6 FOREIGN EXCHANGE ARITHMETIC
6.5 SOME BASIC EXCHANGE RATE ARITHMETIC
(a) 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 the rates in Mumbai market are US$ 1 = Rs. 42.8450/545 and rates in London market are US$ 1 = Euros 0.7587 we will get US$ 1 for Rs. 42.8545 and for one US$ we will get Euro 0.7587. Thus, we can form a sort of chain rule as under:
How many Rs If
If an export customer has a bill for £100,000, the bank has to purchase the £(Pound Sterling) 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 = Rs. 42.8450/545
The London market is quoting cable (STG/DLR) as £ 1 = US$ 1.9720/40
The bank has to sell £'s in the London market at US$ 1.9720, i.e. the market's buying rate for £ 1. The US dollars so obtained have to be disposed off in the local inter -bank market at US$ 1 = Rs. 42.8450 (market's buying rate) for US$.
By chain rule, we get:
£ 1 = 1.9720 x 42.8450 = Rs. 84.4903
The precaution which should be taken is that one should know who is the quoting party and who is facing the quote. The thumb rule of the market is that if you ask for a quote, the quoting party will give you a quote and it is for you to do the deal or not to do a deal on the prices quoted. You cannot dictate prices. However, you can ask for a fresh quote.
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(b) Chain rule
Calculation of the cross rate is based on a commonsense approach. However, it can be reduced to a rule known as the chain rule with similar steps.
(c) Value date
The value date is a date on which the exchange of currencies actually takes place. Based on this concept, we have the following types of exchange rates.
(i) Cash/ready: It is the rate when an exchange of currencies takes place on the date of the deal.
(ii) TOM: When the exchange of currencies takes place on the next working day, i.e. tomorrow it is called the TOM rate.
(iii) SPOT: When the exchange of currencies takes place on the second working day after the date of the deal, it is called the spot rate.
(iv) Forward rate: If the exchange of currencies takes place after a period of spot date, it is called the forward rate. Forward rates generally are expressed by indicating a premium/discount for the forward period.
(v) Premium: When a currency is costlier in forward or say, for a future value date, it is said to be at a premium. In the case of the direct method of quotations, the premium is added to both the selling and buying rate.
(vi) Discount: If currency is cheaper in the forward or for a future value date, it is said to be at a discount. In the case of a direct quotation, the discount is (deducted) subtracted from both the rates, i.e. buying and selling rates.
The forward rates are quoted in terms of forward margins or forward differentials. For example:
Spot Euro 1 =US$ 1.3180/90 1 month forward 35-32 2 month forward 72-70 3 month forward 110-107
It is understandable that if a currency is at a premium vis-a-vis another currency, the natural consequence is that the latter will be at a discount vis-a-vis the former currency. v
In the above exchange rate quotations Euro is at a discount and hence USS is at a premium. We can buy USS, one month forward at
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
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second 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:
(a) Spot rate
(b) Forward points reflecting the interest rate differentials adjustment for different settlement dates.
(a) Forward points
Let us suppose that the 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:
(i) 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.
(ii) Market view, i.e. expectations, about the future and developments likely to take place in interest rates and foreign exchange.
(iii) 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:
Euro
us$
Inflow Outflow Inflow Outflow
Spot borrowing Sells
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$/Euro rate continues to be same for spot and one year forward.
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The person having USS would not like to give this opportunity. Theoretically speaking, the returns on both the currencies will be the same and the forward exchange rate of US$/Euro will be adjusted by the
market forces to eliminate any arbitrage opportunity. The US$/Euro rate will be:
US$159 159 i.e. Euro J
103
= US$ 1.5436 Thus, 0.0436 represents the forward differential between spot and one year forward.
(b) 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 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$ 1.5436, would perfectly offset the interest rate differential and can be calculated as follows:
Principal + interest of US$ investment = USS 159 Principal + interest of Euro loan = Euro 103
Therefore, Euro 103 = US$ 159
Or Euro 1 = USS — = USS 1.5436 (c) Calculating forward points
We can calculate the approximate forward points for a given forward period with the help of the following information:
Spot rate x Interest rate differential x Foward period 100 x No. of days in the year
1.500x3x90
- = 0.01125
Forward differential, is also known as the 'Swap Rate'. Three months forward rate for a USS/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:
. , Forward points x No. of days in the year x 100
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Continuing the above example, we have 0.01125x360x100
= 3% per annum
I
We also know that the forward differential can be calculated by the following formula: i.e., Forward Differential = Spot rate - Forward rate.
(d) Premium and Discount
As discussed earlier the 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. 42.8450 3 months forward US$ 1 = Rs. 42.8725
Thus, if one has to buy three 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-a-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
3 months forward
US$ 1 = Rs. 42.8450 US$ 1 = Rs. 42.7950
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-a-vis rupees. If one buys US$ 1 now, then three 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.
Method of quoting forward rates: As per foreign exchange market convention, forward rates are not quoted for say one month, two months, three months, etc. Instead spot rates and forward differentials are quoted separately. To arrive at forward rates for say three months, the spot rate is adjusted for the forward points for three months.
Let us consider US$/Euro rate Spot Euro 1 =US$ 1.3180/90
The currency which is being bought and sold is the Euro in terms of US$. The bid rate for Euro is US$ 1.3180 whereas the offer rate is 1.3190. The forward quotation is given in the following manner:
Spot Euro 1 = US$ 1.3180/90
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Spot
2 months forward points
(discount) 1.3154
2 months outright offer (selling) rate is
Two months market bid rate is Euro 1 = US$ 1.3210 and the offer rate is Euro 1 = US$ 1.3227. In other words, Euro is costing more in terms of US$ in forwards. Therefore, the US$ is at a premium. It is only logical that the market will add lesser of the two premium points, i.e. 30-37 in bidding for US$ two months forward and since premium is always added, will add to a higher premium in the offer rate, i.e.
the offer rate two months forward will be Euro 1 = US$ 1.3227.
We can say that if in forward points the first figure is lower than the second figure, the base currency is at a premium in forwards.
Let us consider another scenario of the foreign exchange market rates, which are quoted as under:
Spot Rate Euro 1 = US$ 1.3180/90
1 month forwards 24-19
2 month forwards 26-20
3 month forwards 33-25
In these exchange rates, the first figure in the forward differentials is higher than the second figure, therefore, the base currency Euro is at a discount vis-a-vis US$. We know that the discount is always deducted, i.e. it is deducted from the buying and selling rate. Therefore, higher forwards points will be deducted from the bid rate whereas lower forward points will be deducted from the offer rate.
2 months outright bid (buying)
US$ 1.3180 (-) 0.0026 Euro 1 =
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2 months forward points (-)0.0020
(discount) 13170126"
Therefore, 2 months bid and offer rates are
Euro 1 = USS1.3154-1.3I70
It is clear from the above that if the spot rate and forward rates are compared then, there are three possibilities.
(i) At Par if the spot rate and forward rate is the same, they are called at par.
(ii) In case of direct rates, if the forward rate is more than the spot rate, the base currency is called as being at a premium.
(iii) In case of direct rates, if the forward rate 'is less than the spot rate, the base currency is called as being at a discount.
6.7 Keywords
Direct and Indirect Quote: A direct quote is the home currency price of one unit of the foreign currency, e.g. US$ 1 = Rs. 42.8450. An indirect quote is the foreign currency price of one unit of the home currency, e.g. Re.l = US$ 0.0227.
Cross Rate: If rate of currency A is known in terms of currency B and rate of currency B is known in terms of currecy C,we can derive the rate of currency A in terms of currency C by cross-multiplication.
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Chain Rule: The above concept of cross rate is called Chain Rule and can be used in finding the rate of a currency A in terms of other currencies, through cross-multiplications, eventhough the quote of currency A in terms of that currency is not available in the market.
Value date: The value date is a date on which the exchange of currencies actually takes place.
Types of Rates: Depending on the value date, the exchange rates can be; Cash/Ready, TOM, SPOT, or Forward.
Premium: In case of direct rates, if the forward rate is more than the spot rate, the base currency is called as being at a premium.
Discount: In case of direct rates, if the forward rate is less than the spot rate, the base currency is called as being at a discount.
Forward Points: The forward premium or discount, expressed in percentage points, is called Forward Points, e.g. a forward premium of 0.0150 is referred to as premium of 150 points.
Arbitrage: Arbitrage is an operation by which one can make risk free profits by undertaking offsetting transactions.
6.8 Terminal Questions
1. Describe direct quote and indirect quote.
2. What is cross rate?
3. Explain chain rule of foreign exchange conversion.
4. What do you mean by value date?
5. Explain the following terms:
a. Forward points b. Arbitrage
c. Premium and discount
Describe the method of calculation of forward points.
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