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

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