5_Questions on Bid rate and ask rate final.pptx

International financial
management

How bid and ask rates formed
• For computing bid and offer rates we need to
have the reference rate as the mid-rate(R)
which is issued by the RBI in India.
• Let M is exchange margin R is the reference
rate or mid –rate.
• Bid and ask quotes are then given as
S (bid) = R*(1-M)
S (offer) = R*(1+M)

• Hence, spread =S (offer) –S(Bid) = R(1+M)-R(1-
M)= 2RM
• From the above equation, it is clear that the
spread equals twice the one side average cost
of transaction or it may be termed that ones
side of cost of transaction equals half the
spread.

• Suppose RBI reference rate is S(USD/INR) =
54.75 and if one way exchange margin is to be
charged by the authorised dealer is 0.4%, the
direct bid and offer rates would be :
• Bid rate = 54.75-(.004*54.75)=54.531
• Offer rate = 54.75+ (.004*54.75) = 54.979
• Spread= offer rate-bid rate= 54.967-54.531=
.4380 or (R*2M) = 54.75*(.008)= .4380

Direct Quotation
• Given - RBI reference rate (INR/USD) =
Rs.45.7500, Authorised Dealer (AD) margin is
0.3%.Find Bid and Ask rate. Find Spread and
cost of transaction.

Direct Quotation
• Given - RBI reference rate (INR/USD) =
Rs.45.7500, Authorised Dealer (AD) margin is
0.3%.Find Bid and Ask rate. Find Spread and
cost of transaction.
• S (BID) = R*(1-M) = 45.7500(1-.003)= 45.6128
• S(offer) = R(1+M) = 45.7500 (1+.003)=45.8873
• Spread= S(offer)-S(bid)
= 45.8873-45.6128=.2745

• Cost of Transaction = Ask-bid/ask*100

Question:
The RBI reference rate for INR/USD is Rs.
54.8500 and the Authorised Dealer’s (AD)
margin is 0.4%. Find Bid and Ask rate. Also find
Spread and cost of transaction.

Question:
The RBI reference rate for INR/USD is Rs. 54.8500 and
the Authorised Dealer’s (AD) margin is 0.4%. Find Bid
and Ask rate. Also find Spread and cost of transaction.
Answer:
• S (Bid) = R*(1-M) = 54.8500 (1-.004)= 54.6306
• S (Offer) = R(1+M) = 54.8500 (1+.004)=55.0694
= 55.0694 – 54.6306 =0.4388
(55.0694 – 54.6306) / 55.0694 * 100 = 0.7968%

Question:
The RBI reference rate for INR/USD is Rs.
71.21 and the Authorised Dealer’s (AD) margin
is 0.5%. Find Bid and Ask rate. Also find Spread
and cost of transaction.

Question:
The RBI reference rate for INR/USD is Rs. 71.21 and the
Authorised Dealer’s (AD) margin is 0.5%. Find Bid and Ask
rate. Also find Spread and cost of transaction.
Answer:
• S (Bid) = R*(1-M) = 71.21 (1-.005)= 70.85395
• S (Offer) = R(1+M) = 71.21 (1+.005)=71.56605
= 71.56605 – 70.85395 = 0.7121
(71.56605 – 70.85395) / 71.56605 * 100 = 0.9950%

Question:
The Federal Reserve reference rate for
USD/EURO is $1.14 and the Authorised
Dealer’s (AD) margin is 0.2%. Find Bid and Ask

Question:
The Federal Reserve reference rate for USD/EURO is $1.14
and the Authorised Dealer’s (AD) margin is 0.2%. Find Bid
Answer:
• S (Bid) = R*(1-M) = 1.14 (1-.002)= 1.13772
• S (Offer) = R(1+M) = 1.14 (1+.002)=1.14228
= 1.14228 – 1.13772 = 0.00456
(1.14228 – 1.13772) / 1.14228 * 100 = 0.3992%

Question:
USD/POUND is $1.29 and the Authorised

Question:
The Federal Reserve reference rate for USD/POUND is $1.29
Answer:
• S (Bid) = R*(1-M) = 1.29 (1-.003)= 1.28613
• S (Offer) = R(1+M) = 1.29 (1+.003)=1.29387
= 1.29387 – 1.28613 = 0.00774
(1.29387 – 1.28613) / 1.28613 * 100 = 0.6018%

Question:
USD/YEN is $0.0091 and the Authorised

Question:
The Federal Reserve reference rate for USD/YEN is $0.0091
Answer:
• S (Bid) = R*(1-M) = 0.0091 (1-.004)= 0.0090636
• S (Offer) = R(1+M) = 0.0091 (1+.004)=0.0091364
= 0.0091364 – 0.0090363 = 0.0001001
(0.0091364 – 0.0090636) / 0.0091364 * 100 = 1.0956%

Arbritage in forex market
• Single point spot arbitrage:
• Consider the following spot rate quotes:
• Bank A gives
GBP/USD: 1.4550/1.4560
• Bank B gives
GBP/USD: 1.4538/1.4548

In the New York market the quotes of A$/US$
are
GBP$/US$(SR)= $.8576
GBP$/ US$(FR)=$ .8500 (90 days)
Calculate forward discount or Premium.

Foreign Exchange Market
Example : From the data given below calculate
forward premium or discount as the case may be
Particular Spot 3-month forward
Rs/$ 44.5000/7050 44.7000/9990

Example : From the data given below calculate forward premium or
discount as the case may be
Solution
Forward Premium (using bid price)
= [(44.7000 – 44.5000)/ 44.5000] x (12/3) x 100 = 1.18 percent per annum
[Dollar is at premium]
Forward Premium (using ask price)
Rs/$ 44.5000/7050 44.7000/9990

Rs/$ 42.3750/7890 42.4250/8875

Solution
Rs/$ 42.3750/7890 42.4250/8875

Rs/$ 46.4000/8050 46.7980/9520

Solution
Rs/$ 46.4000/8050 46.7980/9520

Example : From the data given below calculate forward
premium or discount (on annualized basis) as the case
may be
Rs/$ 62.15 62.50

premium or discount (on annualized basis) as the case may be
Solution
Forward Premium/ discount
Rs/$ 62.15 62.50

Solution
Rs/$ 60.25 60.12

Solution
Rs/$ 65.75 65.95

Spot 1 month forward 3 month forward 6 month forward
Rs./ £ Rs. 92.1255/92.3279 Rs. 92.4291/6523 Rs. 91.7134/8906 Rs. 93.1900/3200
Question:
From the data given below calculate forward premium or discount, as the case may
be, of the £ in relation to rupee.
Answer:
Since 1 month forward rate and 6 month forward rate are higher than the spot
rate, the British Pond (£) is at a premium in these two periods. The premium
amount is determined separately both for bid price and ask price. The first quote
is the bid price and the second quote (after the slash) is the ask/offer/sell price. It
is the normal way of quotation in foreign exchange markets.

Premium with respect to Bid Price
1 month =
𝑅𝑠.92.4291−𝑅𝑠.92.1255
𝑅𝑠.92.1255
x
12
1
x 100 = 3.29 percent per annum.
6 month =
𝑅𝑠.93.1900−𝑅𝑠.92.1255
𝑅𝑠.92.1255
x
12
6
Premium with respect to Ask Price
1 month =
𝑅𝑠.92.6523−𝑅𝑠.92.3279
𝑅𝑠.92.3279
x
12
1
6 month =
𝑅𝑠.93.3200−𝑅𝑠.92.3279
𝑅𝑠.92.3279
x
12
6

In case of 3 months forward, spot rates are higher than the forward rates,
signaling that forward rates are at a discount.
Discount with respect to Bid Price
3 month =
𝑅𝑠.92.1255−𝑅𝑠.91.7134
𝑅𝑠.92.1255
x
12
3
Discount with respect to Ask Price
3 month =
𝑅𝑠.92.3279−𝑅𝑠.91.8906
𝑅𝑠.92.3279
x
12
3
Note: Here, the British Currency is at a premium for one month and six months
forward exchange deals. It implies that the Indian Rupee is at a discount. Thus, when
one currency is at a forward premium, it is imperative that the other currency is at a
discount.

Question:
Suppose an Indian Importer is to pay to a New Zealand exports firm in New
Zealand dollars. Assume further that the direct quote of Indian Rupee and
New Zealand dollars in not available. Therefore, the exporter is to use the
other two relevant quotes, namely, the New Zealand $/US $ and Rs. / US $.
These rates are as follows:
New Zealand $ / US $ = 1.2806 – 1.2816
Rupee / US $ = 60.148 – 60.163
Determine the exchange rate between Indian Rupee and New Zealand dollar.

Question:
Answer:
Suppose an Indian Importer is to pay to a New Zealand exports firm in New Zealand
dollars. Assume further that the direct quote of Indian Rupee and New Zealand
dollars in not available. Therefore, the exporter is to use the other two relevant quotes,
namely, the New Zealand $/US $ and Rs. / US $. These rates are as follows:
New Zealand $ / US $ = 1.2806 – 1.2816
Rupee / US $ = 60.148 – 60.163
Determine the exchange rate between Indian Rupee and New Zealand dollar.
Determination of Rs./New Zealand dollar exchange rate involves the following steps:
(i) The Indian Importer is to buy US $ at the rate of Rs. 60.163 (when US $ are bought
by the importer, the bank is selling US dollars and hence Rs. 60.163 is the relevant
selling rate and not Rs. 60.148).
(ii) The Indian importer then sells the US $ to buy New Zealand Dollars. When he
sells the US $ the dealer/banks buy US $ 1 in exchange for the New Zealand $ 1.2806.
In other words the Indian importer gets New Zealand $ 1.2806 by selling 1 US $.

(iii) In sum, the Indian importer gets New Zealand $1.2806 in exchange for
Indian Rs. 60.163. Therefore, Rupee/New Zealand $ exchange rate is
(Rs.60.613/1.2806) = Rs. 46.9803/ New Zealand $.
Thus, Rs. 46.9803 / New Zealand $ is a cross rate, derived from the two sets of rates,
namely, New Zealand $/ US $ and Rupee/US $. Cross rates defined as a rate between
a third pair of currencies, by using the rates of two pairs, in which one currency is
common, are derived rates.
Rs. 46.9803/ New Zealand $ is the selling arte from the point of view of the
dealer/bank. This provides one quote of the cross rate. To complete the quote,
bid/buying rate is required. The buying rate would be derived as per the following
steps:
(i) The dealer purchases one US $ for Rs.60.148.
(ii) The dealer sells one US $ in exchange for 1.2816 New Zealand $.
(iii) 1.2816 New Zealand $ are equivalent to Rs. 60.148.
Accordingly, the Rupee / New Zealand $ buying rate is Rs. 60.148/1.2816 = Rs.
46.9319

The complete quote is : Rupee/New Zealand $ = Rs.46.9319 – Rs. 46.9803.
The quote implies that the bank purchases New Zealand $ at Rs. 46.9319 and sells
it for Rs. 46.9803. The term ‘cross’ is used literally to determine bid rate and ask
rate. For instance, bid rate is based on Rs. 60.163 and New Zealand $1.2806 (it is
one cross). Likewise, ask rate is based on Rs. 60.148 and New Zealand $ 1.2816 (it
is another cross).

Question:
From the following rates, determine Rs./Canadian $ exchange rate:
Rs. / US $: Rs. 61.5642 / 61.8358
Canadian $/US $ : 1.0949 / 1.0959

Question:
From the following rates, determine Rs./Canadian $ exchange rate:
Rs. / US $: Rs. 61.5642 / 61.8358
Canadian $/US $ : 1.0949 / 1.0959
Solution:
(Rs./Canadian $)bid = (Rs./US $)bid x (Us $ / Canadian $)bid
= Rs. 61.5642 x 1/(1.0959*) = Rs. 56.1768
(* Since the question provides the rate in terms of Canadian $/US $, the
equation warrants US $/ Canadian $, the values get reversed to have
denomination effect).
(Rs./Canadian $)ask = (Rs./US $)ask x (Us $ / Canadian $)ask
= Rs. 61.8358 x 1/(1.0949) = Rs. 56.4762
Rs./Canadian $ exchange rate is = Rs. 56.1768 – Rs. 56.4762.

Question:
London Rs. 61.5730 – Rs. 61.6100
Tokyo Rs. 61.6350 – Rs. 61.6675
At two forex centers, the following rates with respect to US $ are quoted:
Find out arbitrage possibilities for an arbitrageur who has Rs. 100 million.

Question:
London Rs. 61.5730 – Rs. 61.6100
Tokyo Rs. 61.6350 – Rs. 61.6675
At two forex centers, the following rates with respect to US $ are quoted:
Find out arbitrage possibilities for an arbitrageur who has Rs. 100 million.
Solution:
The following modus operandi will be developed by the arbitrageur:
(i) He will buy US $ from the London forex market at the rate of Rs. 61.6100, as
it is cheaper there compared to the Tokyo market (Rs. 61.6675). He will obtain
(Rs.100 million/Rs. 61.6100) US $1,613,113,130 on conversion.
(ii) He will sell at Tokyo, US $1,623,113.130 at the rate of Rs. 61.6350 per US $
and will obtain Rs. 100,040,577.76.
(iii) As a result of arbitrage, he will earn a profit of Rs. 40,577.76 (Rs.
100,040,577.76 – Rs. 100 million) without risk.

Question
Assume the rate at London remains unchanged as stated in the previous question, but
there is a change in Tokyo.
London Rs. 61.5730 – Rs. 61.6100
Tokyo Rs. 61.6000 – Rs. 61.6450
Are there still any arbitrage possibilities for the arbitrageur of previous
question?

Question
Assume the rate at London remains unchanged as stated in the previous question, but
there is a change in Tokyo.
London Rs. 61.5730 – Rs. 61.6100
Tokyo Rs. 61.6000 – Rs. 61.6450
Are there still any arbitrage possibilities for the arbitrageur of previous
question?
Solution:
While, it is true that it is cheaper to buy US $ in London compared to Tokyo, there
are no possibilities now for arbitrageur as explained in the following steps:
Buying from London and Selling at Tokyo
(i) If he buys US $ from the London forex market at the rate of Rs. 61.6100. He
will obtain (Rs.100 million/Rs. 61.6100) US $1,623,113.130 on conversion.
(ii) If he now sells at Tokyo, US $1,623,113.130 at the rate of Rs. 61.6000 per US $
then he will obtain Rs. 99,983,768.868.
(iii) As a result of arbitrage, he will earn a loss of Rs. 16,231.132 (Rs.
99,983,768.868– Rs. 100 million).

Buying from Tokyo and Selling at London
Since the dollar rate at Tokyo is already very high in compare of London, so again
there is no possibility of earning profit but losses.
The Loss from buying Tokyo and selling at London will be as under:
(i) If he buys US $ from the Tokyo forex market at the rate of Rs. 61.6450. He will
obtain (Rs.100 million/Rs. 61.6450) US $1,622,191.580 on conversion.
(ii) If he now sells at London, US $1,622,191.580 at the rate of Rs. 61.5730 per US $
then he will obtain Rs. 99,883,202.155.
(iii) As a result of arbitrage, he will earn a loss of Rs. 116,797.845
(Rs. 99,883,202.155– Rs. 100 million).

Q1. If direct quote is Rs. 45/US , how can this exchange rate be presented under
indirect quote?
Q2. If indirect quote is Us $ 0.025/Rs., how can this exchange rate be shown under
direct quote?
Q3. Consider the following bid-ask prices: Rs. 40-40.50/ US $. Find the bid-ask
spread.

Q1. If direct quote is Rs. 45/US , how can this exchange rate be presented under
indirect quote?
Ans: US $ 1/ Rs. 45 = US $ 0.0222/Rs.
Q2. If indirect quote is Us $ 0.025/Rs., how can this exchange rate be shown under
direct quote?
Ans: Rs. 1/US $ 0.025 = Rs. 40/ US $.
Q3. Consider the following bid-ask prices: Rs. 40-40.50/ US $. Find the bid-ask
spread.
Ans: (40.50-40.00)/ 40.50 = 0.0123 or 1.23%.

Q4. Find out the bid rate if ask rate is Rs. 40.50/US $ and the bid-ask spread is 1.23%.
Q5. Find out the forward rate differential if spot rate of US $ is Rs. 45.00 and one
month forward rate is Rs. 45.80.

Q4. Find out the bid rate if ask rate is Rs. 40.50/US $ and the bid-ask spread is 1.23%.
Ans: (40.50-x)/40.50 = 0.0123
40.500 – x = 0.0123 x 40.50
40.50 – 0.50 = x
X = 40.00
Q5. Find out the forward rate differential if spot rate of US $ is Rs. 45.00 and one
month forward rate is Rs. 45.80.
Ans: 360/30 {(45.80 – 45.00)/ 45.00} x 100 = 21.33 per cent. It will be known as a
forward premium as the value of US dollar has increased.

Q6. Find the one-month forward rate of US dollar if spot rate is Rs. 45.00 and the
forward premium is 12 per cent.
Q7. Find Rs./Euro exchange rate if: the two exchange rates are: Rs. 43.93-
43.95/US $ and Euro 0.83-0.84/US $.

Q6. Find the one-month forward rate of US dollar if spot rate is Rs. 45.00 and the
forward premium is 12 per cent.
Ans:
360
30
{
𝑥−45.00
45.00
} =0.12
(x-45) = 0.12 x 45 x
360
30
X = 45 + 0.45 or x = 45.45
Q7. Find Rs./Euro exchange rate if: the two exchange rates are: Rs. 43.93-
43.95/US $ and Euro 0.83-0.84/US $.
Ans:
Bid rate= Rs. 43.93/0.84 = Rs. 52.30
Ask rate = Rs. 43.95/0.83 = Rs. 52.95
= Rs. 52.30 – 52.95/Euro

Q8. Calculate the 3-mionth forward rate, if spot rate is Rs. 46/US $; interest rate of India
and the USA is respectively 6 percent and 3 per cent.

Q8. Calculate the 3-mionth forward rate, if spot rate is Rs. 46/US $; interest rate of India
and the USA is respectively 6 percent and 3 per cent.
Ans: Applying the interest rate parity theorem,
3-month forward rate = 46/360/90[(1.06/1.03) – 1] + 46
= Rs. 46.34/US $.

Q9. Find out the amount of profit out of covered interest arbitrage if interest rate in India
and the USA is respectively 9 per cent and 4.50 per cent and the 6-month forward and
the spot exchange rates are respectively Rs. 45.00 $ and Rs. 45.20 $.

Q9. Find out the amount of profit out of covered interest arbitrage if interest rate in India
and the USA is respectively 9 per cent and 4.50 per cent and the 6-month forward and
the spot exchange rates are respectively Rs. 45.00 $ and Rs. 45.20 $.
Ans: There will be covered interest arbitrage in so far as the interest rate and forward
rate differentials are not equal.
To start with, borrowing $ 1,000 in the USA, converting it into rupee for 45,000 and
investing the rupee for six months will fetch Rs. 47,025. Selling Rs. 47,025 forward
will fetch $ 1,045. After repaying dollar loan along with interest for 1,022.50, the
arbitrageur profits $ 1,045-1,022.50 = $ 22.50.

Q10. If the rate of exchange is:
US $ 2.000-2.0100/ in New York
US $ B1.9800-1.9810/ in London
Explain how the arbitrageurs will gain.

Q10. If the rate of exchange is:
US $ 2.000-2.0100/ in New York
US $ B1.9800-1.9810/ in London
Explain how the arbitrageurs will gain.
Ans: The arbitrageur will sell Pound in New York and with then same dollar, buy
Pound in London. The profit per Pound, assuming no transaction cost, will be:
$ 2.0100 – 1.9800 = 0.0300.
Note: It is the difference between the selling rate and the buying rates of Pound in
the two markets.

Q11. What will be the forward rate for 1 month and 10 days (broken date contract)
if:
Spot : Rs. 40.00-40.10/$
1-month forward : Rs. 40.50-40.70/$

Q11. What will be the forward rate for 1 month and 10 days (broken date contract)
if:
Spot : Rs. 40.00-40.10/$
Ans: For one month and 10 days, swap points:
Buying Rate: 50+ (80-50) x 10/60 = 55
Selling Rate: 70 + (110-70) x 10/60 = 77
The forward rate for one month and 10 days = Rs. 40.55-40.77/$.

5_Questions on Bid rate and ask rate final.pptx

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