Question

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A dealer has PKR 100 million and receives the following rates of foreign exchange from the...

A dealer has PKR 100 million and receives the following rates of foreign exchange from the market. Find out how dealer can earn maximum arbitrage profit in FX market transaction. Solve and explain step by step.   

  • USD/PKR 138/139
  • GBP/PKR 199/201
  • GBP/USD 1.2729/35
  • EURO/GBP 1.1520/33

Solutions

Expert Solution

Solution:-

Given,

A dealer has PKR = 100 million

Exchange rate:-

  • USD/PKR 138/139 means 138USD=139PKR
  • GBP/PKR 199/201 means 199GBP=201PKR
  • GBP/USD 1.2729/35 means 1.2729GBP=1.2735USD
  • EURO/GBP 1.1520/33 means 1.1520EURO=1.1533GBP

Now, there are two possible route to  earn arbitrage profit:-

1st Route:-

a. Buy USD from 100 million PKR:

100 million PKR = (138/139)*100USD=99.28 USD

b. Buy GBP from 99.28 USD

99.28USD=(1.2729/1.2735)*99.28GBP=99.23 GBP

c. Buy PKR from 99.23 GBP

99.23GBP=(201/199)*99.23PKR=100.23PKR

Therefore arbitrage profit from 1st Route is (100.23-100)= .23 million PKR

2nd Route:-

a. Buy GBP from 100 million PKR:

100 million PKR = (199/201)*100USD=99.005 GBP

b. Buy USD from 99.005 GBP

99.005 GBP=(1.2735/1.2729)*99.005 USD=99.05 USD

c. Buy PKR from 99.05 USD

99.05 USD=(139/138)*99.05 PKR= 99.77 PKR

Here, no arbitrage profit from 2nd route.

Conclusion:

Arbitrage profit from 1st Route is possible to gain maximum arbitrage profit (100.23-100)= .23 million PKR

hence, follow the given step:

a. Buy USD from 100 million PKR

b. Buy GBP from USD

c. Buy PKR from GBP

jeff jeffy answered 2 years ago
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