Triangular Arb is giving me fits. I saw previous posts explaining how to solve but am stuck on applying it.
This particular problem asks for profit on a $1M trade given the following rates:
$C/USD = 1.2138 - 1.2259
BRL/USD = 2.3844 - 2.4082
Dealer bid quote = $C/BRL .525
This is from topic test Tremblay in Econ
First you need to find the $C/BRL cross-rate given the quotes above from the interbank market. $C/BRL = $C/USD * USD/BRL. We’re not given USD/BRL though, we’re given BRL/USD, so we need to make BRL the base currency (denominator) and USD the price currency. To get those rates the easiest way is to take the reciprocal of your BRL/USD ask price which will be the bid price of the USD/BRL rate ( = 1/2.4082 = USD 0.4152/BRL ). The reciprocal of your BRL/USD bid price will be the ask price of the USD/BRL rate ( = 1/2.3844 = USD 0.4194/BRL ). So USD/BRL bid/ask = 0.4152/0.4194.
Now we can find our cross rates: $C/BRL bid will equal the bid of the USD/BRL rate multiplied by the bid of the $C/USD rate. So, 0.4152 * 1.2138 = 0.5040; the $C/BRL ask will equals the ask of the USD/BRL rate multiplied by the ask of the $C/USD rate. So, 0.4194 * 1.2259 = 0.5141 $C/BRL.
Now we can solve the problem, lol. Hope this wasn’t too much. If the dealer is giving you a price he will buy from you of $C 0.525/BRL and you can buy it yourself from the interbank market at $C 0.5141/BRL, then the arbitrage profit should be = (0.525 - 0.5141 * $1M) = $10,900. I.e., the price you can buy in the interbank - the price you’ll sell to the dealer’s quote above * the notional amount of the trade.
I should have made this a bit clearer in my original post, but the notional is $1M USD, not $C. My apologies for the confusion.