Calculation of Currency Exchange Rate

Exchange Rate always involves two currencies and are mentioned in the following way:

X/Y = 100. This implies that 1 Unit of Y can buy 100 units of X 

In the above nomenclature,
X is called as Price Currency
Y is called as Base Currency (Always set to 1) 

Exchange Rate Quote (FX Quote) Nomenclature

• Direct Currency Quote: The domestic currency of the country is the Price Currency and the foreign currency is the base currency.
• E.g. INR/USD is Direct Currency Quote in India. If INR/USD = 75, it implies that 1USD can be purchased with 75 INR or 1 USD can be sold for 75 INR
• Indirect Currency Quote: The domestic currency of the country is the Base Currency and the foreign currency is the Price Currency.
• E.g. USD/INR is Indirect Currency Quote in India. If USD/INR = 0.0133, it implies that 1 INR can be purchased with 0.0133 USD or 1 INR can be sold for 0.0133 USD. 

Direct and Indirect Rates are reciprocal of each other. 

$$DirectRate=\frac { 1 }{ Indirect\quad Rate } $$

• Cross-Rate Quote: The two currencies involved in this exchange rate are not the domestic currency of the country. The price and base currency are foreign currencies.
• E.g. USD/EUR is a Cross Rate Currency in India. If USD/EUR = 1.22, it implies that 1 EUR can be purchased with 1.22 USD in India.
• The naming convention of cross rate quotes is very important to understand, a cross rate of USD/EUR is written as EURUSD or EUR: USD or EUR-USD.
• The table below gives a comparative picture of all the three nomenclatures of FX Rates:

	Direct	Indirect	Cross
Nomenclature	Domestic/Foreign	Foreign/Domestic	Foreign/Foreign
Base Currency	Foreign	Domestic	Foreign
Price Currency	Domestic	Foreign	Foreign
Example (India as Domestic Country)	INR/USD	USD/INR	USD/EUR
Writing Convention	INR/USD	USD/INR	USD/EUR or EURUSD or EUR: USD or EUR-USD

• Three-Digit Quote: A currency is represented by a three-digit unique word in the FX market like EUR for Euro, INR for Indian Rupee, etc.
• However, the three digits can also be used to denote exchange rates, for Example, EUR as an exchange rate implies USD/EUR. To avoid confusion, the case where the three-digit letter defines an exchange rate is a pre-defined set.
• It must be noted that whenever the three digits are used to denote an Exchange Rate, one of the associated currencies (price or base) is USD.

Therefore, we should focus on the word currency or exchange rate associate with the there-digit letter:

1. If it is said EUR Currency it implies, Euro as a currency
2. If it is said EUR Exchange Rate, it implies USD/EUR

Two-Sided Price (Bid and Offer)

• A bid is a rate at which a person/company is ready to buy, and Offer is the rate at which he is willing to sell. (Bid-Buy, Offer-Sell)
• In FX Market, the institutions such as Bank who are involved in the business of FX act as a buyer and seller both, they offer to sell currencies as well as buy them. To generate profit, the purchase rate is always lower than the sell rate, or in other words, they sell the currency at higher rates than they buy them.
• The price on which a bank is ready to sell a currency is called Offer price and the price on which it is ready to purchase is the bid price. The difference between the Bid Price and Offer Price is known as Spread, which is the income of the bank.

$$Spread=Offer–Bid$$

• The rate quoted by such financial institutions who are engaged in both Sale and Purchase on FX is known as a two-sided price. Two-Sided price is quoted as Offer – Bid. Let us see the following illustration to understand the concept.

Illustration 1: Nikhil goes to PBC Bank to purchase USD by paying the equivalent amount of INR, the bank gives him the rate as INR/USD 75.00 – 74.98. This implies that the PBC Bank will sell 1 USD for 75 INR and at the same time, it will buy 1 USD for 74.98 INR.

The Spread or Profit of the bank will be 75-74.98 = 0.02 INR per USD

The important points regarding two-sided price are:

1. The quote is always given as Offer-Bid
2. Price is always shown in terms of Price currency
3. A bid is always less than the offer.
4. The difference between Bid and Offer is known as Spread.

Cross Rate Calculations

• The two currencies involved in the cross rate are not the domestic currency of the country. The price and base currency are foreign currencies.
• E.g. USD/EUR is a Cross Rate Currency in India. If USD/EUR = 1.22, it implies that 1 EUR can be purchased with 1.22 USD in India.

Let us see, how the cross rate is calculated with the help of a few illustrations:

Illustration 2: In India, the USD/INR = 0.0133 and INR/EUR = 82, we have to calculate the USD/EUR cross rate in India.
The process is very simple, we just need to multiply these two rates,

$$\frac { USD }{ INR } \times \frac { INR }{ EUR } =0.0133×82$$ $$\frac { USD }{ EUR } =1.0906$$ Hence, USD/EUR cross rate in India = 1.0906

Illustration 3: In India, INR/USD = 75.00 and INR/EUR = 82, we have to calculate the USD/INR cross rate in India.
The process is simple, we just need to multiply the reciprocal of INR/USD with INR/EUR
$$\frac { 1 }{ \frac { INR }{ USD } } \times \frac { INR }{ USD } =\frac { 1 }{ 75 } \times \quad 82\quad $$ $$\frac { USD }{ INR } \times \frac { INR }{ EUR } =0.0133×82$$ $$\frac { USD }{ EUR } =1.0906$$ Hence, USD/EUR cross rate in India = 1.0906

Illustration 4: In India, USD/INR = 0.0133 and EUR/INR = 0.0122, we have to calculate the USD/INR cross rate in India.
The process is simple, we just need to multiply the INR/USD with the reciprocal of EUR/INR
$$\frac { USD }{ INR } \times \frac { 1 }{ \frac { EUR }{ INR }  } =0.0133\times \frac { 1 }{ 0.0122 } $$ $$\frac { USD }{ INR } \times \frac { INR }{ EUR } =0.0133×81.97$$ $$\frac { USD }{ EUR } =1.0902$$ Hence, USD/EUR cross rate in India = 1.0902

Forward Calculations

• Forward Exchange Rates are quoted in terms of points or pips. The point is the difference between the forward rate and the spot rate. The value of Point may be positive or negative $$Points\quad or\quad Pips=Forward\quad Rate-Spot\quad Rate$$
• If Forward Rate > Spot Rate, then the Point is Positive, and the base currency is said to be trading at a forward premium.
• And if Forward rate < Spot Rate, then the Point is Negative, and the base currency is said to be trading at a forward discount.

Illustration 5: In INR/USD spot rate is 75 and INR/USD forwards rate is 73 then,
Point = 73 – 75 = -2.00
and the base currency (USD) is said to be trading at a forward discount.

Illustration 6: If INR/USD spot rate is 75 and INR/USD forward rate is 76 the,
Point = 76 – 75 = +1.00
and the base currency (USD) is said to be trading at a forward premium

• In the FX Market, the quotes for the forward rates are shown as the number of forwarding points at each maturity. The forward points are also called swap points because an FX swap consists of simultaneous spot and forward transactions.

Illustration 6: The following table shows various rates for INR/USD.

Maturity	Spot or Forward Rates
Spot	75.0
One Week	+1.0
One Month	+1.10
Three Month	+1.35
6 Months	+1.50
9 Months	+1.58