Exchange Rate Arithmetic: Forward Rates


Forex dealers normally quote forward rates at regular intervals like one month or three months. For example, dealers normally quote 1-week, 2-week, 1,2,3 6 months forward rate. However, depending on customer’s requirement, these delaers quote forward rate on a specific future date that is not an exact multiple of months. Such kinds of forwards quotes are known as broken period quotes.

Banks normally quote broken period rates by method of interpolation. Let us take an example to understand this.

On July 14th the following rates are quoted by a bank as given in Table 15.1. However a corporate customer wants to buy 100,000 USD on October 21st. The bank has to quote a forward rate for this date.
Table 15.1: Cash/Swap rates in points

USDINR
Maturity Date
Bid Rate
Ask Rate
Spot
July 14th
47.0725
47.0745
1 Month
August 14th
135
130
2 Month
September 14th
140
133
3 month
October 14th
160
145
4 months
November 14th
175
155




 The interpolation method is used as follows:

•      The forward rate points applicable are (160 to 175) for bid and (145-155) for ask.

•      For 31 days (October 14th to November 14th), the bid spread is 15 points (175 to 160).

•      For 7 days, the spread in bid point = 1531 ∗ 7 = 3.89 . So the spread applicable for October 21st is 160 + 3.89 = 163.89

•      Similarly, for 31 days (October 14th to November 14th), the ask spread is 10 points (155 to 145). For 7 days, the spread in bid point = 1031 ∗ 7 = 2.26 . So the spread applicable for October 21st is 145 + 2.26 = 147.26

•      The applicable bid rate for 31 days (October 14th  to November 14th), the ask
spread is 15 points (175 to 160). For 7 days, the spread in ask point = 1531 ∗ 7 = 3.89 . So the ask spread applicable for October 21st is 160 + 2.26 = 163.89


•      So the applicable bid rate will be = 47.0725 - 0.014726 = 47.0577.

•      Ask spread is = 47.0745- 0.016389=47.0581.

Table 15.2: Interpolated Bid-Ask Spread ( USDINR)

Maturity Date
Bid Rate
Ask Rate
October 21st
47.0576
47.0581

For a forward contract maturing on October 21st, the bank would quote a rate (47.0576-47.0581) given in Table 15.2. As the company wants to buy USD 100,000, the bank will offer USD at a rate of INR 47.0581. If the company would like to sell USD, then applicable rate would be INR 47.0576.

As forward contracts are OTC contracts, in real life, most of the contracts would be for a broken periods.
 15.3: Premium & Discount on Forward Quotations:


Forward quotations can be expressed as percentage premium or discount to the spot rate. Table 15.3 details the forward quotations expressed as percentage premium/discount to forward quotations.

Table 15.3 Forward Quotations in Outright and Percentage form

USDINR
Outright Quotations
USD
Percentage



Premium/Discount (*)

Bid Rate
Ask Rate
Bid Rate
Ask Rate
Spot
47.0725
47.0745


1 week
47.0750
47.0775
0.28%
0.33%
2 weeks
47.0795
47.0835
0.40%
0.52%
1 month
47.0840
47.0890
0.29%
0.37%
2 months
47.0900
47.0965
0.22%
0.28%
(*) : Annualized premium/discount

The forward rate (1 week) is expressed as a percentage premium/discount in relation to spot in the following manner.

Compared to spot and 1 week forward, forward bid price of USD is more expensive by 0.0025.

% Pr emium / Discount =
n day forward bid − spot bid
*
365
*100

n day forward rate





spot bid


=
47.0750 − 47.0725
*
365
*100 = 0.28%



47.0725
7










The above equation indicates that forward 1 week USD is at premium.

Similarly % premium/discount in forward ask rate (1 week) can be calculated in the

above manner by comparing 1 week ask rate with the spot ask rate.

As the forward rates (for different maturities) are higher than the spot rates, the forward rates are at a premium. In other words, as USD is expected appreciate (as INR is expected to depreciate), forward USD is at premium.

To find out the % premium/discount of INR, we need to find out the bid-ask spread with INR as base currency. Table 15.4 lists the INRUSD bid-ask spread.


 Table 15.4 Forward Quotations in outright and percentage form

 As the forward rates (for different maturities) are lesser than the spot rates, INR is expected to depreciate as USD is expected to appreciate). Hence, forward INR is at discount to USD.

To sum up, when forward quote/variable currency appreciates (depreciates), the base currency is at discount (premium).

15.5 : Factors affecting forward rates.

By now, we are familiar with the intricacies of bid-ask quotations, broken period quotation, forward rate premium/discount aspects. But how do the banks/dealers quote these forward rates? What factors do they take into consideration for quoting a forward rate.


Besides supply, demand factors, the most important factor which governs the forward point quotation is the prevailing interest rates in two currencies.


I
v
− I
B




D


Spot  *






*












360

Forward point =




100








I
B




D












1 +




*








100
360








Where: S = spot rate

IV = Interest rate in Variable/Quote/Term currency IB = Interest rate in Base currency.

D= Actual No. of days between the spot and forward date.

360= No. of days in year. Different countries use different day count conventions. It can also be 365.

If the forward point is positive, it is added to the spot rate otherwise, it is subtracted form the spot rate.

Let us take an example to understand this aspect: A bank wants to quote forward rate for 6 month from the spot date. The details are


S = Rs. 46.60/USD

IV = Interest rate in India is 8% per annum IB = Interest rate in US is 4% per annum. D= 182 days

360= No. of days in year.



I
v
− I
B




D


Spot  *







*













360

Forward point =





100









I
B




D













1 +





*








100
360













8 − 4
182



46 .60 *




*














Forward point =



100



360

= 0.485= 48.5 points.


4

182




1 +
*
















100
360















Forward point calculated in the above manner is also known as forward swap points.

Hence the 6-month forward rate would be = 46.60 +0.485= INR 47.085/ USD


Now suppose, the interest rate in India is 3% while in USA it is 5%. The forward point would be calculated as



3 − 5
182



46 .60 *




*














Forward point =



100



360

= -0.459= -45.9 points.


5

182




1 +
*
















100
360













Hence the 6-month forward rate would be = 46.60 - 0.459= INR 46.141/ USD



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