Question

5. Exchange Rates

           a) Suppose you want to convert your 1,000 GBP (British pound) to Australian dollars (AUD). Gate City Bank and US Bank post the following currency quotes. What bank you should choose to exchange your British pounds to Australian dollars and how much AUD will you get as a result of this transaction?         

Bank	Currency	Bid	Ask
Gate City	GBP/USD	1.60	1.70
	AUD/USD	1.05	1.15
US Bank	GBP/AUD	1.30	1.40

b) Fargo Bank expects that Russian Ruble will depreciate against the dollar from 0.25$ to 0.20$ in 90 days. The following interbank lending and borrowing rates exist:

Currency	Lending Rate	Borrowing Rate
USD	6.0%	6.5%
Russian Ruble	13%	15%

Assume that Fargo Bank has a borrowing capacity of either $5,000,000 or 20 million rubles. How could Fargo Bank attempt to capitalize on its expectations without using deposited funds? Estimate the profits that could be generated from this strategy.

c) How would your answer to b) change if Fargo Bank expected Russian ruble to appreciate from 0.25$ to 0.28$ in 90 days? Estimate the profits that could be generated from the revised strategy.

Answer 1

Solution:

Part (a) Question has asked us that we have 1000 GBP and we want to covert in into Australian $ and we have two options to convert it

1. Gate Bank   GBP/USD     BID 1.60    ASK 1.70 and AUD/USD   BID 1.05 ASK 1.15

2. US Bank GBP/AUD          BID 1.30   ASK 1.40

Now we know that in what exchange rate we can get AUD from different bank, let’s start converting GBP into AUD by using above rates

First take Gate Bank rate

GBP/USD = 1.60, we take bid rate as we are selling GBP, ask rate is for buying GBP

It is saying for every GBP we will get 1.60 USD, let’s convert 1000 GBP and find out how many USD we get 1.60*1000 = 1600 USD

But we need AUD not USD let’s again convert it into AUD by using given exchange rate of Gate Bank for AUD/USD, we need AUD in exchange of USD, but we they not given USD/AUD rate lets convert the AUD/USD rate into USD/AUD rate but when we do such reversal of exchange rate ask rate become bid rate and bid rate become ask rate

USD/AUD = 1/AUD/USD

= 1/1.05

= 0.9524

USD/AUD = 1/AUD/USD

= 1/1.15

= 0.8696

New exchange rate for USD/AUD bid rate 0.8696 and ask rate 0.9524

Now we now USD/AUD bid rate lets convert our USD 1600 into AUD

= 1600*0.8696

=1391 AUD

To confirm whether we are getting more AUD from Gate Bank we need to convert our GBP from US bank too to find out the difference in AUD after exchange

US bank Exchange we know GBP/AUD    1.30

Let’s convert available GBP into AUD with above rate

= 1000*1.30

=1300 AUD

The total AUD we got from US bank is 1300 only whereas we got 1391 AUD from Gate Bank which is 91 AUD greater than US Bank exchange rate, so we will exchange our GBP from Gate Bank.

Part (b)

Fargo Bank expect exchange rate of dollar will be 0.20$ in 90 days as comparison to 0.25$

Interest rate available in the market       (Lending rate)                   (Borrowing Rate)

USD                                                                       6.0%                                                      6.5%

Russian Ruble                                                    13%                                                        15%

Bank has a borrowing capacity of $5,000,000 or 20,000,000 ruble, we need calculate how bank can earn a profit in the given situation.

Let’s understand the above equation, it is saying that today 1 Ruble is equal to $0.25$ but after 90 days 1 ruble is equal to 0.20$, it means today we are getting more dollar in exchange of ruble in comparison to 90 days, As we have learn the arbitrage process in which we have to borrow from that country whose currency is getting weaker in future and invest in that country whose currency getting stronger in future and from the above explanation we know, ruble is weakening and dollar is getting stronger, So use the arbitrage process and ascertain the profit.

Let’s borrow the ruble today i.e. 20,000,000 @ of borrowing rate 15% p.a than 90 days interest rate will be 15% divided by 4(360/90) equals to 3.75% and convert it into dollar and invest in USD

1 rubble = 0.25$, then

20,000,000 ruble =5,000,000 USD

Now investment this money in USD @ of lending rate 6.0% and calculate the Amount with interest

Amount = Principal (1+R)^t

= 5,000,000 (1+0.06/4)

= 5,075,000 USD, now convert this USD into ruble at exchange rate of 1 ruble equals to 0.20$ or convert this rate into USD= Ruble i.e. 1 USD = 1/0.20 or 5 ruble

Now we know the exchange rate of 1 dollar in ruble i.e. 5, convert it into ruble and repay the borrow money.

Ruble = USD*Exchange rate

= 5075000*5

=25,375,000 ruble

Let’s calculate the borrowed money with interest

20000000 (1+0.0375)

=20,750,000 ruble

Net Profit earned through arbitrage process equals to Invested money –borrowed money

= 25375000-20750000

=4,625,000 ruble

Part (c)

Now question is asking us that if exchange rate of ruble/dollar after 90 days will be 0.28$ in comparison of today rate of 0.25$, as we have discussed above that for using arbitrage process we have to borrow from that country whose currency is getting weaker in future and invest in that country whose currency getting stronger in future and from the above explanation we know, ruble is appreciating and dollar is getting weak, So use the arbitrage process and ascertain the profit.

Let’s borrow in USD an amount of $5000000 with a borrowing rate of 6.5%p.a covert annual interest rate into 90 days rate i.e. 6.50%*90/360 = 1.625%

Convert borrowed fund of $5000000 into ruble with existing exchange rate of $0.25$/ruble or 4Ruble/dollar (1/0.25)

Total Ruble = 5000000*4

= 20,000,000 ruble

Now invest this amount in ruble with lending rate of 13% p.a or 3.25% for 90 days (13/4)

Total investment after 90 days

= 20000000*(1+0.0325)

=20,650,000 ruble

Now convert ruble into USD with the exchange of 90 days i.e. 0.28$/ruble

=20650000*0.28

=5,782,000 USD

Now ascertain the borrowed USD with interest, 90 days interest rate as per above calculation is 1.625%

i.e. 5000000 (1+0.01625)

= 5,081,250

Net Profit from arbitrage process = Invested funds – borrowed funds

=5782000-5081250

=700,750 USD

So we have seen that by using arbitrage process Fargo bank has earned the profit in both the situations, this is the beauty of arbitrage process.