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FREE VIRTUAL COACHING CLASSESORGANISED BY BOS(ACADEMIC), ICAI
FINAL LEVEL- MAY 2021PAPER 2: STRATEGIC FINANCIAL MANAGEMENT
Faculty Name: CA. Parvesh Aghi
Date: 29th Dec 2020
EXCHANGE RATE DETERMINATION
30 December 2020 2
Theories of Exchange Rate Determination
The Mint Parity Theory
Gold price Britain £ 20 per ounce & in the US $ 80 per ounce : £ 1 = $ 4.
The Purchasing Power Parity Theory
If price of computer is 500 US $ in NY & it costs 2500 HK $ in HK
$1 = 5HK$
Inflation rate differential.
International Fisher Effect (IFE) Theory
is based on the present and the future risk free nominal interest rates..
The Interest Rate Parity Theory (IRP)
Strong relationship between interest rate and movement in of currency
values.
US interest 2% p.a
India 6% p.a
Spot rate Rs 70/$ – one year Fwd. rate should be Rs 70 ( 1.04) =Rs 72.8/$
3
What Is Interest Rate Parity (IRP)?
Interest rate parity is a theory which states that ‘the size of
the forward premium (or discount)
should be equal to the interest rate differential between the two countries of concern
If the 1-year interest rate in the US is 2 percent &
that in India is 6 percent, the USD would trade at a 4 percent premium against
the Rupee
When interest rate parity exists, covered interest
arbitrage (means foreign exchange risk is covered) is
not feasible
because any interest rate advantage in the foreign
country will be offset by the discount on the forward rate
Thus, the act of covered interest arbitrage would
generate a return that is nohigher than what would begenerated by a domestic
investment
4
Covered interest rate arbitrage is the practice of using favorable interest rate differentials to invest in a higher-yielding currency, and hedging the exchange risk through a forward currency contract.
Question
■ According to the interest parity condition, if the domestic interest rate is 12
percent and the foreign interest rate is 10 percent, then
A. the expected appreciation of the foreign currency must be 4 percent.
B. the expected appreciation of the foreign currency must be 2 percent.
C. the expected depreciation of the foreign currency must be 2 percent.
D. the expected depreciation of the foreign currency must be 4 percent
30 December 2020 5
Answer
■ According to the interest parity condition, if the domestic interest rate is 12 percent
and the foreign interest rate is 10 percent, then
A. the expected appreciation of the foreign currency must be 4 percent.
B. the expected appreciation of the foreign currency must be 2 percent.
C. the expected depreciation of the foreign currency must be 2 percent.
D. the expected depreciation of the foreign currency must be 4 percent
Answer: B
30 December 2020 6
Covered Interest Arbitrage
Covered Interest Arbitrage has an advantage as there is an incentive to invest in the higher-interest currency to
the point where the discount of that currency in the
forward market is less than the interest differentials.
If the discount on the forward market of the
currency with the higher interest rate becomes larger than the interest differential,
then it pays to invest in the lower-interest currencyand take advantage of the
excessive forward premiumon this currency.
7
Example
If the 1-year interest rate in the US is 2 percent &
that in India is 6 percent, the USD would trade at a
4 percent premium against the Rupee
If USD/INR spot rate is 70, the 1-year forward rate would be 72.80
(1.04x 70)
72.80 is referred to as the no-arbitrage forward price
If the 1-year forward trades at any rate other
than 72.80, it would present an arbitrage
opportunity.
30 December 2020 8
Example
If it trades lower than 72.80, let’s say at 72.50, then, one can exploit the
arbitrage opportunity
by borrowing in USD at 2 percent, converting USD into INR at 70 today, entering into a forward contract to Buy USD 1-year
forward and lending the INR at 6 percent. )
The transaction would result in an arbitrage profit of 0.43 percent.).
30 December 2020 9
Example
Arbitrage Profit (0.43 percent) = -2 percent (cost of borrowing USD) -3.57 percent (cost of Selling USD
today and buying USD 1-year forward*)
+ 6 percent (rate earned by lending/investing in INR).
30 December 2020 10
( 72.50-70.00) 70 x100 = 3.57%
Example
If it trades higher than 72.80, let’s say 73.00,
then, one can exploit the arbitrage opportunity by
borrowing in INR at 6 percent
By borrowing in INR at 6 percent, converting
Rupee into USD at 70, entering into a forward
contract to sell USD after 1-year at 73 and lending the USD (investing USD
at 2 percent).
30 December 2020 11
73-70 /70 = 4.28%
Example
The transaction would result in an arbitrage profit of 0.28 percent (Since the interest of Rs 3 on Rs 70 for 1-year is equivalent to
4.28 percent).
Arbitrage Profit (0.28 percent) = -6 percent (cost
of borrowing in INR) + 4.28 percent (implied rate in the Buy USD today, Sell USD forward transaction*) + 2 percent (rate earned by investing/lending in USD).
30 December 2020 12
73-70 /70 = 4.28%
The Formula For Interest Rate Parity (IRP) Is
13
According to the interest parity theory ,
forward rate are dependent on the prevailing
interest rate in the two currencies .
The forward rate can be calculated by the
following formula :
F = 1+ Rh
S 1+ Rf
Where F and S are future and spot currency
rates . Rh and Rf are Simple interest rate in the
home and foreign currency
PRACTICE QUESTIONS
30 December 2020 14
Exercise 1
On April 1, 3 months interest rate in the UK £ and US $ are 7.5% and 3.5% per annum respectively.
The UK £/US $ spot rate is 0.7570
What would be the forward rate for US $ for delivery on 30th June?
15
Answer
■ 1$ = £ .7570
■𝑭
𝑺=𝟏+𝑹𝑯
𝟏+𝑹𝑭
■𝑭
£.𝟕𝟓𝟕𝟎=
(𝟏+.𝟎𝟕𝟓÷𝟒)
(𝟏.+.𝟎𝟑𝟓÷𝟒)
■ F = £.7570 x(𝟏.𝟎𝟏𝟖𝟕𝟓)
(𝟏.𝟎𝟎𝟖𝟕𝟓)=
■ F= £.7570 x 1.009913
■ 1$ ( 3 month fwd rate) = £.7645
16
Exercise 2
The rate of inflation in India is 8% per annum and in the U.S.A. it is 4%. The current spot rate for USD in India is Rs 74. What will be the expected rate after 1 year and after 4 years applying the Purchasing Power Parity Theory.
17
Answer
2 Rs 76.85 x 1.08/1.04 Rs 79.80
3 Rs 79.80 x 1.08/1.04 Rs 82.87
4 Rs 82.87 x 1.08/1.04 Rs 86.06
18
End of Year Calculations Forward Rate
1 Rs 74 x 1.08/1.04 Rs 76.85
Example
■ Citi Bank quotes JPY/ USD 105-106.5, and Honk Kong Bank
quotes USD/JPY 0.0090- 0.0093.
(a) Are these quotes identical?
(b) If not, is there a possibility of arbitrage?
(c) If there is an arbitrage opportunity, how would you profit from it?
30 December 2020 19
Example
Citi Bank quotes
JPY/ USD 105-106.5
and Honk Kong Bank quotes USD/JPY 0.0090- 0.0093
Are these quotes
identical?
Solution
BID ASK
CITI BANK JPY/ USD 105-106.5 $1 = JPY 105 JPY 106.5
HONG KONG USD/JPY 0.0090- 0.0093 JPY 1 = $ 0.00900 $ 0.00930
Solution
BID ASK
CITI BANK JPY/ USD 105-106.5 $1 = JPY 105 JPY 106.5
CITI BANK JPY 1= $ 0.00939 $ 0.00952
HONG
KONG
USD/JPY 0.0090-
0.0093
JPY1 = $ 0.00900 $ 0.00930
1/106.5 1/105
Solution
BID ASK
CITI BANK JPY/ USD 105-106.5 $1 = JPY 105 JPY 106.5
CITI BANK JPY 1= $ 0.00939 $ 0.00952 High
HONG
KONG
USD/JPY 0.0090-
0.0093
JPY1 = $ 0.00900 $ 0.00930 Low
SolutionBID ASK
CITI
BANK
JPY/ USD 105-106.5 $1 = JPY 105 JPY 106.5
CITI
BANK
JPY 1= $ 0.00939 $ 0.00952 high
HONG
KONG
USD/JPY 0.0090-
0.0093
JPY1 = $ 0.00900 $ 0.00930 low
Buy JPY from Hong Kong Bank at USD/JPY 0.00930 and sell them to Citi Bank
at USD /JPY 0.00939
Buy JPY from
Hong Kong
Bank
Sell
them to
Citi
Bank
Gain of $.00009 per yen
Yen 10,00,00,000 Profit = $ 9000
Alternate Solution
BID ASK
CITI BANK JPY/ USD 105-106.5 $1 = JPY 105 JPY 106.5
HONG KONG USD/JPY 0.0090- 0.0093 JPY1 = $ 0.00900 $ 0.00930
$1 = JPY 107.52 JPY 111.11
1/.00930 1/.00900
Solution
BID ASK
CITI BANK JPY/ USD 105-106.5 $1 = JPY 105 JPY 106.5
HONG KONG USD/JPY 0.0090- 0.0093 JPY1 = $ 0.00900 $ 0.00930
$1 = JPY 107.52 JPY 111.11
buy USD from Citi Bank at 106.5 and sell them to Honk Kong at
107.5269
Sell
them to
HK bank
Buy USD
from Citi
Bank
Gain of Yen 1.02 per $
EXERCISE 3
■ If the present interest rate for 6 months borrowings in India is 9% per annum and the corresponding rate in USA is 2% per annum, and the US$ is selling in India at Rs 64.50 /$.
■ Then :■ (i) Will US $ be at a premium or at a discount in the Indian forward market?■ (ii) Find out the expected 6 month forward rate for US$ in India.
■ (iii) Find out the rate of forward premium/discount.
30 December 2020 27
Solution
■ Under the given circumstances, the USD is expected to quote at a premium in India as the interest rate is higher in India.
■𝑭
𝑺=𝟏+𝑹𝑯
𝟏+𝑹𝑭
■ Where: Rh is home currency interest rate, Rf is foreign currency interest rate, F is end of the period forward rate, and S is the spot rate.
■ Therefore
■𝑭
𝑹𝒔.𝟔𝟒.𝟓𝟎=
(𝟏+.𝟎𝟗÷𝟐)
(𝟏.+.𝟎𝟐÷𝟐)
■ Fwd rate = 64.5 x 𝟏.𝟎𝟒𝟓
𝟏.𝟎𝟏= Rs 66.74
■ Rate of premium = 66.74−64.5
64.5x 12
6x 100 = 6.94%
30 December 2020 28
Example
■ The US dollar is selling in India at Rs 74.86 . If the interest rate for a 6 months borrowing in India is
■ 8% per
■ annum and the corresponding rate in USA is 2%.
■ (i) Do you expect that US dollar will be at a premium or at discount in the Indian Forex Market?
■ (ii) What will be the expected 6-months forward rate for US dollar in India? and
■ (iii) What will be the rate of forward premium or discount?
Solution
■ Under the given circumstances, the USD is expected to quote at a premium in India as the interest rate is higher in India.
■𝑭
𝑺=𝟏+𝑹𝑯
𝟏+𝑹𝑭
■ Where: Rh is home currency interest rate, Rf is foreign currency interest rate, F is end of the period forward rate, and S is the spot rate.
■ Therefore
■𝑭
𝑹𝒔.𝟕𝟒.𝟖𝟔=
(𝟏+.𝟎𝟖÷𝟐)
(𝟏.+.𝟎𝟐÷𝟐)
■ Fwd rate = 74.86. x 𝟏.𝟎𝟒
𝟏.𝟎𝟏= Rs 77.08
■ Rate of premium = 77.08−74.86
74.86x 12
6x 100 = 5.93%
30 December 2020 30
Exercise 4
■ Followings are the spot exchange rates quoted at three different forex markets:
■ USD/INR 48.30 in Mumbai■ GBP/INR 77.52 in London■ GBP/USD 1.6231 in New York
■ The arbitrageur has USD1,00,00,000. Assuming that there are no transaction costs, explain whether there is any arbitrage gain possible from the quoted spot exchange rates
30 December 2020 31
Solution
➢ USD/INR 48.30 in Mumbai➢ GBP/INR 77.52 in London➢ GBP/USD 1.6231 in New York
➢ GBP 1= Rs 77.52
➢ GBP1 = USD 1.6231
➢ USD 1.6231= Rs 77.52
➢ USD 1 = Rs 47.76
➢ So, sell $ in India and buy abroad
30 December 2020 32
Solution■ The arbitrageur can proceed as stated below to realize
arbitrage gains.
■ USD/INR: 48.30 in Mumbai
■ Sell $ and Buy Rs from USD 1,00,00,000 At Mumbai
■ 48.30 × 10,000,000 = Rs 48,30,00,000
30 December 2020 33
Solution
■ GBP/INR 77.52 in London
■ GBP 1 = Rs 77.52
■ Convert Rs to GBP at London
■𝟒𝟖,𝟑𝟎,𝟎𝟎,𝟎𝟎𝟎
𝟕𝟕.𝟓𝟐= GBP 62,30,650.155
30 December 2020 34
solution
■ GBP/USD 1.6231 in New York
■ GBP 1= USD 1.6231
■ Convert GBP to USD at New York
■ GBP 62,30,650.155 × 1.6231 USD=
■ USD 1,01,12,968.26
Solution
■ There is net gain of
■ USD 1,01,12,968.26 - USD 1,00,00,000 = USD 1,12,968.26
Exercise 5
■ Spot rate 1 US $ = Rs 48.0123
■ 180 days Forward rate for 1 US $ = Rs 48.8190
■ Annualized interest rate for 6 months – Rupee = 12%■ Annualized interest rate for 6 months – US $ = 8%
■ Is there any arbitrage possibility? If yes how an arbitrageur can take advantageof the situation, if he is willing to borrow Rs 40,00,000 or US $83,312.
30 December 2020 37
Solution
➢ Spot Rate = Rs 40,00,000 / US$83,312 = 48.0123
➢ Forward Premium on US$ = [(48.8190 – 48.0123)/48.0123] x 12/6 x 100 == 3.36%
➢ Interest rate differential = 12% - 8%= 4%
➢ Since the dollar has not appreciated to the extent interest rate differential their exist arbitrate opportunity
➢ The advantage of this situation can be taken in the following manner:
30 December 2020 38
Solution
Step 4 Converting the same at the forward rate @ 48.8190 Rs 42,40,000/ Rs
48.8190
US$ 86,851.43
HENCE THE GAIN IS US $ (86,851.43 –
86,644.48)
US$ 206.95
($206.95 x Rs 48.8190) Rs 10,103
30 December 2020 39
No PARTICULARS WORKINGS AMOUNT
Step 1 Borrow US$ 83,312 for 6 months
Amount to be repaid after 6 months $ at 8% US $ 83,312 (1+0.08 x
6/12)
US$ 86,644.48
Step 2 Convert US$ 83,312 @ spot rate of 48.0123 into Rupee
and get the principal i.e.
US$ 83,312 x Rs
48.0123
Rs 40,00,000
Step 3 Invest @ 12% : Interest on Investments for 6 months Rs 40,00,000/- x 0.06 Rs 2,40,000
Total amount at the end of 6 months 40,00,000 + 2,40,000 Rs 42,40,000
Exercise 6
■ Spot rate 1 US $ = Rs 74.8325
■ 180 days Forward rate for 1 US $ = Rs 75.9200
■ Annualized interest rate for 6 months – Rupee = 6%
■ Annualized interest rate for 6 months – US $ = 2%
■ Is there any arbitrage possibility? If yes how an arbitrageur can take advantage
■ of the situation, if he is willing to borrow Rs 50,00,000 or US $66,816.
30 December 2020 40
■ Forward premium =(75.9200-74.8325) / 74.8325 x 12/6 x 100 = 2.906%
➢ Interest rate differential 6% - 2%= 4%
➢ Since the negative Interest rate differential is greater than forward premium there is a possibility of arbitrage inflow into India
➢ The advantage of this situation can be taken in the following manner:
30 December 2020 41
solutionParticulars workings Amount
Borrow US $66,816 for 6 months
Amount to be repaid after 6 months US $ 66816 (1+0.02 x 6/12) US$67,484
Convert US$ 66816 into Rupee and get the
principal i.e.
US$ 66816 x Rs 74.8325 Rs 50,00,000
Interest on Investments for 6 months Rs 50,00,000/- x 0.03 Rs 1,50,000
Total amount at the end of 6 months 50,00,000 + 1,50,000 Rs 51,50,000
Converting the same at the forward rate Rs 51,50,000/ Rs 75.92 US$67,834.56
Hence the gain is US $ (67834.56-67484) US$ 350.56
($350.56 x Rs 75.92) 26614
30 December 2020 42
30 December 2020 © THE INSTITUTE OF CHARTERED ACCOUNTANTS OF INDIA 43
THANK YOU
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