Reading 12, currency exchange

CFA L2 curriculum, page 484 - 485

Question 4 from page 484.

Implied JPY/CAD interbank rate: 85,76 bid ; 85,80 ask Dealer offered JPY/CAD rate: 85,74 bid ; 85,81 ask

Why is answere C incorrect? “Its possible to make arbitrage profits buying CAD from the dealer and selling it in the interbank market” ? The correct answere given is that no arbitrage profits are possible.

Why can we not buy CAD from the dealer (using JPY @ 85,74 “down-the-bid”) and sell in the interbank market CAD @ 85,80 “up-the-ask” ?

I would appreciate some help in understanding this seemingly simple topic.

Many thanks!

It’s up the bid and multiply, down the ask and divide

Yup, all clear now - thanks.

I wrote an article on exchange rates (and triangular arbitrage) that may be of some help here:

The simple answer is that if you’re multiplying, you use the smaller number, and if you’re dividing, you use the larger number: either way, you end up with the _ smaller _ amount of the new currency.

I’m sorry, I have already read Magician’s article and Schweser material, but I can’t get all this about “multiply” and “divide”: what and where?

Could you please clarify.

Hi all, I’m having the same issue in understanding here. I think now I sort of undertsand triangular arbitrage when 3 currencies involved… But would someone who understands the above original question be kind enough to post there workings, hopefully if I see the workings I will finally be able to grasp the concept here… Please, please help

Suppose that you have JPY1,000,000. You go to the dealer and buy CAD. How many CAD do you get?

JPY1,000,000 ÷ (JPY85.81/CAD1.0) = CAD11,653.65

You go to the interbank market and buy USD. How many USD do you get?

CAD11,653.65 ÷ (CAD0.9546/USD1.0) = USD12,207.89

You then buy JPY in the interbank market. How many JPY do you get?

USD12,207.89 × (JPY81.87/USD1.0) = JPY999,460.

No profit.

You should try the transactions the other way – start with JPY, buy USD in the interbank market, then buy CAD in the interbank market, then buy JPY from the dealer – and discover that you don’t get a profit that way, either.

Cheers so much mate, this is absolute gold!!! I now see the forrest for the trees

Hot dog!

Glad to hear it.

Take a look at the transactions I wrote out three posts above.

In particular, note which exchange rate I used in each transaction:

  • In the first transaction, I divided by the larger (ask) rate, so that I got the smaller number of CAD
  • In the second transaction, I divided by the larger (ask) rate, so that I got the smaller number of USD
  • In the third transaction, I multiplied by the smaller (bid) rate, so that I got the smaller number of JPY

That’s the key: you decide to multiply depending on how the exchange rate is quoted (e.g., if the dealer had quoted CAD/JPY, then I would have multiplied, so that the JPY cancelled and I was left with CAD), and you decide on which rate to use by picking the one that gives you the _ smaller amount of the new currency _: multiply by the smaller number, or divide by the larger number.