starting from the date of transaction onwards.
Generally, the exchange rates are quoted on a spot basis, i.e. the settlement takes place on the 2^nd working day after the date of transaction.
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 points reflecting the interest rate differentials adjustment for different settlement dates.

Forward Points

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

Spot Euro 1 = US$ 1.2180

the exchange rate 3 months forward is

3 months Euro 1 = US$ 1.2330

The difference of 150 points referred to are the forward points.

The following factors determine the forward points:

Supply and demand for the currency for the settlement date. If there are more buyers for a particular date than sellers, the forward points 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.
However, if there are no controls on capital flows, the interest rate differential between the two currencies is the most dominant factor in determining the forward points.
This is based on the simple logic of a trade off between the interest earned on one currency and the opportunity foregone to earn interest on another currency.

Let us take an example for illustrating as to how forward differential points arises:

Spot Euro 1 = US$ 1.5000

Interest, Euro @ 3% per annum,

US$ @ 6% per annum.

Suppose someone borrows Euro 100 for one year @ 3% per annum converting it into US$ and places the same as a deposit for one year @ 6%, his cash flows will be as under:

Thus, a person can make Euro 3 in one year by borrowing Euro and converting the same into US$ and after one year converting US$ again into Euro.

However, it is being presumed that US$/Euro rate continues to be same for spot and one year forward.

The US$/Euro rate will be: Euro 103 = US$159 i.e. Euro 1 = 159/103

= US$ 1.5436

Thus, 0.0436 represents the forward differential between spot and one year forward.

Arbitrage

Arbitrage is an operation by which one can make risk free profits by undertaking offsetting transactions.
Arbitrage can be in interest rates, i.e. borrow at one centre and lend at 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$ 1.5436, would perfectly offset the interest rate differential and can be calculated as follows:

Principal + interest of US$ investment = US$ 159

Principal + interest of Euro loan = Euro 103

Therefore, Euro 103 = US$ 159 Or

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

Calculating Forward Points

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

Spot exchange rate = 1.5000

Interest rate differential = 3% per annum

Forward period = 90 days

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

The formula is as follows

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 points is as under:

Premium and Discount

forward exchange rates are quoted when the value date in the foreign exchange transaction is beyond the spot date.
Spot exchange rate and forward rates are different.
The difference between spot rate and forward rate is known as the forward differential and the same can be at a premium or a discount. Let us illustrate this with the help of spot and forward exchange rates:

Spot inter-bank rate US$ 1 = Rs. 74.8450

3 months forward US$ 1 = Rs. 74.8725

Thus, if one has to buy 3 months forward US$ against rupees he has to pay more for the same US$ by 0.0275. To understand this, it can be said that the three months forward US$ is costlier by Rs. 0.0275 as compared to spot. Therefore, US$ is at a premium in forwards vis-à-vis rupee.

In case of direct quotations, a premium is always added, i.e. added to both buying and selling side.
Take another situation when the inter-bank quotes are as under:

Spot US$ 1 = Rs. 74.8450

3 months forward US$ 1 = Rs. 74.7950

It is clear from the above quotes that one US$ is available for lesser rupees as compared to the spot.
In other words, it can be said that US$ is cheaper in forward as compared to spot, i.e. US$ is at a discount vis-à-vis rupees.
If one buys US$ 1 now, then 3 months forward he has to pay a lesser amount in rupee terms by 0.0500.
In case of direct quotations, a discount is always deducted, i.e. deducted both from the buying and selling side.

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JAIIB Paper 3 (AFM) Module C Unit 5 – Financial Mathematics forex Arithmetic (Ambitious baba)