Question

Assume at Chase Bank the bid rate of a Brazilian real is $.25 while the ask rate is $.27. Assume at the Bank of America the bid rate of a Brazilian real is $.29 while the ask rate is $.30. Given this information, what would be your gain if you use $1,000,000 and execute locational arbitrage? That is, how much will you end up with over and above the $1,000,000 you started with?

Answer 1

• First we need to understand what bid and ask rates mean
  • Bid is the rate at which the bank buys the base currency
  • If the quote is $0.25 it means that the bank will buy 1 unit of Brazilian Real for $0.25
  • Ask is the rate at which the bank sells the base currency
  • If the quote is $0.27 it means that the bank will sell 1 unit of Brazilian Real for $0.27
• Next step is to understand the investor's position
  • If it wants to create an arbitrage with $1,000,000 then step 1 is to sell it in exchange of Real.
  • If the investor wants to sell $ then it will have to buy the Brazilian Real. This means that the bank has to sell the Real so we need to look at the ask rate.
• With this clarity we need to execute the arbitrage
  • Sell $1000000 to Chase bank for Brazillian Real at the ask rate of $0.27 per Real
    • $0.27 = 1 Real
    • $1 = 1/0.27 Real
    • $1000000 = 1000000/0.27 Real
    • So $1000000 = 3703703.704 Real
  • Sell 3703703.704 Real To Bank of America
    • The bank will buy Real so we need to look at the bid rate
    • 1 Real = $0.29
    • 3703703.704 Real = $0.29 x 3703703.704
    • So 3703703.704 Real = $1074074.074
  • Calculate arbitrage profit
    • We started with $1000000 and ended up with $1074074.074
    • So the profit is $1074074.074 - $1000000 = $74074.07407
    • You can round off the gain to 2 decimal places $74074.07