Question

In: Economics

1 unit of Currency A costs 1.47 units of Currency B, 1 unit of Currency B...

1 unit of Currency A costs 1.47 units of Currency B, 1 unit of Currency B costs 0.68 units of Currency C, and 1 unit of Currency C costs 1.03 units of Currency A. Assume that you are starting out with 1,000,000 units of Currency A and that there are no transaction costs. How much money will you make in one set of triangular arbitrage transactions? Round to the nearest unit of Currency A.

Solutions

Expert Solution

We have a starting with 1,000,000 units of Currency A.  

1 unit of Currency A costs or is equal to 1.47 Units of Currency B

Or, 1 unit of Currency A = 1.47 Units of Currency B , This implies:-

1,000,000 unit of A = (1.47 * 1,000,000) units of B

Now,

1 unit of Currency B = 0.68 Unit of Currency C , This implies:-

(1.47 * 1,000,000) units of B = 0.68 * (1.47 * 1,000,000) Units of Currency C.

Now,

1 unit of Currency C = 1.03 Unit of Currency A , This implies:-

(0.68 * 1.47 * 1,000,000) Units of Currency C = 1.03 * (0.68 * 1.47 * 1,000,000) Units of Currency A.

We can see we had started with currency A and at last we have returned back to Currency A. On evaluating the Units of A that we have arrrived at and comparing it to Initial 1,000,000 units of Currency A applied we will be able to find the money made.

So,Value of the Currency A after Triangular Arbitration = ( 1.03 * 0.68 * 1.47 * 1,000,000) Units of Currency A =  1,029,588 Units of Currency A

Money Made will be the difference with the Initial Amount =  1,029,588 - 1,000,000 =  29,588 Units of Currency A.

Hence, Money Made after Triangular Arbitration is 29,588 Units of Currency A.


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