In: Economics
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.
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.