Triangular Arbitrage

CFA Level II Economics
#1

Can someone please explain why in triangular arbitrage that you use the reciprocal of the offer price to find the bid price?

An example from IFT:

Dealer INR/PKR bid-offer= 0.6460-0.6490

Interbank Spot Rate: INR/USD=68.2210-68.2450 PKR/USD=104.75-104.95

Need to find Interbank INK/PKR bid-offer

To find Interbank INK/PKR bid, you multiply INR/USD bid x USD/PKR bid (got it).

We first try and find the Bid of INK/PKR, which again = INR/USD x USD/PKR bid.

To get the USD/PKR bid part of the equation, you take reciprocal of Interbank Spot Rate offer, so INK/PKR bid= INR/USD bid x 1/(PKR/USD offer), which is 68.2210 x 1/104.95.

***Why do you take the reciprocal of the OFFER instead of the reciprocal of the BID?

#2

When you exchange INK for PKR:

  • If you’re buying INK you’re selling PKR
  • If you’re selling INK you’re buying PKR
#3

Thanks. I understand that concept, but not sure how it ties into the equation.

#4

Reciprocal of high = low and reciprocal of low = high.